*Corresponding author: Huan Zhao, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA, e-mail: huanzhao@usc.edu Qiushi Guo and Fengnian Xia: Department of Electrical Engineering, Yale University, New Haven, CT 06511, USA Han Wang: Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA

Edited by Volker Sorger

Review

Huan Zhao * , Qiushi Guo , Fengnian Xia and Han Wang

Two-dimensional materials for nanophotonics application Abstract: In this article, we review the various topics on the applications of 2D materials, including both elemental and compound 2D materials, for nanophotonics applica-tion from detectors, modulators to plasmonics and light generating devices. With this review, we hope to provide an overview of the past development in this field while offering our perspectives on its future directions.

Keywords: 2D materials; nanophotonics; grapheme; black phosphorus; transition metal dichalcogenides.

DOI 10.1515/nanoph-2014-0022 Received September 18 , 2014 ; accepted December 17 , 2014

1 Introduction Since the successful isolation of graphene ( Figure 1 A) a decade ago, the family of two-dimensional (2D) materials has attracted tremendous interest in the research com-munity. Graphene is the first extensively studied material with true two-dimensional nature. With its unique band structures at the limit of 2D quantum confinement, this honeycomb monolayer of carbon atoms has inspired many interesting applications in nanophotonics and nanoelec-tronics. The most appealing features of graphene for nan-ophotonics applications originate from its zero-bandgap nature with linear dispersion near the Dirac point. Due to its unique band structure, graphene offers highly sensi-tive responses to optical signals over a very wide spectral range through various types of light-matter interaction

mechanisms. At the terahertz and mid-infrared range, graphene supports localized and propagating plasmons. Due to the controllable Fermi energy in graphene, such plasmonic responses are tunable by electro-static biasing with an external gate, a feature not available in traditional metal-based plasmonic devices. On the other hand, gra-phene can also be utilized to construct photodetectors and modulators for many optoelectronics applications at near-infrared, visible and ultra-violet spectrum range, leverag-ing its broadband absorption of light through interband transitions. However, graphene is not suitable for light generation functions due to its metallic nature, for which properties of other 2D materials needs to be explored. Besides graphene, hexagonal boron nitride (hBN), shown in Figure 1B, is also a layered material with honey-comb lattice structure. Its large bandgap (6 eV) makes it an outstanding dielectric for other 2D materials, which has enhanced the electronic and optoelectronic performance of various devices.

Recently, the research community has witnessed the rise of another family of two-dimensional materials  – the single-layer transition metal dichalcogenides (TMDCs), such as molybdenum disulphide (Figure 1C) and tung-sten diselenide. This rich family of mono-molecular-layer semiconductors can cover the energy range 1.5 – 2.5 eV and beyond, offering new opportunities to construct devices that can perform light generation functions due to its finite and direct bandgap in the monolayer form, such as light emitting diodes (LED) and lasers. In addi-tion, the valley coherence and valley-selective circular dichroism observed in various monolayer TMDCs offer exciting opportunities for the research of novel optical phenomena.

Since the beginning of year 2014, we have also seen the arrival of the latest member of the 2D material family – black phosphorus (Figure 1D). This layered material with a moderate bandgap of 0.3 eV in its thin film form that is widely tunable to around 2.0 eV in its single-layer form bridges the energy gap between zero-bandgap graphene and relatively wide bandgap transition metal dichalcoge-nides. It can potentially cover a broad wavelength range

from mid-infrared to partial visible spectrum for light detection, modulation and generation applications.

Here, we review the various topics on the applica-tions of 2D materials for nanophotonics application as introduced above. With this article, we hope to provide an overview of the past development in this field while offer-ing our perspectives on its future directions.

2 Graphene photonics: photo-detector, modulator, and plasmonics

2.1 Photodetectors

High speed, broad bandwidth photodetectors are essen-tial for communication, sensing, and digital imaging. Most traditional commercial photodetectors are based on silicon or III-V semiconductors. When photons are absorbed into the photodiode ’ s depletion region, they excite electron-hole pairs and their separation leads to photocurrent generation. This mechanism (usually called photovoltaic effect) was also claimed to be the operational principle of graphene based photodetectors in early research [1 – 3] . However, more complex princi-ples have been revealed recently. First, the lifetimes of excited carriers in graphene are found to be too short to generate efficient channel current. In addition, the

slow electron-lattice relaxation in graphene results in an elevated carrier temperature under light excitation due to a thermal decoupling between the lattice and photo-generated carriers. Therefore, if graphene is doped non-uniformly, “ hot ” carriers will diffuse due to the electronic temperature gradient, generating a net photocurrent, which is called photo-thermoelectric effect [4] . Further-more, due to the Auger-type processes in graphene, mul-tiple electron-hole pairs can be generated with merely a single photon [5 – 7] , which can potentially enhance the detection efficiency. Besides the photo-thermoelectric and photovoltaic effects, bolometric effects in graphene can also play a role in photoresponse [8] . To sum, due to the reduced dimensionality and its metallic nature, the generation of photocurrent in gapless graphene is more complex than that in traditional three-dimensional semi-conductors with a sizable bandgap.

Owning to its zero bandgap nature and the interband transitions of carriers, graphene is able to absorb photons from mid-infrared to ultraviolet wavelengths [9, 10] . Unfortunately, the small optical absorption of monolayer graphene arising from its innate thinness has limited the photoresponsivity of graphene based photodetectors. The first graphene based photodetector [11] demonstrated a potential bandwidth of 500 GHz, a measured 40 GHz response without gain degradation, and a maximum pho-toresponsivity of ∼ 0.5 mAW -1 . The effective photo-genera-tion region in this device is as short as 0.2 μ m. To extend the operation region, a metal-graphene-metal (MGM) photodetector with asymmetric electrodes ( Figure 2 A) has

Figure 1   Lattice structure of various 2D materials. (A) The honey-comb lattice structure of monolayer graphene. (B) Lattice structure of monolayer hexagonal boron nitride. Boron and nitrogen atoms repeat alternatively in a graphene-like honeycomb lattice, forming sp2 bonds. (C) Lattice structure of MoS2 monolayer, a typical TMDC, with S-Mo-S sandwich structure. Atoms colored yellow are S atoms, while the blue ones are Mo atoms. (D) Single layer black phos-phorus with a puckered orthorhombic lattice. The anisotropic lattice results in various novel physical properties of this emerging material.

Nanophotonics 2015; 4:128–142

© 2015 Huan Zhao et al., licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

*Corresponding author: Huan Zhao, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA, e-mail: huanzhao@usc.edu Qiushi Guo and Fengnian Xia: Department of Electrical Engineering, Yale University, New Haven, CT 06511, USA Han Wang: Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA

Edited by Volker Sorger

Review

Huan Zhao * , Qiushi Guo , Fengnian Xia and Han Wang

Two-dimensional materials for nanophotonics application Abstract: In this article, we review the various topics on the applications of 2D materials, including both elemental and compound 2D materials, for nanophotonics applica-tion from detectors, modulators to plasmonics and light generating devices. With this review, we hope to provide an overview of the past development in this field while offering our perspectives on its future directions.

Keywords: 2D materials; nanophotonics; grapheme; black phosphorus; transition metal dichalcogenides.

DOI 10.1515/nanoph-2014-0022 Received September 18 , 2014 ; accepted December 17 , 2014

1 Introduction Since the successful isolation of graphene ( Figure 1 A) a decade ago, the family of two-dimensional (2D) materials has attracted tremendous interest in the research com-munity. Graphene is the first extensively studied material with true two-dimensional nature. With its unique band structures at the limit of 2D quantum confinement, this honeycomb monolayer of carbon atoms has inspired many interesting applications in nanophotonics and nanoelec-tronics. The most appealing features of graphene for nan-ophotonics applications originate from its zero-bandgap nature with linear dispersion near the Dirac point. Due to its unique band structure, graphene offers highly sensi-tive responses to optical signals over a very wide spectral range through various types of light-matter interaction

mechanisms. At the terahertz and mid-infrared range, graphene supports localized and propagating plasmons. Due to the controllable Fermi energy in graphene, such plasmonic responses are tunable by electro-static biasing with an external gate, a feature not available in traditional metal-based plasmonic devices. On the other hand, gra-phene can also be utilized to construct photodetectors and modulators for many optoelectronics applications at near-infrared, visible and ultra-violet spectrum range, leverag-ing its broadband absorption of light through interband transitions. However, graphene is not suitable for light generation functions due to its metallic nature, for which properties of other 2D materials needs to be explored. Besides graphene, hexagonal boron nitride (hBN), shown in Figure 1B, is also a layered material with honey-comb lattice structure. Its large bandgap (6 eV) makes it an outstanding dielectric for other 2D materials, which has enhanced the electronic and optoelectronic performance of various devices.

Recently, the research community has witnessed the rise of another family of two-dimensional materials  – the single-layer transition metal dichalcogenides (TMDCs), such as molybdenum disulphide (Figure 1C) and tung-sten diselenide. This rich family of mono-molecular-layer semiconductors can cover the energy range 1.5 – 2.5 eV and beyond, offering new opportunities to construct devices that can perform light generation functions due to its finite and direct bandgap in the monolayer form, such as light emitting diodes (LED) and lasers. In addi-tion, the valley coherence and valley-selective circular dichroism observed in various monolayer TMDCs offer exciting opportunities for the research of novel optical phenomena.

Since the beginning of year 2014, we have also seen the arrival of the latest member of the 2D material family – black phosphorus (Figure 1D). This layered material with a moderate bandgap of 0.3 eV in its thin film form that is widely tunable to around 2.0 eV in its single-layer form bridges the energy gap between zero-bandgap graphene and relatively wide bandgap transition metal dichalcoge-nides. It can potentially cover a broad wavelength range

from mid-infrared to partial visible spectrum for light detection, modulation and generation applications.

Here, we review the various topics on the applica-tions of 2D materials for nanophotonics application as introduced above. With this article, we hope to provide an overview of the past development in this field while offer-ing our perspectives on its future directions.

2 Graphene photonics: photo-detector, modulator, and plasmonics

2.1 Photodetectors

High speed, broad bandwidth photodetectors are essen-tial for communication, sensing, and digital imaging. Most traditional commercial photodetectors are based on silicon or III-V semiconductors. When photons are absorbed into the photodiode ’ s depletion region, they excite electron-hole pairs and their separation leads to photocurrent generation. This mechanism (usually called photovoltaic effect) was also claimed to be the operational principle of graphene based photodetectors in early research [1 – 3] . However, more complex princi-ples have been revealed recently. First, the lifetimes of excited carriers in graphene are found to be too short to generate efficient channel current. In addition, the

slow electron-lattice relaxation in graphene results in an elevated carrier temperature under light excitation due to a thermal decoupling between the lattice and photo-generated carriers. Therefore, if graphene is doped non-uniformly, “ hot ” carriers will diffuse due to the electronic temperature gradient, generating a net photocurrent, which is called photo-thermoelectric effect [4] . Further-more, due to the Auger-type processes in graphene, mul-tiple electron-hole pairs can be generated with merely a single photon [5 – 7] , which can potentially enhance the detection efficiency. Besides the photo-thermoelectric and photovoltaic effects, bolometric effects in graphene can also play a role in photoresponse [8] . To sum, due to the reduced dimensionality and its metallic nature, the generation of photocurrent in gapless graphene is more complex than that in traditional three-dimensional semi-conductors with a sizable bandgap.

Owning to its zero bandgap nature and the interband transitions of carriers, graphene is able to absorb photons from mid-infrared to ultraviolet wavelengths [9, 10] . Unfortunately, the small optical absorption of monolayer graphene arising from its innate thinness has limited the photoresponsivity of graphene based photodetectors. The first graphene based photodetector [11] demonstrated a potential bandwidth of 500 GHz, a measured 40 GHz response without gain degradation, and a maximum pho-toresponsivity of ∼ 0.5 mAW -1 . The effective photo-genera-tion region in this device is as short as 0.2 μ m. To extend the operation region, a metal-graphene-metal (MGM) photodetector with asymmetric electrodes ( Figure 2 A) has

Figure 1   Lattice structure of various 2D materials. (A) The honey-comb lattice structure of monolayer graphene. (B) Lattice structure of monolayer hexagonal boron nitride. Boron and nitrogen atoms repeat alternatively in a graphene-like honeycomb lattice, forming sp2 bonds. (C) Lattice structure of MoS2 monolayer, a typical TMDC, with S-Mo-S sandwich structure. Atoms colored yellow are S atoms, while the blue ones are Mo atoms. (D) Single layer black phos-phorus with a puckered orthorhombic lattice. The anisotropic lattice results in various novel physical properties of this emerging material.

Two-dimensional materials for nanophotonics application   129

Source

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SiO2

Si

Gate

Graphene

Pd

Ti

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-8 -4 0 4 8

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White light,laser field

Transmitted light

GrapheneAI2O3

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I

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Figure 2   Graphene photodetectors and modulators. (A) Schematic of the metal-graphene-metal photodetector. Scale bar, 5 μ m. Reproduced with permission from Ref. [12] . (B) geometry-dependent photoresponse in antenna-graphene sandwich structure. Reproduced with permission from Ref. [13] . (C) Schematic of the graphene-microcavity photodetector. The Si 3 N 4 -graphene-Al 2 O 3 structure is embedded within two Ag mirrors. The resonance wavelength of the cavity λ is defined by L, the thickness of the dielectric. Inset: sectional view of the device. Reproduced with permission from Ref. [14] . (D) Top: the layout of a graphene modulator; a monolayer graphene on top of a doped-silicon waveguide. Bottom: cross-section view of the device. The optical mode plot is obtained from finite element simulation. The purple curve on the right demonstrates the magnitude of the electric field. Reproduced with permis-sion from Ref. [15] . (E) Schematic demonstration of a graphene-clad microfiber optical modulator. Reproduced with permission from Ref. [16] .

been invented [17] , which was able to achieve an external responsivity of 6.1 mAW -1 .

Although graphene based photodetectors are promis-ing for their ultra-broadband, high speed, and its compat-ibility to circuits. Its low photoresponsivity compared with traditional semiconductor-based ones remains a major drawback. Recently, several methods have been applied to enhance the optical absorption of graphene-based pho-todetectors. First, combining graphene with plasmonic nanostructures is able to concentrate light using plas-monic resonances, resulting in a significantly enhanced local electric field [12, 18] . Besides the huge enhancement in quantum efficiency, multicolor detection can also be achieved through the wavelength-dependent photore-sponse amplification of plasmonic nanostructures [19] . A quantum efficiency up to 20% was achieved by sand-wiching plasmonics nano-antennas within two sheets of graphene monolayer [13] (Figure 2B). However, the reso-nance of nanostructures or nanoparticles in these systems can determine the working wavelength of the photodetec-tors, typically leading to a reduced operation bandwidth, which is a potential shortcoming of this type of devices.

Second, integrating quantum dots with graphene is another powerful approach to enhance responsivity of graphene photodetectors. Konstantatos et al. [20] covered graphene with colloidal quantum dots to make a hybrid photodetector with ultrahigh photodetection gain ( ∼ 10 8 electrons/photon) and a photoresponsivity of ∼ 10 7 A W -1 . The quantum dots assist photogenerated carriers to reach graphene sheets while trap all oppositely charged carri-ers in quantum dot layer, resulting in a field-effect doping phenomenon. Another similar sample is the graphene-PbS quantum dots photodetector fabricated on a flexible substrate [21] with a responsivity of 10 7 A W -1 , making use of the photogating effect. Graphene-quantum dot photo-detectors perform tremendous responsivity, but they also suffer low operational speed, due to the long time needed to generate gain. In addition, the working bandwidth in these devices are mainly determined by the quantum dot rather than graphene.

Moreover, integrating graphene with microcavity [14,  22 – 24] is another useful way to increase photo-response. In the first graphene-cavity photodetector [14] , two opposite mirrors were used as a Fabry-P é rot micro-cavity (Figure  2C) to achieve a 20-fold enhancement of photocurrent at a given wavelength. The cavity-induced optical confinement can enhance photoresponse, but also narrows its bandwidth.

Finally, coupling graphene to various waveguide can lead to photodetectors with excellent performance [25 – 30] . These devices are marked by high photoresponsivity

( ∼ 0.1 A W -1 ), ultra-wide bandwidth (from visible to infrared wavelengths), high efficiency, high speed ( ∼ 10 Gbit s -1 ), and small footprint. In graphene-waveguide photodetec-tors, the waveguide convey light to graphene either by batt-coupling or evanescent coupling. The latter has been applied to many novel devices like graphene/silicon-heterostructure waveguide photodetectors [26] , though integration with waveguide inevitably leads to larger device dimension [29] . The wide adsorption bandwidth of graphene-waveguide photodetectors make them advanta-geous over traditional photodetectors.

2.2 Optical modulators

Optical modulators play a crucial role in optical commu-nications. Graphene based optical modulators are marked by their strong graphene-light interaction, ultrafast oper-ation speed, large bandwidth, and high compatibility to silicon electronics. Despite that the absorption coefficient of graphene is large ( ∼ 5  ×  10 7   m -1 in visible range), the ultra-thin nature of monolayer graphene has limited its absorption significantly. Hence, it is necessary to enhance graphene-photon interaction, typically by waveguide or by optical cavity, which will be discussed in this section.

Liu et  al. [15] made the first graphene based modu-lator in 2011. In their devices, mono-layer graphene was transferred on top of a silicon waveguide, with a 7-nm-thick Al 2 O 3 between them serving as a spacer (Figure 2D). A drive voltage is applied between graphene and the wave-guide to tune the Fermi level. When the absolute value of Fermi level is over a transition threshold (E F (V D )  =  hv 0 /2), interband transitions will be suppressed due to Pauli state blocking, hence graphene stays transparent. On the other hand, if a low drive voltage is applied to keep the Fermi level of graphene close to the Dirac point, optical adsorp-tion will be enabled. Thus light transmission in graphene can be effectively modulated via tuning driving voltage. With a high working speed (1.2 GHz at 3 dB), broad opera-tion bandwidth (1.35 mm – 1.6 mm) and tiny footprint (25  μ m 2 ), this graphene-waveguide optical modulator demonstrates the potential of using graphene for modu-lator applications. However, the silicon back gate inevi-tably induces high insertion loss and degrades carrier mobility, resulting in a limited modulation depth and reduced operation speed. To solve this problem, Liu et al. [31] replaced the doped silicon layer with monolayer gra-phene to form a double-layer graphene optical modulator. In this modulator, two graphene layers were separated by Al 2 O 3 to form a p-oxide-n junction. The modulation depth ( ∼ 0.16 dB/ μ m) in this device is higher than that in the first

130   H. Zhao et al.

Source

Pd

Ti

Drain

SiO2

Si

Gate

Graphene

Pd

Ti

-80

-8 -4 0 4 8

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White light,laser field

Transmitted light

GrapheneAI2O3

SiO2

Standard fiber Microfiber

Graphene coatingSi

Vg

Vd

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I

λ/2-cavity mode

-40

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rren

t (nA

) 40

80

BA

C

D E

Without patternDimer array

Laser: 10 μW

Gate: 0 V

Heptamer array

0

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Figure 2   Graphene photodetectors and modulators. (A) Schematic of the metal-graphene-metal photodetector. Scale bar, 5 μ m. Reproduced with permission from Ref. [12] . (B) geometry-dependent photoresponse in antenna-graphene sandwich structure. Reproduced with permission from Ref. [13] . (C) Schematic of the graphene-microcavity photodetector. The Si 3 N 4 -graphene-Al 2 O 3 structure is embedded within two Ag mirrors. The resonance wavelength of the cavity λ is defined by L, the thickness of the dielectric. Inset: sectional view of the device. Reproduced with permission from Ref. [14] . (D) Top: the layout of a graphene modulator; a monolayer graphene on top of a doped-silicon waveguide. Bottom: cross-section view of the device. The optical mode plot is obtained from finite element simulation. The purple curve on the right demonstrates the magnitude of the electric field. Reproduced with permis-sion from Ref. [15] . (E) Schematic demonstration of a graphene-clad microfiber optical modulator. Reproduced with permission from Ref. [16] .

been invented [17] , which was able to achieve an external responsivity of 6.1 mAW -1 .

Although graphene based photodetectors are promis-ing for their ultra-broadband, high speed, and its compat-ibility to circuits. Its low photoresponsivity compared with traditional semiconductor-based ones remains a major drawback. Recently, several methods have been applied to enhance the optical absorption of graphene-based pho-todetectors. First, combining graphene with plasmonic nanostructures is able to concentrate light using plas-monic resonances, resulting in a significantly enhanced local electric field [12, 18] . Besides the huge enhancement in quantum efficiency, multicolor detection can also be achieved through the wavelength-dependent photore-sponse amplification of plasmonic nanostructures [19] . A quantum efficiency up to 20% was achieved by sand-wiching plasmonics nano-antennas within two sheets of graphene monolayer [13] (Figure 2B). However, the reso-nance of nanostructures or nanoparticles in these systems can determine the working wavelength of the photodetec-tors, typically leading to a reduced operation bandwidth, which is a potential shortcoming of this type of devices.

Second, integrating quantum dots with graphene is another powerful approach to enhance responsivity of graphene photodetectors. Konstantatos et al. [20] covered graphene with colloidal quantum dots to make a hybrid photodetector with ultrahigh photodetection gain ( ∼ 10 8 electrons/photon) and a photoresponsivity of ∼ 10 7 A W -1 . The quantum dots assist photogenerated carriers to reach graphene sheets while trap all oppositely charged carri-ers in quantum dot layer, resulting in a field-effect doping phenomenon. Another similar sample is the graphene-PbS quantum dots photodetector fabricated on a flexible substrate [21] with a responsivity of 10 7 A W -1 , making use of the photogating effect. Graphene-quantum dot photo-detectors perform tremendous responsivity, but they also suffer low operational speed, due to the long time needed to generate gain. In addition, the working bandwidth in these devices are mainly determined by the quantum dot rather than graphene.

Moreover, integrating graphene with microcavity [14,  22 – 24] is another useful way to increase photo-response. In the first graphene-cavity photodetector [14] , two opposite mirrors were used as a Fabry-P é rot micro-cavity (Figure  2C) to achieve a 20-fold enhancement of photocurrent at a given wavelength. The cavity-induced optical confinement can enhance photoresponse, but also narrows its bandwidth.

Finally, coupling graphene to various waveguide can lead to photodetectors with excellent performance [25 – 30] . These devices are marked by high photoresponsivity

( ∼ 0.1 A W -1 ), ultra-wide bandwidth (from visible to infrared wavelengths), high efficiency, high speed ( ∼ 10 Gbit s -1 ), and small footprint. In graphene-waveguide photodetec-tors, the waveguide convey light to graphene either by batt-coupling or evanescent coupling. The latter has been applied to many novel devices like graphene/silicon-heterostructure waveguide photodetectors [26] , though integration with waveguide inevitably leads to larger device dimension [29] . The wide adsorption bandwidth of graphene-waveguide photodetectors make them advanta-geous over traditional photodetectors.

2.2 Optical modulators

Optical modulators play a crucial role in optical commu-nications. Graphene based optical modulators are marked by their strong graphene-light interaction, ultrafast oper-ation speed, large bandwidth, and high compatibility to silicon electronics. Despite that the absorption coefficient of graphene is large ( ∼ 5  ×  10 7   m -1 in visible range), the ultra-thin nature of monolayer graphene has limited its absorption significantly. Hence, it is necessary to enhance graphene-photon interaction, typically by waveguide or by optical cavity, which will be discussed in this section.

Liu et  al. [15] made the first graphene based modu-lator in 2011. In their devices, mono-layer graphene was transferred on top of a silicon waveguide, with a 7-nm-thick Al 2 O 3 between them serving as a spacer (Figure 2D). A drive voltage is applied between graphene and the wave-guide to tune the Fermi level. When the absolute value of Fermi level is over a transition threshold (E F (V D )  =  hv 0 /2), interband transitions will be suppressed due to Pauli state blocking, hence graphene stays transparent. On the other hand, if a low drive voltage is applied to keep the Fermi level of graphene close to the Dirac point, optical adsorp-tion will be enabled. Thus light transmission in graphene can be effectively modulated via tuning driving voltage. With a high working speed (1.2 GHz at 3 dB), broad opera-tion bandwidth (1.35 mm – 1.6 mm) and tiny footprint (25  μ m 2 ), this graphene-waveguide optical modulator demonstrates the potential of using graphene for modu-lator applications. However, the silicon back gate inevi-tably induces high insertion loss and degrades carrier mobility, resulting in a limited modulation depth and reduced operation speed. To solve this problem, Liu et al. [31] replaced the doped silicon layer with monolayer gra-phene to form a double-layer graphene optical modulator. In this modulator, two graphene layers were separated by Al 2 O 3 to form a p-oxide-n junction. The modulation depth ( ∼ 0.16 dB/ μ m) in this device is higher than that in the first

Two-dimensional materials for nanophotonics application   131

graphene-based modulator. Another similar double-layer graphene modulator was proposed by Koester et al. [32] . In their modeling, two layers of graphene separated by a thin insulator were placed on top of a silicon waveguide. The upper graphene sheet acts as a transparent electrode, while the lower one functions as a light-absorber. Their calculation revealed that the 3-dB bandwidths of this device at near-infrared bands and mid-infrared bands can reach 120 GHz and 30 GHz, respectively.

Coupling two-dimensional material to optical cavity offers an alternative way to enhance light-matter interac-tion. Gan et al. [33] have fabricated high-contrast, energy-efficient, and broad-band electro-optic modulators by electronically gating graphene deposited onto a HfO 2 covered silicon photonic crystal nanocavity. In this case, the Fermi energy of graphene is tuned by the electrostatic bias, resulting in tunable absorption. Once the interband transitions are Pauli blocked, graphene adsorbs less light and appears to be transparent. Therefore, the quality factor and reflectivity of the cavity can be effectively mod-ulated by tuning the gate voltage.

The nature of gate-tunable Fermi level in graphene has led to various progresses in electro-optic modulators. However, the response time of the bias circuits typically limits the modulation bandwidth to below 1 GHz. To elimi-nate this “ electrical bottleneck ” , an all-optical modulator [16] (Figure 2E) was designed by wrapping graphene mon-olayer around a microfiber. This graphene-clad microfiber (GCM) can reach a response time of 2.2 picoseconds and a modulation depth of 38%, with a calculated bandwidth of 200 GHz. To tune the attenuation of weak infrared signals coupled into the GCM, a switch light is applied to excite carriers, leading to Pauli blocking-suppressed interband transitions. Thus the absorption threshold of graphene increases, lowering the attenuation of weak infrared signals. Ultrafast, flexible, and easily integrated to tradi-tional optical devices, this all-optical modulator is prom-ising for future fiber-optic circuits.

2.3 Graphene plasmonics

Because of its simultaneously high carrier mobility and high conductivity, graphene has also emerged to be a very promising candidate for terahertz to mid-infrared plas-monic devices applications. As a subfield of nanophoton-ics, plasmonics studies the excitation, propagation, and utilization of the collective oscillation of carriers. There are several types of plasmon polaritons, and for graphene, we are more interested in the surface plasmon polaritons (SPP), the collective excitations of electrons and light at

the interface between a conductor and a dielectric. The field of plasmonics has attracted significant interests due to its ability to confine and manipulate light below the diffraction limit and/or produce high local field intensi-ties. Nowadays, plasmonics has triggered a plethora of applications including optical antenna [34, 35] , near-field optical microscopy [36] , chemical and biological sensing [37 – 39] and subwavelength optics [40 – 42] , to name a few. Despite the fact that noble metals such as silver and gold are still the predominant materials of choice for plasmon-ics, devices fabricated from these materials face several constraints. For example, their operating wavelengths are hardly tunable once the geometry of the structure is fixed. Moreover, they suffer from large Ohmic losses due to the limitation of carrier mobilities, surface roughness, grain microstructure and impurities. Compared to conventional plasmonic materials, graphene plasmons (GPs) presents the following unique properties: (i) Tunability. Due to the relativistic nature of carriers in graphene, the plasmon mass increases proportionally with the Fermi level. There-fore, the optical response of doped graphene strongly depends on the doping level, which can be chemically or electrostatically tuned. (ii) Strong field confinement. GPs propagate at a speed comparable to the Fermi velocity v F , which is much smaller than the light velocity. As a result, GPs have plasmon wavelengths that are typically 1 ∼ 3 orders of magnitude smaller than the light wavelength. (iii) Low losses and long lifetime. The high conductivity of graphene can be translated to a fairly long optical relaxa-tion times ( ∼ 10 -13 s), compared to ∼ 10 -14  s in gold, indicating less plasmon dissipation and longer plasmon lifetime. (iv) Crystallinity. The strong carbon chemical bonds make gra-phene structures defect-free over several plasmon wave-lengths [43] . While fabrication imperfections limit the performance of nanometallic plasmonic structures.

The strong subwavelength confinement of light is accompanied by the technical difficulty to excite plas-mons experimentally. The incident light usually does not have sufficient momentum to excite plasmons directly because the free-space photons often have much longer wavelength and hence lower momentum than the plas-mons. Artificially creating discontinuities in the elec-tric permittivity of graphene enables standing localized plasmon waves confined to the metal surfaces, when the light frequency is tuned to its plasmon resonance fre-quency [44] . By patterning graphene, for example, into ribbons or disks, localized plasmon modes can be excited by normally incident light [45 – 49] . In graphene ribbons, plasmonic resonances occur when the plasmon wavevec-tor q  =   (2 n + 1) π / W , where W is the ribbon ’ s width and n  =  0, 1, 2, which means that the plasmon half-wavelengths

should be able to fit within the ribbon width. Only plas-monic modes with odd multiples of half-wavelengths couple with light as this produces an effective charge dipole that creates the necessary restoring force for collec-tive carrier oscillations. For incident light polarized par-allel to the ribbons, the measured spectral line shape are very close to that in a continuous sheet of graphene and the response can be described by the Drude model [inset of Figure 3 A]. For incident light polarized perpendicular to the ribbon, as shown in Figure 3A, distinctive absorption peaks originated from plasmon oscillation dominates the optical response are observed. A good agreement between the observed GP resonances to the damped oscillator model was found.

It is worth noting that GP resonances can be tuned in situ over a broad terahertz frequency range by varying micro-ribbon width and electrostatic doping, as shown in Figure 3A. Plasmon absorption peaks can be shifted to higher energies and gain oscillator strength with increased carrier concentration. In the experiment carried out by Ju et al., an ion gel was used for gating, and the induced carrier concentration was about 10 13 cm -2 , which enabled the plasmon resonance to access the terahertz spectral range. In general, the ribbon width and carrier doping dependences of graphene plasmon frequency reveal a power-law behavior characteristic of two-dimensional massless Dirac electronsc [53] . The plasmon frequency scales like W -1/2 , where W is the width of the ribbon, and like n 1/4 , where n is the carrier density, as predicted by the random phase approximation (RPA). Besides the tunable terahertz plasmons in graphene ribbons, plasmon hybrid-ization in coupled graphene ribbons has been demon-strated [54] and splitting of GPs into bulk and edge modes in high magnetic fields has been achieved [55] .

In addition to graphene ribbons, closely packed gra-phene micro/nanodisks can also support tunable localized GPs and in turn, significantly increase the light absorption at the wavelength of interest [56, 57] . In order to further increase the degree of light matter interaction and the tunability of plasmon resonance, researchers have made attempts to distribute Dirac fermions in a single layer of graphene disks into multiple layers of closely stacked gra-phene disks [50] . The extinction spectrum of microdisk arrays with one, two, and five graphene layers are shown in Figure 3B. In the design, the disk diameter d and the lattice constant a are 4.4 μ m and 9 μ m, respectively. The graphene disk array is patterned on 300  nm of SiO 2 on a highly resistive silicon substrate. As can be seen from Figure 3B, significantly increased the plasmonic reso-nance frequency as well as the peak intensity have been obtained. This is resulted from the Columbic interaction

between adjacent layers: the in-phase collective motion of carries among layers leads to a stronger restoring force through dipole-dipole coupling [50, 58] . Interestingly, it was also found that the plasmonic frequency exhibits an n 1/2 dependence other than n 1/4 for the case of monolayer, which can only be explained in the context of quantum mechanics. In addition, stacked graphene disks could be used as an electromagnetic radiation shield with 97.5% effectiveness, a tunable, far-infrared notch filter with a rejection ratio of 8.2 dB and a tunable terahertz linear polarizer with an extinction ratio of 9.5 dB.

The extraordinary field confinement ( ∼ 10 6 smaller than diffraction limit) of GPs also facilitates the research of fundamentally new regimes of strong light-matter coupling or vacumm Rabi splitting (VRS) [49] . Strong light-matter coupling is one of the most intriguing fields in condensed matter physics since it has inspired the research from quantum optics such as single-atom lasing, quantum entanglement, classical regime such as nonu-biquitous many-atom sensing to the boundary explora-tion between quantum and classical physics [59 – 62] . VRS usually occurs when one of the oscillators consists of a two-level atom or quantum dot (QD), and the other is that of a small-volume high-quality (high- Q ) cavity. When the coupling strength g between two same-energy oscillators exceeds the mean of their decay rates ½ ( κ + γ ), then the coupled system will have two eigen-energies. The cou-pling strength is measured by Purcell factor F p [63] , which describes spontaneous emission modified by coupling to an optical cavity. The F p is proportional to the ratio of the Q factor of the photonic or plasmonic resonance to the effective mode volume V eff [64] . VRS has been difficult to achieve with conventional metal plasmonics since they exhibit large Ohmic losses and are hardly tunable. Con-ventional optical microcavities provides an effective way to enhance light-matter coupling due to the achievement of Q -factor as high as even 10 8 and is widely employed in the study of cavity quantum electrodynamics (QEDs) [65, 66] . The damping time τ , i.e., 1/ γ , is long enough to allow the sufficient energy exchange between the emitter and the cavity. However, the reduction of V eff in the cavity is constrained by the diffraction limit, which limits the further enhancement of F p . In addition, the technique of temperature scanning of the QD transition through the cavity resonance was usually used to map out the anticrossing, which may cause acoustic phonon broadening of the QD [62] . In comparison, graphene offers remarkable degree of confinement. Therefore, very small mode confinement compensates for the low quality factors ( Q ∼ 10) for graphene plasmons in mid-infrared regime. More importantly, the doping level tunable E F

132   H. Zhao et al.

graphene-based modulator. Another similar double-layer graphene modulator was proposed by Koester et al. [32] . In their modeling, two layers of graphene separated by a thin insulator were placed on top of a silicon waveguide. The upper graphene sheet acts as a transparent electrode, while the lower one functions as a light-absorber. Their calculation revealed that the 3-dB bandwidths of this device at near-infrared bands and mid-infrared bands can reach 120 GHz and 30 GHz, respectively.

Coupling two-dimensional material to optical cavity offers an alternative way to enhance light-matter interac-tion. Gan et al. [33] have fabricated high-contrast, energy-efficient, and broad-band electro-optic modulators by electronically gating graphene deposited onto a HfO 2 covered silicon photonic crystal nanocavity. In this case, the Fermi energy of graphene is tuned by the electrostatic bias, resulting in tunable absorption. Once the interband transitions are Pauli blocked, graphene adsorbs less light and appears to be transparent. Therefore, the quality factor and reflectivity of the cavity can be effectively mod-ulated by tuning the gate voltage.

The nature of gate-tunable Fermi level in graphene has led to various progresses in electro-optic modulators. However, the response time of the bias circuits typically limits the modulation bandwidth to below 1 GHz. To elimi-nate this “ electrical bottleneck ” , an all-optical modulator [16] (Figure 2E) was designed by wrapping graphene mon-olayer around a microfiber. This graphene-clad microfiber (GCM) can reach a response time of 2.2 picoseconds and a modulation depth of 38%, with a calculated bandwidth of 200 GHz. To tune the attenuation of weak infrared signals coupled into the GCM, a switch light is applied to excite carriers, leading to Pauli blocking-suppressed interband transitions. Thus the absorption threshold of graphene increases, lowering the attenuation of weak infrared signals. Ultrafast, flexible, and easily integrated to tradi-tional optical devices, this all-optical modulator is prom-ising for future fiber-optic circuits.

2.3 Graphene plasmonics

Because of its simultaneously high carrier mobility and high conductivity, graphene has also emerged to be a very promising candidate for terahertz to mid-infrared plas-monic devices applications. As a subfield of nanophoton-ics, plasmonics studies the excitation, propagation, and utilization of the collective oscillation of carriers. There are several types of plasmon polaritons, and for graphene, we are more interested in the surface plasmon polaritons (SPP), the collective excitations of electrons and light at

the interface between a conductor and a dielectric. The field of plasmonics has attracted significant interests due to its ability to confine and manipulate light below the diffraction limit and/or produce high local field intensi-ties. Nowadays, plasmonics has triggered a plethora of applications including optical antenna [34, 35] , near-field optical microscopy [36] , chemical and biological sensing [37 – 39] and subwavelength optics [40 – 42] , to name a few. Despite the fact that noble metals such as silver and gold are still the predominant materials of choice for plasmon-ics, devices fabricated from these materials face several constraints. For example, their operating wavelengths are hardly tunable once the geometry of the structure is fixed. Moreover, they suffer from large Ohmic losses due to the limitation of carrier mobilities, surface roughness, grain microstructure and impurities. Compared to conventional plasmonic materials, graphene plasmons (GPs) presents the following unique properties: (i) Tunability. Due to the relativistic nature of carriers in graphene, the plasmon mass increases proportionally with the Fermi level. There-fore, the optical response of doped graphene strongly depends on the doping level, which can be chemically or electrostatically tuned. (ii) Strong field confinement. GPs propagate at a speed comparable to the Fermi velocity v F , which is much smaller than the light velocity. As a result, GPs have plasmon wavelengths that are typically 1 ∼ 3 orders of magnitude smaller than the light wavelength. (iii) Low losses and long lifetime. The high conductivity of graphene can be translated to a fairly long optical relaxa-tion times ( ∼ 10 -13 s), compared to ∼ 10 -14  s in gold, indicating less plasmon dissipation and longer plasmon lifetime. (iv) Crystallinity. The strong carbon chemical bonds make gra-phene structures defect-free over several plasmon wave-lengths [43] . While fabrication imperfections limit the performance of nanometallic plasmonic structures.

The strong subwavelength confinement of light is accompanied by the technical difficulty to excite plas-mons experimentally. The incident light usually does not have sufficient momentum to excite plasmons directly because the free-space photons often have much longer wavelength and hence lower momentum than the plas-mons. Artificially creating discontinuities in the elec-tric permittivity of graphene enables standing localized plasmon waves confined to the metal surfaces, when the light frequency is tuned to its plasmon resonance fre-quency [44] . By patterning graphene, for example, into ribbons or disks, localized plasmon modes can be excited by normally incident light [45 – 49] . In graphene ribbons, plasmonic resonances occur when the plasmon wavevec-tor q  =   (2 n + 1) π / W , where W is the ribbon ’ s width and n  =  0, 1, 2, which means that the plasmon half-wavelengths

should be able to fit within the ribbon width. Only plas-monic modes with odd multiples of half-wavelengths couple with light as this produces an effective charge dipole that creates the necessary restoring force for collec-tive carrier oscillations. For incident light polarized par-allel to the ribbons, the measured spectral line shape are very close to that in a continuous sheet of graphene and the response can be described by the Drude model [inset of Figure 3 A]. For incident light polarized perpendicular to the ribbon, as shown in Figure 3A, distinctive absorption peaks originated from plasmon oscillation dominates the optical response are observed. A good agreement between the observed GP resonances to the damped oscillator model was found.

It is worth noting that GP resonances can be tuned in situ over a broad terahertz frequency range by varying micro-ribbon width and electrostatic doping, as shown in Figure 3A. Plasmon absorption peaks can be shifted to higher energies and gain oscillator strength with increased carrier concentration. In the experiment carried out by Ju et al., an ion gel was used for gating, and the induced carrier concentration was about 10 13 cm -2 , which enabled the plasmon resonance to access the terahertz spectral range. In general, the ribbon width and carrier doping dependences of graphene plasmon frequency reveal a power-law behavior characteristic of two-dimensional massless Dirac electronsc [53] . The plasmon frequency scales like W -1/2 , where W is the width of the ribbon, and like n 1/4 , where n is the carrier density, as predicted by the random phase approximation (RPA). Besides the tunable terahertz plasmons in graphene ribbons, plasmon hybrid-ization in coupled graphene ribbons has been demon-strated [54] and splitting of GPs into bulk and edge modes in high magnetic fields has been achieved [55] .

In addition to graphene ribbons, closely packed gra-phene micro/nanodisks can also support tunable localized GPs and in turn, significantly increase the light absorption at the wavelength of interest [56, 57] . In order to further increase the degree of light matter interaction and the tunability of plasmon resonance, researchers have made attempts to distribute Dirac fermions in a single layer of graphene disks into multiple layers of closely stacked gra-phene disks [50] . The extinction spectrum of microdisk arrays with one, two, and five graphene layers are shown in Figure 3B. In the design, the disk diameter d and the lattice constant a are 4.4 μ m and 9 μ m, respectively. The graphene disk array is patterned on 300  nm of SiO 2 on a highly resistive silicon substrate. As can be seen from Figure 3B, significantly increased the plasmonic reso-nance frequency as well as the peak intensity have been obtained. This is resulted from the Columbic interaction

between adjacent layers: the in-phase collective motion of carries among layers leads to a stronger restoring force through dipole-dipole coupling [50, 58] . Interestingly, it was also found that the plasmonic frequency exhibits an n 1/2 dependence other than n 1/4 for the case of monolayer, which can only be explained in the context of quantum mechanics. In addition, stacked graphene disks could be used as an electromagnetic radiation shield with 97.5% effectiveness, a tunable, far-infrared notch filter with a rejection ratio of 8.2 dB and a tunable terahertz linear polarizer with an extinction ratio of 9.5 dB.

The extraordinary field confinement ( ∼ 10 6 smaller than diffraction limit) of GPs also facilitates the research of fundamentally new regimes of strong light-matter coupling or vacumm Rabi splitting (VRS) [49] . Strong light-matter coupling is one of the most intriguing fields in condensed matter physics since it has inspired the research from quantum optics such as single-atom lasing, quantum entanglement, classical regime such as nonu-biquitous many-atom sensing to the boundary explora-tion between quantum and classical physics [59 – 62] . VRS usually occurs when one of the oscillators consists of a two-level atom or quantum dot (QD), and the other is that of a small-volume high-quality (high- Q ) cavity. When the coupling strength g between two same-energy oscillators exceeds the mean of their decay rates ½ ( κ + γ ), then the coupled system will have two eigen-energies. The cou-pling strength is measured by Purcell factor F p [63] , which describes spontaneous emission modified by coupling to an optical cavity. The F p is proportional to the ratio of the Q factor of the photonic or plasmonic resonance to the effective mode volume V eff [64] . VRS has been difficult to achieve with conventional metal plasmonics since they exhibit large Ohmic losses and are hardly tunable. Con-ventional optical microcavities provides an effective way to enhance light-matter coupling due to the achievement of Q -factor as high as even 10 8 and is widely employed in the study of cavity quantum electrodynamics (QEDs) [65, 66] . The damping time τ , i.e., 1/ γ , is long enough to allow the sufficient energy exchange between the emitter and the cavity. However, the reduction of V eff in the cavity is constrained by the diffraction limit, which limits the further enhancement of F p . In addition, the technique of temperature scanning of the QD transition through the cavity resonance was usually used to map out the anticrossing, which may cause acoustic phonon broadening of the QD [62] . In comparison, graphene offers remarkable degree of confinement. Therefore, very small mode confinement compensates for the low quality factors ( Q ∼ 10) for graphene plasmons in mid-infrared regime. More importantly, the doping level tunable E F

Two-dimensional materials for nanophotonics application   133

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Figure 3   Plasmonics of graphene. (A) Plasmon resonance in gated graphene microribbon arrays. Left: top and side views of a graphene microribbon array. Right: gate-dependent relative transmission spectra. Reproduced with permission from Ref. [46] . (B) Top: SEM image of a graphene microdisk array. Bottom: Extinction spectra of graphene microdot arrays with one, two and five graphene layers, separated by polymer buffer layers. Reproduced with permission from Ref. [50] (C) Fermi- and photon-energy dependence of the extinction cross section of a combined emitter-nanodisk system. The emitter has a resonance at ħ ω 0   =  0.3eV and is oriented parallel to the disk. Reproduced with permission from Ref. [49] . (D) Schematic of graphene nanoresonators fabricated on a monolayer h-BN sheet on a SiO 2 (285 nm)/Si wafer. Reproduced with permission from Ref. [51] . (E) Diagram of an infrared nano-imaging experiment at the surface of graphene on SiO 2 . Reproduced with permission from Ref.  [52] .

of graphene provides an elegant approach to manipu-late the coupling strength. By putting a dipole 10  nm above the center of a self-standing 100 nm graphene disk (within the decay length of localized GPs sustained by a graphene nanodisk), Koppens et  al. theoretically pre-dicted the Rabi splitting mediated by the localized GP as shown in Figure 3C. The emitter used in the calculation has an excited energy of ħ ω 0   =  0.3 eV and natural decay rate Γ 0   =  5  ×  10 7 s -1 . Importantly, the quantum mechanical strong light matter coupling of GPs and single emitter has also inspired the research of strong GP interaction with ensemble of oscillators, which can be treated classically. This may have far-reaching implications for development of the highly sensitive infrared bio/chemical sensing and molecule detection techniques [67, 68] .

The electronic degrees of freedom in graphene can also couple strongly to substrate polar phonons [47] and the intrinsic IR-active phonons of bilayer graphene [69] . In these experiments, graphene devices have shown a strongly modified graphene plasmon dispersion rela-tion caused by substrate phonons. For example, in the case of a SiO 2 substrate, the surface polar phonon modes at 806  cm -1 , and 1168  cm -1 hybridize with the graphene plasmon to form the plasmon-phonon resonances [47] . Recent study by Freitag et al. has revealed that the sub-strate ’ s phonons can also affect the photocurrent gen-eration process in graphene [70] . Besides, the high confinement of graphene plasmons even allow them to couple strongly to optical phonons in an atomically thin layer, such as monolayer hexagonal boron nitride (h-BN) sheet [51] , as shown in Figure 3D. The plasmon dispersion ω pl ( q ) of graphen/h-BN/SiO 2 nanoresonator was mapped out by performing measurements on graphene ribbon arrays with various widths. A clear anti-crossing behavior has been displayed, indicating the existence of hybridized plasmon-phonon mode near the surface polar phonon frequency. This hybridized mode can be phenomenologi-cally modeled by two electromagnetically coupled oscil-lators [71] . The local polarization field created by lattice displacement in the h-BN applies a force on the free car-riers in the graphene resonator. And in turn, the polari-zation due to displaced carriers in the graphene exerts a force on the h-BN lattice. As a consequence, the polariza-tions of the two modes cancel each other out, creating a transparency window where no absorption occurs. This phenomena, which is also denoted as phonon induced transparency (PIT) [71] , is analogous to electromagneti-cally induced transparency (EIT) which is the result of destructive interference effect between a direct transition and an indirect transition pathway. The study of phonon-plasmon interaction offers physical insights towards

plasmon dampings in graphene and serves as an impor-tant design consideration for graphene based plasmonic devices, such as waveguides, modulators and detectors in mid-infrared regime. Moreover, the realization of the EIT-like phenomenon in tunable graphene plasmonic systems opens up new opportunities for the exploration of quantum nonlinear optics [72] , quantum information processing [73] , and slow light [74] at room temperature without external pumps.

An alternative way of exciting GPs besides pattern-ing graphene arrays is scattering-type near-field optical microscopy [52, 75] . A schematic picture of the experi-ments is shown in Figure 3E. This technique involves illuminating a sharp metallic tip with infrared light. The tip can “ emit ” radiation over a large span in momentum space that can be used to launch Dirac plasmons locally. These propagating plasmons will be reflected from the edge of the sample and interfere with the forward-prop-agating plasmon through the tip. Infrared nano-imaging revealed that the plasmon wavelength compression λ 0 / λ sp reached 40 and the plasmon in confined geometries can be tuned or switched by gating.

In general, the field of graphene plasmonics utilizes the semi-metallic nature of graphene to create plas-monic devices with their resonance frequency tunable by changing the Fermi level in graphene. This provides a new degree of freedom in the design and operation of plasmonic devices, which is not previously available in the traditional metal-based plasmonic devices. There are many promising applications of these graphene-based plasmonic devices in optical communications, sensing and imaging, especially in the strategically important mid-infrared and far-infrared region.

3 Photonics of TMDCs Transition metal dichalcogenides (TMDCs) are materi-als with the chemical formula MX 2 , where M stands for a transition metal element like Mo, W, Nb, Re, and X is a chalcogen (S, Se, Te). Typically one layer of TMDCs con-sists of an X-M-X sandwich structure. The inter-layer inter-action of TMDCs is the weak Van der Waals force, while the in-plane bonding is the strong covalent bond. Thus, bulk TMDCs can be exfoliated down to few-layer films similar to graphene, extending the zoo of two-dimen-sional materials significantly. Some 2D TMDCs, such as molybdenum- and tungsten-based dichalcogenides, have an indirect bandgap in multi-layer forms, while become direct-bandgap-semiconductors in their monolayer forms

134   H. Zhao et al.

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Figure 3   Plasmonics of graphene. (A) Plasmon resonance in gated graphene microribbon arrays. Left: top and side views of a graphene microribbon array. Right: gate-dependent relative transmission spectra. Reproduced with permission from Ref. [46] . (B) Top: SEM image of a graphene microdisk array. Bottom: Extinction spectra of graphene microdot arrays with one, two and five graphene layers, separated by polymer buffer layers. Reproduced with permission from Ref. [50] (C) Fermi- and photon-energy dependence of the extinction cross section of a combined emitter-nanodisk system. The emitter has a resonance at ħ ω 0   =  0.3eV and is oriented parallel to the disk. Reproduced with permission from Ref. [49] . (D) Schematic of graphene nanoresonators fabricated on a monolayer h-BN sheet on a SiO 2 (285 nm)/Si wafer. Reproduced with permission from Ref. [51] . (E) Diagram of an infrared nano-imaging experiment at the surface of graphene on SiO 2 . Reproduced with permission from Ref.  [52] .

of graphene provides an elegant approach to manipu-late the coupling strength. By putting a dipole 10  nm above the center of a self-standing 100 nm graphene disk (within the decay length of localized GPs sustained by a graphene nanodisk), Koppens et  al. theoretically pre-dicted the Rabi splitting mediated by the localized GP as shown in Figure 3C. The emitter used in the calculation has an excited energy of ħ ω 0   =  0.3 eV and natural decay rate Γ 0   =  5  ×  10 7 s -1 . Importantly, the quantum mechanical strong light matter coupling of GPs and single emitter has also inspired the research of strong GP interaction with ensemble of oscillators, which can be treated classically. This may have far-reaching implications for development of the highly sensitive infrared bio/chemical sensing and molecule detection techniques [67, 68] .

The electronic degrees of freedom in graphene can also couple strongly to substrate polar phonons [47] and the intrinsic IR-active phonons of bilayer graphene [69] . In these experiments, graphene devices have shown a strongly modified graphene plasmon dispersion rela-tion caused by substrate phonons. For example, in the case of a SiO 2 substrate, the surface polar phonon modes at 806  cm -1 , and 1168  cm -1 hybridize with the graphene plasmon to form the plasmon-phonon resonances [47] . Recent study by Freitag et al. has revealed that the sub-strate ’ s phonons can also affect the photocurrent gen-eration process in graphene [70] . Besides, the high confinement of graphene plasmons even allow them to couple strongly to optical phonons in an atomically thin layer, such as monolayer hexagonal boron nitride (h-BN) sheet [51] , as shown in Figure 3D. The plasmon dispersion ω pl ( q ) of graphen/h-BN/SiO 2 nanoresonator was mapped out by performing measurements on graphene ribbon arrays with various widths. A clear anti-crossing behavior has been displayed, indicating the existence of hybridized plasmon-phonon mode near the surface polar phonon frequency. This hybridized mode can be phenomenologi-cally modeled by two electromagnetically coupled oscil-lators [71] . The local polarization field created by lattice displacement in the h-BN applies a force on the free car-riers in the graphene resonator. And in turn, the polari-zation due to displaced carriers in the graphene exerts a force on the h-BN lattice. As a consequence, the polariza-tions of the two modes cancel each other out, creating a transparency window where no absorption occurs. This phenomena, which is also denoted as phonon induced transparency (PIT) [71] , is analogous to electromagneti-cally induced transparency (EIT) which is the result of destructive interference effect between a direct transition and an indirect transition pathway. The study of phonon-plasmon interaction offers physical insights towards

plasmon dampings in graphene and serves as an impor-tant design consideration for graphene based plasmonic devices, such as waveguides, modulators and detectors in mid-infrared regime. Moreover, the realization of the EIT-like phenomenon in tunable graphene plasmonic systems opens up new opportunities for the exploration of quantum nonlinear optics [72] , quantum information processing [73] , and slow light [74] at room temperature without external pumps.

An alternative way of exciting GPs besides pattern-ing graphene arrays is scattering-type near-field optical microscopy [52, 75] . A schematic picture of the experi-ments is shown in Figure 3E. This technique involves illuminating a sharp metallic tip with infrared light. The tip can “ emit ” radiation over a large span in momentum space that can be used to launch Dirac plasmons locally. These propagating plasmons will be reflected from the edge of the sample and interfere with the forward-prop-agating plasmon through the tip. Infrared nano-imaging revealed that the plasmon wavelength compression λ 0 / λ sp reached 40 and the plasmon in confined geometries can be tuned or switched by gating.

In general, the field of graphene plasmonics utilizes the semi-metallic nature of graphene to create plas-monic devices with their resonance frequency tunable by changing the Fermi level in graphene. This provides a new degree of freedom in the design and operation of plasmonic devices, which is not previously available in the traditional metal-based plasmonic devices. There are many promising applications of these graphene-based plasmonic devices in optical communications, sensing and imaging, especially in the strategically important mid-infrared and far-infrared region.

3 Photonics of TMDCs Transition metal dichalcogenides (TMDCs) are materi-als with the chemical formula MX 2 , where M stands for a transition metal element like Mo, W, Nb, Re, and X is a chalcogen (S, Se, Te). Typically one layer of TMDCs con-sists of an X-M-X sandwich structure. The inter-layer inter-action of TMDCs is the weak Van der Waals force, while the in-plane bonding is the strong covalent bond. Thus, bulk TMDCs can be exfoliated down to few-layer films similar to graphene, extending the zoo of two-dimen-sional materials significantly. Some 2D TMDCs, such as molybdenum- and tungsten-based dichalcogenides, have an indirect bandgap in multi-layer forms, while become direct-bandgap-semiconductors in their monolayer forms

Two-dimensional materials for nanophotonics application   135

[76] . Their sizable and tunable bandgap (1-2 eV) not only generates strong photoluminescence [77] , but also open doors to various optoelectronic applications such as photodetectors [78 – 80] , energy harvesting [81 – 83] and electroluminescence [84 – 87] , with operational spectrum range that is different from graphene based devices. In addition, exotic optical properties such as valley coher-ence [88] and valley-selective circular dichroism [89] have been demonstrated in some 2D TMDCs, making these materials very promising for the discovery of new physical phenomena.

3.1 2D TMDCs based photodetectors

Compared to graphene based photodetectors, few-layer TMDCs based photodetectors have higher photorespon-sivity, though they work mainly at the visible region.

High-performance photodetectors have been made by various 2D TMDCs, such as MoS 2 , WS 2 , and ReSe 2 . Lopez-Sanchez et  al. [80] have made monolayer MoS 2 pho-totransistors of high sensitivity. Owning to the high gain of monolayer MoS 2 , their devices can reach a photore-sponsivity of 880 A/W at wavelength of 561 nm, with an operational range from 400  nm to 680  nm ( Figure 4 A). Nengjie Huo et al. [79] made a multi-layer WS 2 phototran-sistor which demonstrated a responsivity of 5.7A/W and an external quantum efficiency (EQE) of 1118% at 633 nm red light. Shengxue Yang et al. [78] have fabricated pho-todetector with Mo doped ReSe 2 nanosheets, obtaining a photoresponsivity of 55.5 A/W and an EQE of 10893% at 633  nm light in ammonia environment. Most of these detectors operate at the visible spectrum, as a result of their bandgaps being around 1.5 – 2.5 eV. At the visible range, these photodetectors possess much better perfor-mance than pristine graphene-based photodetectors.

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3.2 2D TMDCs based LEDs

Light-emitting diodes (LED) is widely used for display, lighting, and sensing. Since monolayer TMDCs like WSe 2 are direct-bandgap semiconductors, electrons and holes can easily recombine with each other in radiative pro-cesses to generate photons. Electroluminescence local-ized at the contact region [90] and occurred on heavily p-doped silicon substrates [91] has been obtained in single layer MoS 2 field effect transistors. However, the optoelectronic efficiency of MoS 2 based LEDs is relatively low and drops significantly with increasing carrier injec-tion [92] . Indeed, the difficulty to obtain hole conduction, the ineffective contacts, and the limited optical quality of monolayer MoS 2 have hindered the potential applications of MoS 2 LEDs.

Recently, WSe 2 monolayer lateral diodes have been demonstrated by applying multiple independent gate voltages. Through tuning electrostatic doping, both p-n and n-p diodes can be defined, leading to effective bright electroluminescence. Zhang et al. [84] have made use of the valley degrees of freedom of few-layer WSe 2 to get cir-cularly polarized luminescence. The emitted light came from an electrostatically formed in-channel p-i-n junc-tions (Figure 4B). Ross et  al. [85] also demonstrated a monolayer WSe 2 based LED. They made electrostatically formed p-n junctions in WSe 2 with a boron nitride film underneath served as a dielectric layer. Electrons and holes can thus be injected into channels effectively via this structure, leading to a strong electroluminescence. The total photon emission rate can reach 16 million s -1 at an applied current of 35 nA. They also found that both electroluminescence and photoluminescence in this system came from the same valley excitions (Figure 4C). At this point, the research of the light emitting devices based on TMDCs are still in their early stage. More efforts are needed to further improve their efficiency and gain. Fur-thermore, it is still a long way from obtaining high optical gain in TMDCs and more work is still needed in exploring the possibility of achieving lasing in these materials.

4 Black phosphorus for photonics application

Few-layer black phosphorus (BP) is an emerging 2D mate-rial with a puckered orthorhombic lattice (Figure 1D). Its anisotropic in-plane lattice structure lowered its spatial symmetry, resulting in highly anisotropic electronic and optoelectronic properties. Bulk BP has a moderate

bandgap of 0.3 eV [93 – 95] , which increases monotonously with reducing number of layers, eventually reaching 2 eV [96, 97] for monolayer. Hence, for photonic applications, black phosphorus can cover a broad spectrum, from the visible to mid-infrared. The moderate and tunable direct bandgap of BP bridges the zero-bandgap graphene and relatively wide bandgap TMDCs, making BP a promising material for future electronics and optoelectronics.

Xia et  al. [98] have characterized the polarization-resolved infrared relative extinction spectra of multi-layer BP flakes. The incident light was polarized towards six different angles, uniformly separated by 30 degrees ( Figure  5 A). The relative extinction indicated a narrow bandgap of 0.3 eV. Their extinction spectra coincides with the theoretical calculation precisely [101] . Polarization-resolved Raman spectra of a BP film was also measured, indicating a polarization-dependent relative intensities of three characteristic vibration modes.

Calculations have revealed that black phosphorus has a strongly layer-dependent bandgap [102] . Bandgap of BP increases with decreased layers, due to the enhanced two-dimensional quantum confinement and reduced screen-ings in fewer layers. According to the calculation, the energy bandstructure of layered BP is significantly tuned by its strong many-electron effects: large self-energy cor-rections have contributed to enhance the bandgap of mon-olayer BP from 0.8eV (as calculated) to more than 2.0 eV, while a huge exciton binding energy ( ∼ 0.9eV according to a recent report [103] ) has lowered its first optical adsorp-tion peak location from 2.2ev to 1.3 eV. These effects improve the tunability of the bandstructure of layered BP, making it promising for broadband device applications.

Buscema et  al. [99] investigated the photoresponse of few-layer BP transistors by performing electrical meas-urement in dark and bright environment. Their device worked from the visible region to infrared, with a response time of 1 ms (rise) and 4 ms (fall), see Figure 5B. The pho-toresponsivity in visible region can reach 4.8 mA/W, which decreased with incident power. Engel et  al. [104] performed photocurrent measurement and high-resolu-tion imaging with a 120  nm-thick BP. They verified that BP photodetector is capable of recording images in both the visible (532 nm) and the infrared (1500 nm) region with ultrahigh resolution. The measured responsivity is 20 mA/W at visible region and 5 mA/W at infrared region. An analysis [105] based on this experiment and related modeling revealed that photothermal effects in BP are responsible for its low bias photoresponse, while the bolo-metric effects dominate at large bias. In addition, the pho-tocurrent polarities, according to their analysis, originate from these two effects, rather than the photovoltaic effect.

136   H. Zhao et al.

[76] . Their sizable and tunable bandgap (1-2 eV) not only generates strong photoluminescence [77] , but also open doors to various optoelectronic applications such as photodetectors [78 – 80] , energy harvesting [81 – 83] and electroluminescence [84 – 87] , with operational spectrum range that is different from graphene based devices. In addition, exotic optical properties such as valley coher-ence [88] and valley-selective circular dichroism [89] have been demonstrated in some 2D TMDCs, making these materials very promising for the discovery of new physical phenomena.

3.1 2D TMDCs based photodetectors

Compared to graphene based photodetectors, few-layer TMDCs based photodetectors have higher photorespon-sivity, though they work mainly at the visible region.

High-performance photodetectors have been made by various 2D TMDCs, such as MoS 2 , WS 2 , and ReSe 2 . Lopez-Sanchez et  al. [80] have made monolayer MoS 2 pho-totransistors of high sensitivity. Owning to the high gain of monolayer MoS 2 , their devices can reach a photore-sponsivity of 880 A/W at wavelength of 561 nm, with an operational range from 400  nm to 680  nm ( Figure 4 A). Nengjie Huo et al. [79] made a multi-layer WS 2 phototran-sistor which demonstrated a responsivity of 5.7A/W and an external quantum efficiency (EQE) of 1118% at 633 nm red light. Shengxue Yang et al. [78] have fabricated pho-todetector with Mo doped ReSe 2 nanosheets, obtaining a photoresponsivity of 55.5 A/W and an EQE of 10893% at 633  nm light in ammonia environment. Most of these detectors operate at the visible spectrum, as a result of their bandgaps being around 1.5 – 2.5 eV. At the visible range, these photodetectors possess much better perfor-mance than pristine graphene-based photodetectors.

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Figure 4   Photonics of TMDCs. (A) Drain-source characteristic of the monolayer MoS 2 based photodetector in dark and under various incident intensities. Raising illumina-tion intensities results in enhanced photocurrent owning to electron-hole pair generation in the direct bandgap of monolayer MoS 2 . Repro-duced with permission from Ref. [80] . (B) Schematic of the WSe 2 p-i-n junction formed by electric-double-layer transistors. Reproduced with permission from Ref. [84] . (C)  electroluminescence spectrum (blue) and the photoluminescence spectrum (red) of the WSe 2 p-n junction closely resemble each other. Reproduced with permission from Ref. [85] .

3.2 2D TMDCs based LEDs

Light-emitting diodes (LED) is widely used for display, lighting, and sensing. Since monolayer TMDCs like WSe 2 are direct-bandgap semiconductors, electrons and holes can easily recombine with each other in radiative pro-cesses to generate photons. Electroluminescence local-ized at the contact region [90] and occurred on heavily p-doped silicon substrates [91] has been obtained in single layer MoS 2 field effect transistors. However, the optoelectronic efficiency of MoS 2 based LEDs is relatively low and drops significantly with increasing carrier injec-tion [92] . Indeed, the difficulty to obtain hole conduction, the ineffective contacts, and the limited optical quality of monolayer MoS 2 have hindered the potential applications of MoS 2 LEDs.

Recently, WSe 2 monolayer lateral diodes have been demonstrated by applying multiple independent gate voltages. Through tuning electrostatic doping, both p-n and n-p diodes can be defined, leading to effective bright electroluminescence. Zhang et al. [84] have made use of the valley degrees of freedom of few-layer WSe 2 to get cir-cularly polarized luminescence. The emitted light came from an electrostatically formed in-channel p-i-n junc-tions (Figure 4B). Ross et  al. [85] also demonstrated a monolayer WSe 2 based LED. They made electrostatically formed p-n junctions in WSe 2 with a boron nitride film underneath served as a dielectric layer. Electrons and holes can thus be injected into channels effectively via this structure, leading to a strong electroluminescence. The total photon emission rate can reach 16 million s -1 at an applied current of 35 nA. They also found that both electroluminescence and photoluminescence in this system came from the same valley excitions (Figure 4C). At this point, the research of the light emitting devices based on TMDCs are still in their early stage. More efforts are needed to further improve their efficiency and gain. Fur-thermore, it is still a long way from obtaining high optical gain in TMDCs and more work is still needed in exploring the possibility of achieving lasing in these materials.

4 Black phosphorus for photonics application

Few-layer black phosphorus (BP) is an emerging 2D mate-rial with a puckered orthorhombic lattice (Figure 1D). Its anisotropic in-plane lattice structure lowered its spatial symmetry, resulting in highly anisotropic electronic and optoelectronic properties. Bulk BP has a moderate

bandgap of 0.3 eV [93 – 95] , which increases monotonously with reducing number of layers, eventually reaching 2 eV [96, 97] for monolayer. Hence, for photonic applications, black phosphorus can cover a broad spectrum, from the visible to mid-infrared. The moderate and tunable direct bandgap of BP bridges the zero-bandgap graphene and relatively wide bandgap TMDCs, making BP a promising material for future electronics and optoelectronics.

Xia et  al. [98] have characterized the polarization-resolved infrared relative extinction spectra of multi-layer BP flakes. The incident light was polarized towards six different angles, uniformly separated by 30 degrees ( Figure  5 A). The relative extinction indicated a narrow bandgap of 0.3 eV. Their extinction spectra coincides with the theoretical calculation precisely [101] . Polarization-resolved Raman spectra of a BP film was also measured, indicating a polarization-dependent relative intensities of three characteristic vibration modes.

Calculations have revealed that black phosphorus has a strongly layer-dependent bandgap [102] . Bandgap of BP increases with decreased layers, due to the enhanced two-dimensional quantum confinement and reduced screen-ings in fewer layers. According to the calculation, the energy bandstructure of layered BP is significantly tuned by its strong many-electron effects: large self-energy cor-rections have contributed to enhance the bandgap of mon-olayer BP from 0.8eV (as calculated) to more than 2.0 eV, while a huge exciton binding energy ( ∼ 0.9eV according to a recent report [103] ) has lowered its first optical adsorp-tion peak location from 2.2ev to 1.3 eV. These effects improve the tunability of the bandstructure of layered BP, making it promising for broadband device applications.

Buscema et  al. [99] investigated the photoresponse of few-layer BP transistors by performing electrical meas-urement in dark and bright environment. Their device worked from the visible region to infrared, with a response time of 1 ms (rise) and 4 ms (fall), see Figure 5B. The pho-toresponsivity in visible region can reach 4.8 mA/W, which decreased with incident power. Engel et  al. [104] performed photocurrent measurement and high-resolu-tion imaging with a 120  nm-thick BP. They verified that BP photodetector is capable of recording images in both the visible (532 nm) and the infrared (1500 nm) region with ultrahigh resolution. The measured responsivity is 20 mA/W at visible region and 5 mA/W at infrared region. An analysis [105] based on this experiment and related modeling revealed that photothermal effects in BP are responsible for its low bias photoresponse, while the bolo-metric effects dominate at large bias. In addition, the pho-tocurrent polarities, according to their analysis, originate from these two effects, rather than the photovoltaic effect.

Two-dimensional materials for nanophotonics application   137

Hong et  al. demonstrated transport and optoelec-tronic measurement on few-layer BP based phototransis-tors [100] . Their work indicated that BP photoresponse near the BP-electrode interface mainly arises from the photovoltaic effect in off-state, while in on state photo-thermoelectric effect dominates. They also revealed that the anisotropic photoresponse should be attributed to angle-dependent absorption of BP crystals. Figure 5C is the anisotropic photoresponse measurements of a BP FET under zero source-drain bias and a back-gate voltage of

10 V. The red/blue curve demonstrates the angle depend-ence of the strongest positive/negative photoresponse at BP-metal interface, respectively.

Besides the advantages mentioned above, black phos-phorus also has other impressive properties such as linear dichroism [96] , high hole mobility [106] , Large thermo-electric power factors [107] , and anisotropic plasmonic excitations [108] . However, some challenges remain in BP research and application. For example, monolayer BP degrades rapidly in air, due to oxidation [109] and water

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Figure 5   Photonics of black phosphorus. (A) Top: the polarization-resolved infrared relative extinction spectra of multi-layer BP flakes. Bottom: angle-dependent measurement of DC conductivity (solid dots) and IR extinction (hollow squares). Reproduced with permission from Ref. [98] . (B) Photocurrent measured of a BP FET, the response time is 1 ms (rise) and 4 ms (fall). Reproduced with permission from Ref. [99] . (C) The room-temperature anisotropic photoresponse measurements of a BP FET under zero source-drain bias and a back-gate voltage of 10V. Top: Schematic diagram of the BP FET setup. Bottom: The angle dependence of the strongest positive (red)/negative (blue) photoresponse at BP-metal interface. Reproduced with permission from Ref. [100] .

adsorption [110] . Therefore, developing clean and efficient protection methods are necessary. Moreover, currently the fabrication of few-layer BP relies on mechanical exfo-liation method [43, 111, 112] , which is of rather low yield. So we need to develop large-area synthesis methods to produce wafer-scale few-layer black phosphorus. Solving these problems will push forward various novel applica-tions of BP. Nevertheless, black phosphorus has demon-strated intriguing properties and promising potential for applications in infrared optoelectronics while its aniso-tropic properties may lead to the invention of conceptu-ally new devices.

5 Future directions Atomically thin materials such as graphene, transition metal dichalcogenides and the emerging black phospho-rus are being developed as the building blocks for a wide range of optoelectronic devices. These materials offer diverse choices including metals, semimetals, and semi-conductors with small or large optical gaps allowing for different and new application space even beyond what conventional bulk materials can possibly offer. To fully exploit their potentials, there is an apparent need to gain more fundamental understandings on their intrinsic and extrinsic optical behaviors, e.g., excitonics, optical non-linearity, mechanisms of photoresponse et  al. Further-more, issues involving low light absorption and short light-matter interaction length of 2D materials need to be addressed. This could open up the new areas of research into the symbiotic relation between these materials with conventional photonic elements including cavities, wave-guides or plasmonic nanostructures. The potential of mid-infrared and terahertz graphene plasmons is also being realized, demonstrating very attractive features includ-ing extremely high field confinement, tunability and long lifetime, which can serve as a platform for efficient light-matter interaction in the quantum optical regime. Beyond the graphene plasmonics, the extraordinary optical non-linearity and fast modulation speed of graphene are also favored for optical communication applications. One remaining challenge is to extend the operating window of tunable graphene optical response from the infrared toward other regions of the electromagnetic spectrum where it can find a larger range of applications from optical modulation, spectral light detection to sensing. To this end, the development of controllable and stable chemical doping for graphene and even other 2D materi-als is highly desirable. In addition to the optical properties

of a material itself, the availability of hybrid heterostruc-tures will give rise to intriguing optical properties as well as expanded device functionalities involving efficient solar cells, ultrafast optical modulators or detectors and 2D light emitting devices or lasers in the near future.

References [1] Lee EJH, Balasubramanian K, Weitz RT, Burghard M, Kern K.

Contact and edge effects in graphene devices. Nat Nanotech-nol 2008;3:486 – 90.

[2] Park J, Ahn YH, Ruiz-Vargas C. Imaging of photocurrent generation and collection in single-layer graphene. Nano Lett 2009;9:1742 – 6.

[3] Xia F, Mueller T, Golizadeh-Mojarad R, Freitag M, Lin YM, Tsang J, Perebeinos V, Avouris P. Photocurrent imaging and efficient photon detection in a graphene transistor. Nano Lett 2009;9:1039 – 44.

[4] Xu X, Gabor NM, Alden JS, van der Zande AM, McEuen PL. Photo-thermoelectric effect at a graphene interface junction. Nano Lett 2009;10:562 – 6.

[5] Kim R, Perebeinos V, Avouris P. Relaxation of optically excited carriers in graphene. Phys Rev B 2011;84:75449.

[6] Winzer T, Knorr A, Malic E. Carrier multiplication in graphene. Nano Lett 2010;10:4839 – 43.

[7] Tielrooij KJ, Song JCW, Jensen SA, Centeno A, Pesquera A, Zurutuza Elorza A, Bonn M, Levitov LS, Koppens FHL. Pho-toexcitation cascade and multiple hot-carrier generation in graphene. Nat Phys 2013;l9:248 – 52.

[8] Freitag M, Low T, Xia F, Avouris P. Photoconductivity of biased graphene. Nat Photon 2013;7:53 – 9.

[9] Nair RR, Blake P, Grigorenko AN, Novoselov KS, Booth TJ, Stauber T, Peres NMR, Geim AK. Fine structure constant defines visual transparency of graphene. Science 2008;320:1308.

[10] Mak KF, Ju L, Wang F, Heinz TF. Optical spectroscopy of graphene: from the far infrared to the ultraviolet. Solid State Commun 2012;152:1341 – 9.

[11] Xia F, Mueller T, Lin Y-m, Valdes-Garcia A, Avouris P. Ultrafast graphene photodetector. Nat Nanotechnol 2009;4:839 – 43.

[12] Echtermeyer TJ, Britnell L, Jasnos PK, Lombardo A, Gorbachev RV, Grigorenko AN, Geim AK, Ferrari AC, Novoselov KS. Strong plasmonic enhancement of photovoltage in graphene. Nat Commun 2011;2:458.

[13] Fang Z, Liu Z, Wang Y, Ajayan PM, Nordlander P, Halas NJ. Graphene-antenna sandwich photodetector. Nano Lett 2012;12:3808 – 13.

[14] Engel M, Steiner M, Lombardo A, Ferrari AC, L ö hneysen HV, Avouris P, Krupke R. Light – matter interaction in a microcavity-controlled graphene transistor. Nat Commun 2012;3:906.

[15] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L, Wang F, Zhang X. A graphene-based broadband optical modulator. Nature 2011;474:64 – 7.

[16] Li W, Chen B, Meng C, Fang W, Xiao Y, Li X, Hu Z, Xu Y, Tong L, Wang H, Liu W, Bao J, Shen YR. Ultrafast all-optical graphene modulator. Nano Lett 2014;14:955 – 9.

[17] Mueller T, Xia F, Avouris P. Graphene photodetectors for high-speed optical communications. Nat Photon 2010;4:297 – 301.

138   H. Zhao et al.

Hong et  al. demonstrated transport and optoelec-tronic measurement on few-layer BP based phototransis-tors [100] . Their work indicated that BP photoresponse near the BP-electrode interface mainly arises from the photovoltaic effect in off-state, while in on state photo-thermoelectric effect dominates. They also revealed that the anisotropic photoresponse should be attributed to angle-dependent absorption of BP crystals. Figure 5C is the anisotropic photoresponse measurements of a BP FET under zero source-drain bias and a back-gate voltage of

10 V. The red/blue curve demonstrates the angle depend-ence of the strongest positive/negative photoresponse at BP-metal interface, respectively.

Besides the advantages mentioned above, black phos-phorus also has other impressive properties such as linear dichroism [96] , high hole mobility [106] , Large thermo-electric power factors [107] , and anisotropic plasmonic excitations [108] . However, some challenges remain in BP research and application. For example, monolayer BP degrades rapidly in air, due to oxidation [109] and water

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Figure 5   Photonics of black phosphorus. (A) Top: the polarization-resolved infrared relative extinction spectra of multi-layer BP flakes. Bottom: angle-dependent measurement of DC conductivity (solid dots) and IR extinction (hollow squares). Reproduced with permission from Ref. [98] . (B) Photocurrent measured of a BP FET, the response time is 1 ms (rise) and 4 ms (fall). Reproduced with permission from Ref. [99] . (C) The room-temperature anisotropic photoresponse measurements of a BP FET under zero source-drain bias and a back-gate voltage of 10V. Top: Schematic diagram of the BP FET setup. Bottom: The angle dependence of the strongest positive (red)/negative (blue) photoresponse at BP-metal interface. Reproduced with permission from Ref. [100] .

adsorption [110] . Therefore, developing clean and efficient protection methods are necessary. Moreover, currently the fabrication of few-layer BP relies on mechanical exfo-liation method [43, 111, 112] , which is of rather low yield. So we need to develop large-area synthesis methods to produce wafer-scale few-layer black phosphorus. Solving these problems will push forward various novel applica-tions of BP. Nevertheless, black phosphorus has demon-strated intriguing properties and promising potential for applications in infrared optoelectronics while its aniso-tropic properties may lead to the invention of conceptu-ally new devices.

5 Future directions Atomically thin materials such as graphene, transition metal dichalcogenides and the emerging black phospho-rus are being developed as the building blocks for a wide range of optoelectronic devices. These materials offer diverse choices including metals, semimetals, and semi-conductors with small or large optical gaps allowing for different and new application space even beyond what conventional bulk materials can possibly offer. To fully exploit their potentials, there is an apparent need to gain more fundamental understandings on their intrinsic and extrinsic optical behaviors, e.g., excitonics, optical non-linearity, mechanisms of photoresponse et  al. Further-more, issues involving low light absorption and short light-matter interaction length of 2D materials need to be addressed. This could open up the new areas of research into the symbiotic relation between these materials with conventional photonic elements including cavities, wave-guides or plasmonic nanostructures. The potential of mid-infrared and terahertz graphene plasmons is also being realized, demonstrating very attractive features includ-ing extremely high field confinement, tunability and long lifetime, which can serve as a platform for efficient light-matter interaction in the quantum optical regime. Beyond the graphene plasmonics, the extraordinary optical non-linearity and fast modulation speed of graphene are also favored for optical communication applications. One remaining challenge is to extend the operating window of tunable graphene optical response from the infrared toward other regions of the electromagnetic spectrum where it can find a larger range of applications from optical modulation, spectral light detection to sensing. To this end, the development of controllable and stable chemical doping for graphene and even other 2D materi-als is highly desirable. In addition to the optical properties

of a material itself, the availability of hybrid heterostruc-tures will give rise to intriguing optical properties as well as expanded device functionalities involving efficient solar cells, ultrafast optical modulators or detectors and 2D light emitting devices or lasers in the near future.

References [1] Lee EJH, Balasubramanian K, Weitz RT, Burghard M, Kern K.

Contact and edge effects in graphene devices. Nat Nanotech-nol 2008;3:486 – 90.

[2] Park J, Ahn YH, Ruiz-Vargas C. Imaging of photocurrent generation and collection in single-layer graphene. Nano Lett 2009;9:1742 – 6.

[3] Xia F, Mueller T, Golizadeh-Mojarad R, Freitag M, Lin YM, Tsang J, Perebeinos V, Avouris P. Photocurrent imaging and efficient photon detection in a graphene transistor. Nano Lett 2009;9:1039 – 44.

[4] Xu X, Gabor NM, Alden JS, van der Zande AM, McEuen PL. Photo-thermoelectric effect at a graphene interface junction. Nano Lett 2009;10:562 – 6.

[5] Kim R, Perebeinos V, Avouris P. Relaxation of optically excited carriers in graphene. Phys Rev B 2011;84:75449.

[6] Winzer T, Knorr A, Malic E. Carrier multiplication in graphene. Nano Lett 2010;10:4839 – 43.

[7] Tielrooij KJ, Song JCW, Jensen SA, Centeno A, Pesquera A, Zurutuza Elorza A, Bonn M, Levitov LS, Koppens FHL. Pho-toexcitation cascade and multiple hot-carrier generation in graphene. Nat Phys 2013;l9:248 – 52.

[8] Freitag M, Low T, Xia F, Avouris P. Photoconductivity of biased graphene. Nat Photon 2013;7:53 – 9.

[9] Nair RR, Blake P, Grigorenko AN, Novoselov KS, Booth TJ, Stauber T, Peres NMR, Geim AK. Fine structure constant defines visual transparency of graphene. Science 2008;320:1308.

[10] Mak KF, Ju L, Wang F, Heinz TF. Optical spectroscopy of graphene: from the far infrared to the ultraviolet. Solid State Commun 2012;152:1341 – 9.

[11] Xia F, Mueller T, Lin Y-m, Valdes-Garcia A, Avouris P. Ultrafast graphene photodetector. Nat Nanotechnol 2009;4:839 – 43.

[12] Echtermeyer TJ, Britnell L, Jasnos PK, Lombardo A, Gorbachev RV, Grigorenko AN, Geim AK, Ferrari AC, Novoselov KS. Strong plasmonic enhancement of photovoltage in graphene. Nat Commun 2011;2:458.

[13] Fang Z, Liu Z, Wang Y, Ajayan PM, Nordlander P, Halas NJ. Graphene-antenna sandwich photodetector. Nano Lett 2012;12:3808 – 13.

[14] Engel M, Steiner M, Lombardo A, Ferrari AC, L ö hneysen HV, Avouris P, Krupke R. Light – matter interaction in a microcavity-controlled graphene transistor. Nat Commun 2012;3:906.

[15] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L, Wang F, Zhang X. A graphene-based broadband optical modulator. Nature 2011;474:64 – 7.

[16] Li W, Chen B, Meng C, Fang W, Xiao Y, Li X, Hu Z, Xu Y, Tong L, Wang H, Liu W, Bao J, Shen YR. Ultrafast all-optical graphene modulator. Nano Lett 2014;14:955 – 9.

[17] Mueller T, Xia F, Avouris P. Graphene photodetectors for high-speed optical communications. Nat Photon 2010;4:297 – 301.

Two-dimensional materials for nanophotonics application   139

[18] Shi S-F, Xu X, Ralph DC, McEuen PL. Plasmon resonance in individual nanogap electrodes studied using graphene nano-constrictions as photodetectors. Nano Lett 2011;11:1814 – 8.

[19] Liu Y, Cheng R, Liao L, Zhou H, Bai J, Liu G, Liu L, Huang Y, Duan X. Plasmon resonance enhanced multicolour photo-detection by graphene. Nat Commun 2011;2:579.

[20] Konstantatos G, Badioli M, Gaudreau L, Osmond J, Bernechea M, Garcia de Arquer FP, Gatti F, Koppens FH. Hybrid graphene-quantum dot phototransistors with ultrahigh gain. Nat Nanotechnol 2012;7:363 – 8.

[21] Sun Z, Liu Z, Li J, Tai G-a, Lau S-P, Yan F. Infrared photo-detectors based on CVD grown graphene and PbS quantum dots with ultrahigh responsivity. Adv Mater 2012;24:5878 – 83.

[22] Gan X, Mak KF, Gao Y, You Y, Hatami F, Hone J, Heinz TF, Englund D. Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity. Nano Lett 2012;12:5626 – 31.

[23] Furchi M, Urich A, Pospischil A, Lilley G, Unterrainer K, Detz H, Klang P, Andrews AM, Schrenk W, Strasser G, Mueller T. Microcavity-integrated graphene photodetector. Nano Lett 2012;12:2773 – 7.

[24] Ferreira A, Peres NMR, Ribeiro RM, Stauber T. Graphene-based photodetector with two cavities. Phys Rev B 2012;85:115438.

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[34] Cubukcu E, Kort EA, Crozier KB, Capasso F. Plasmonic laser antenna. Appl Phys Lett 2006;89:93120.

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[34] Cubukcu E, Kort EA, Crozier KB, Capasso F. Plasmonic laser antenna. Appl Phys Lett 2006;89:93120.

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[40] Barnes WL, Dereux A, Ebbesen TW. Surface plasmon subwave-length optics. Nature 2003;424:824 – 30.

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[43] Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK. Two-dimensional atomic crystals. Proc Natl Acad Sci USA 2005;102:10451 – 3.

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[46] Ju L, Geng B, Horng J, Girit C, Martin M, Hao Z, Bechtel HA, Liang X, Zett A, Shen YR, Wang F. Graphene plasmonics for tunable terahertz metamaterials. Nat Nanotechnol 2011;6:630 – 4.

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[48] Brar VW, Jang MS, Sherrott M, Lopez JJ, Atwater HA. Highly confined tunable mid-infrared plasmonics in graphene nanoresonators. Nano Lett 2013;13:2541 – 7.

[49] Koppens FHL, Chang DE, Garcia De Abajo FJ. Graphene plas-monics: a platform for strong light-matter interactions. Nano Lett 2011;11:3370 – 7.

[50] Yan H, Li X, Chandra B, Tulevski G, Wu Y, Freitag M, Zhu W, Avouris P, Xia F. Tunable infrared plasmonic devices using graphene/insulator stacks. Nat Nanotechnol 2012;7:330 – 4.

[51] Brar VW, Jang MS, Sherrott M, Kim S, Lopez JJ, Kim LB, Choi M, Atwater H. Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN Heterostructures. Nano Lett 2014;14:3876 – 80.

[52] Fei Z, Rodin AS, Andreev GO, Bao W, McLeod AS, Wagner M, Zhang LM, Zhao Z, Thiemens M, Dominguez G, Fogler MM, Castro Neto AH, Lau CN, Keilmann F, Basov DN. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 2012;487:82 – 5.

[53] Sarma SD, Hwang EH. Collective modes of the massless Dirac plasma. Phys Rev Lett 2009;102:206412.

[54] Christensen J, Manjavacas A, Thongrattanasiri S, Koppens FHL, Garc í a de Abajo FJ. Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons. ACS nano 2011;6:431 – 40.

[55] Yan H, Li Z, Li X, Zhu W, Avouris P, Xia F. Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene. Nano Lett 2012;12:3766 – 71.

[56] Fang Z, Wang Y, Schlather AE, Liu Z, Ajayan PM, Garc í a de Abajo FJ, Nordlander P, Zhu X, Halas NJ. Active tunable absorp-tion enhancement with graphene nanodisk arrays. Nano Lett 2013;14:299 – 304.

[57] Fang Z, Thongrattanasiri S, Schlather A, Liu Z, Ma L, Wang Y, Ajayan PM, Nordlander P, Halas NJ, Garc í a de Abajo FJ. Gated tunability and hybridization of localized plasmons in nano-structured graphene. ACS Nano 2013;7:2388 – 95.

[58] Halas NJ, Lal S, Chang W-S, Link S, Nordlander P. Plasmons in strongly coupled metallic nanostructures. Chem Rev 2011;111:3913 – 61.

[59] Hennessy K, Badolato A, Winger M, Gerace D, Atat ü re M, Gulde S, F ä lt S, Hu EL, Imamoglu A. Quantum nature of a strongly coupled single quantum dot-cavity system. Nature 2007;445:896 – 9.

[60] Yoshie T, Scherer A, Hendrickson J, Khitrova G, Gibbs HM, Rupper G, Ell C, Shchekin OB, Deppe DG. Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity. Nature 2004;432:200 – 3.

[61] McKeever J, Boca A, Boozer AD, Buck JR, Kimble HJ. Experi-mental realization of a one-atom laser in the regime of strong coupling. Nature 2003;425:268 – 71.

[62] Khitrova G, Gibbs HM, Kira M, Koch SW, Scherer A. Vacuum Rabi splitting in semiconductors. Nat Phys 2006;2:81 – 90.

[63] G é rard JM, Sermage B, Gayral B, Legrand B, Costard E, Thierry-Mieg V. Enhanced spontaneous emission by quan-tum boxes in a monolithic optical microcavity. Phys Rev Lett 1998;81:1110.

[64] Boroditsky M, Vrijen R, Krauss TF, Coccioli R. Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals. J Lightwave Technol 1999;17:2096 – 112.

[65] Vahala KJ. Optical microcavities. Nature 2003;424:839 – 46. [66] Spillane SM, Kippenberg TJ, Vahala KJ, Goh KW, Wilcut E,

Kimble HJ. Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys Rev A 2005;71:13817.

[67] Liu F, Cubukcu E. Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons. Phys Rev B 2013;88:11.

[68] Li Y, Yan H, Farmer DB, Meng X, Zhu W, Osgood RM, Heinz TF, Avouris P. Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers. Nano Lett 2014;14:1573 – 7.

[69] Low T, Guinea F, Yan H, Xia F, Avouris P. Novel midinfrared plasmonic properties of bilayer graphene. Phys Rev Lett 2014;112:116801.

[70] Freitag M, Low T, Martin-Moreno L, Zhu W, Guinea F, Avouris P. Substrate-sensitive mid-infrared photoresponse in graphene. ACS Nano 2014;8:8350 – 6.

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[72] Tanji-Suzuki H, Chen W, Landig R, Simon J, Vuletic V. Vacuum-induced transparency. Science 2011;333:1266 – 9.

[73] Yanik MF, Suh W, Wang Z, Fan S. Stopping light in a waveguide with an all-optical analog of electromagnetically induced trans-parency. Phys Rev Lett 2004;93:233903.

[74] Hau LV, Harris SE, Dutton Z, Behroozi CH. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 1999;397:594 – 8.

[75] Chen J, Badioli M, Alonso-Gonz á lez P, Thongrattanasiri S, Huth F, Osmond J, Spasenovic M, Centeno A, Pesquera A, Godignon P, Elorza AZ, Camara N, Garc í a de Abajo FJ, Hillenbrand R, Koppens FHL. Optical nano-imaging of gate-tunable graphene plasmons. Nature 2012;487:77 – 81.

[76] Mak KF, Lee C, Hone J, Shan J, Heinz TF. Atomically thin MoS2: a new direct-gap semiconductor. Phys Rev Lett 2010;105:136805.

[77] Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C-Y, Galli G, Wang F. Emerging photoluminescence in monolayer MoS2. Nano Lett 2010;10:1271 – 5.

[78] Yang S, Tongay S, Yue Q, Li Y, Li B, Lu F. High-performance few-layer mo-doped ReSe2 nanosheet photodetectors. Scientific reports 2014;4:5442.

[79] Huo N, Yang S, Wei Z, Li S-S, Xia J-B, Li J. Photoresponsive and gas sensing field-effect transistors based on multilayer WS2 nanoflakes. Scientific reports 2014;4:5209.

[80] Lopez-Sanchez O, Lembke D, Kayci M, Radenovic A, Kis A. Ultrasensitive photodetectors based on monolayer MoS2. Nat Nanotechnol 2013;8:497 – 501.

[81] Britnell L, Ribeiro RM, Eckmann A, Jalil R, Belle BD, Mishchenko A, Kim Y-J, Gorbachev RV, Georgiou T, Morozov SV, Grigorenko AN, Geim AK, Casiraghi C, Castro Neto AH, Novoselov KS. Strong light-matter interactions in hetero-structures of atomically thin films. Science 2013;340:1311 – 4.

[82] Yu WJ, Liu Y, Zhou H, Yin A, Li Z, Huang Y, Duan X. Highly efficient gate-tunable photocurrent generation in vertical hetero-structures of layered materials. Nat Nanotechnol 2013;8:952 – 8.

[83] Fontana M, Deppe T, Boyd AK, Rinzan M, Liu AY, Paranjape M, Barbara P. Electron-hole transport and photovoltaic effect in gated MoS2 Schottky junctions. Scientific reports 2013;3:1634.

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