nanoptics - École normale supérieure · 2014. 5. 5. · the photon statistics from a typical...

NanopticsM. Kociak, LPS, Orsay

[email protected]

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Nanooptics

• Nanophotonics concerns all activities for which the nanoscale is crucial in the design, manufacturing, analysis of the optical properties of the objects of interest . Works in nanophotonics usually take part of original properties related to the location, quantification and confinement of the electromagnetic field at sub-wavelengths scales. Objects usually studied in nanophotonics are individual objects such as molecules, nanoparticles (nanowires, nanotubes) quantum dots of semiconductors and their combinations, materials structured at sub-wavelength scales (metamaterials) as the nano-antennas, photonic crystals and plasmonic structures.

• [From the RTRA website]

Size matters

Plasmon confinement:

d<<𝝺

Exciton confinement:

d<<R

Classical and quantum confinementIn particles which are smaller than the typical wavelength of light, plasmons may be confined: size/geometry and wavelength of the plasmons excitations are intimately linked

In particles which are smaller than the typical exciton radius, excitons may be confined: size/geometry and wavelength of the excitons are intimately linked

Also, excitations become resonant and are responsible for the main optical properties of the nanoparticles: the color of shape!

Plasmon confinement:

d<<𝝺

Exciton confinement:

d<<R

-1.0

0.0

1.0

-4 -2 0 2 4

-1.0

0.0

1.0

-4 -2 0 2 4

d

d+- ++ - ++ - -

Outline Sub-wavelength microscopy and spectroscopy

Metamaterials

Nanotube optical properties

Some applications of plasmons

The European Physical Journal Applied Physics

Fig. 3. (Color online) Summary of data on the analyzed particles. From left to right: S0, S1, S2, S3. From top to bottom:on-line HAADF image, relative thickness map (t/!), energy map for the low-energy LSP, intensity map for the low-energy LSP.The black line in the maps is taken from the on-line HAADF images. The white pixels in the maps indicate that the fittingprocedure was not valid; this was likely due to a poor SNR in the spectrum. A detailed description is given in the main text.

Only one main plasmon mode of energy ranging fromabout 2.0 eV to about 2.3 eV is detected in S0. The averageenergy of the plasmon resonance is 2.15 eV. In a small zoneof the particle, in a range of about 8 nm, the plasmonenergy reaches its minimum value of about 2.0 eV, thesame zone also shows the highest plasmon intensity. Bycomparing the energy and intensity maps (Fig. 3), onecan see that the regions of the particle where the energyis lower exhibit a higher intensity.

3.2 S1: quasi-star

Particle S1 has a degree of complexity greater than thatof S0. Three tips protrude from the spherical core, thelonger one lies on a thin mica substrate (visible only in therelative thickness map) whose thickness rapidly decreases.The core diameter is about 50 nm, the longer tip is about34 nm while the shorter tips measure about 20 nm.

Because of its quasi-spherical core with two short tipsand a longer one, particle S1 has been defined a “quasi-

star”. Despite its shape being still rather simple, the pres-ence of the tips gives rise to supplementary LSP modeswith respect to the case of the spheroid S0. The high-energy mode at the core of the particle lies at about 2.2 eV.Besides this mode, additional LSP resonances are detectedat each tip of the nanostar. The longer tip, that lies on athin mica substrate, has a resonance at 1.8 eV; the energyof the mode associated to the two shorter tips is instead2.1 eV. Also, the highest LSP intensity is measured at thetips, where the modes are 3 to 4 times stronger than thecore mode.

3.3 S2: multi-tipped star, first example

Particle S2 is a well-formed nanostar with five long tipsvisible in the image plane; each tip along the left-right di-rection of the HAADF image presents two supplementary“sub-tips”. Other tips might be present on the central corein the direction parallel to the electron beam. They could

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Rep. Prog. Phys. 74 (2011) 076501 I Aharonovich et al

Figure 3. The NV center. (a) Crystallographic model of the NV center in diamond, consisting of a substitutional nitrogen (shown in yellow)adjacent to a vacancy (V). (b) Room-temperature PL spectrum showing the ZPLs of the neutral (575 nm) and the negatively charged(637 nm) NV center with pronounced and wide phonon side bands at the lower energy side of each ZPL.

diamonds [44, 45] and later in nanodiamonds [32, 46, 47].They are readily fabricated using the ion implantationtechnique or synthesized during chemical vapor deposition(CVD) growth. The complex has six unpaired electrons: fivefrom the neighboring carbon and intrinsic nitrogen atom, plusan additional electron trapped at the defect site to form thenegatively charged state [48]. Figure 3(b) shows clearly itsemission spectrum with ZPL at 637 nm and a phonon sidebandextended to 800 nm [49]. The excited state lifetime of thecenter, approximately tens of nanoseconds, suggest a relativelystrong overall electronic dipole moment of about 2 !1029 C m[50], although only 4% of its emission is concentrated inthe ZPL with a Debye–Waller (DW) factor of 0.04. Thefluorescence lifetime of the NV" center is, however, foundto be dependent on the host material, in bulk diamond singleNV" centers display lifetimes around 10 ns [47, 51], whilst innanodiamonds (NDs) the lifetime is considerably longer andvariable up to #24 ns [52–54]. Due to non-radiative transitionsvia the shelving state, the quantum efficiency (QE) of thecenter, defined as the probability of emitting a photon once thesystem is prepared in the excited state, is estimated to be around0.7, based on the temperature independent measurements of theexcited state lifetime [55, 56].

Most quantum based applications utilize the fluorescenceproperties of the NV" center, but in many instances bothcharge states can be found within the same defect center[57]. Detailed time resolved experiments show that switchingfrom NV0 to NV" is photo-induced, whereas the reversephotochromic transformation from NV" to NV0 occurs underdark conditions with a time constant between 0.3 and 3.6 µs[57] and irreversible transformation can occur under intensefemtosecond illumination [58]. The mechanism which givesrise to this inter-conversion is at the present time unclear.The current hypothesis is that the excess electron forming theNV" complex can become trapped by defects (e.g. graphiticsurface damage [59]). This hypothesis may also explain theenhanced stability of NV" centers seen deep in ultra-highpurity diamond.

The photon statistics from a typical single NV" centershow significant bunching at high excitation powers consistentwith the presence of a shelving state. Therefore, the system’sdynamic results in the NV" center being modeled as a standard

Figure 4. Electronic structure of the negatively charged NV center.The boxes depict the fine structure of the electronic states fordifferent temperature and strain regimes. The red and blue solidarrows indicate allowed optical and magnetic transitionsrespectively. The dashed black arrows indicate the sequence ofnon-radiative transitions that are believed to be responsible for theoptical spin-polarization of the ground-state triplet. Schematic iscourtesy of M Doherty.

three-level system [47]. In general, the count rates from singleNV" centers in bulk and nanocrystal diamond are #40 ! 103

[46, 60] and 200 ! 103 [61] counts s"1, respectively, withtypical collection efficiencies between 1 and 2% reported formost imaging systems. Several techniques have been proposedto increase the collection efficiency from single NV" centersand are discussed in detail later in this review.

Since the NV" center has an even number of electronsand C3! symmetry, group theory states that the many-electronconfiguration forms spin triplet states (3A2 and 3E), and spinsinglet states (1E and 1A1) [62]. The ordering of the tripletground and excited states is now well established; however, theenergetic ordering of the ‘dark’ singlet states is still contentiousand the currently accepted electronic structure is depicted infigure 4.

5

Nanosources of light


Metamaterials




Working at the relevant size

‣Optical signal down to the nanometer‣Structure down to the atomic size‣Spectral resolution down to the meV‣On the same object

λ0/2

100 nm

λsp/2

100 nm

λsp/2

1 nm

Roussow et al. Nanoletters (2011)Boudarham et al. PRL (2010)Mazzucco et al. EPJAP (2011)

Zagonel et al. Nanoletters (2011)

Sherry et al. Nanoletters 2060 (2006)‣Can we measure optical phenomena at the nanometer scale?

Nanometer scale measurements of optical properties

10 µm 500 nm

Diffraction limited techniques

confocalUV-NIR spectroscopy

Sub-diffraction techniques

0.5 nm

Fast Electrons based

spectroscopy

e-

10 nm

Scanning Probe (Near Field) microscopy

The Optical properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric EnvironmentK.L. Kelly, E. Coronado, L.L. Zhao and G.C. SchatzJ. Phys. Chem. B 2003, 107, 668-677

Scanning Near Field Optical Microscopy

H. Okamoto and K. Imura, J. Mater. Chem. 16, 3920 (2006).

Mapping plasmons waves

Nanoantennas

H. Okamoto and K. Imura, J. Mater. Chem. 16, 3920 (2006).

‣... with a sub-nm resolution

... in a (S)TEM

Tungsten cold FEG operated at 100 KeV Initial energy resolution : 0.3 – 0.4 eV Spatial resolution : 0.5 nm (probe size)‏

Magnetic lens

Electron source

Deflecting coils

Sample

Brigth fielddetector

HAADF ‏

Magnetic prism

EELS

J. Nelayah, M. Kociak, O. Stéphan, FJ Garcia de Abajo et al. Nature Physics 3, 348 (2007)

‣Surface plasmons mapping?

Nanometer scale mapping of optical properties of silver nanoprisms proper

A BC D

Energy map of the „tip“ mode


Metamaterials




A stereotype: the Split Ring Resonator

Metamaterials and artificial atoms

+-

H

E

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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C. Soukoulis, Phys. Rev. Lett. 95, (2005).

of the SRR around 950 nm wavelength. As this resonancewill become important below as well, we briefly recapitu-late its physics. Here the electric field of the light leads to acharge accumulation at the surfaces of the vertical SRRarms, resulting in a depolarization field. Depending on thepermittivity of the metal, hence depending on the fre-quency of light, this depolarization field can enhance orsuppress the external electric field. (We also observe aweaker short-wavelength Mie resonance around 600 nmin Fig. 1, which is due to the depolarization field of theshort axis, i.e., the width of the SRR arms.) Notably, thefundamental Mie resonance of our SRR changes in spectralposition and width between the two different polarizationconfigurations. This can be understood as follows: For

horizontal incident polarization and for the frequencies ofinterest here, only the fundamental Mie resonance of theSRR bottom arm is excited. For vertical polarization, thetwo similarly shaped vertical SRR arms contribute. Thelatter are coupled via the SRR’s bottom arm (and via theradiation field). As usual, the coupling of two degeneratemodes leads to an avoided crossing with two new effectiveoscillation modes, a symmetric and an antisymmetric one,which are frequency down-shifted and up-shifted as com-pared to the uncoupled resonances, respectively. The anti-symmetric mode cannot be excited at all for normalincidence as it has zero effective electric-dipole moment.The redshifted symmetric mode can be excited. It even hasa larger effective electric-dipole moment than a single arm.

The optical response of SRR is not only polarization-dependent but also highly anisotropic. Thus, we haveperformed transmission experiments under oblique inci-dence (Fig. 2) using a dedicated homebuilt setup [12].Compared with the Fourier-transform microscope spec-trometer used above, this setup has improved polarizationoptics by using Glan-Thomson polarizers and a smaller

FIG. 1 (color). Electron micrograph of a split ring array with atotal size of !100 !m"2. The lower right-hand side inset showsthe dimensions of an individual split ring. The correspondingmeasured normal-incidence transmission and reflection spectrafor horizontal and vertical polarization are shown in (b) and (c),respectively. For (b), one can couple to the fundamental mag-netic mode at 1:5 !m wavelength via the electric-field compo-nent of the incident light; for (c), one cannot.

FIG. 2 (color). Measured transmission spectra taken foroblique incidence for the configurations shown as insets (where" # 60$). In (a), coupling to the fundamental magnetic mode at1:5 !m wavelength is only possible via the magnetic-fieldcomponent of the incident light; for (b), both electric andmagnetic field can couple. Note the small but significant featurein (a) for 60$ around 1:5 !m wavelength. The lower gray area in(a) is the transmission into the linear polarization orthogonal tothe incident one for " # 60$. We argue that this observable canbe viewed as a fingerprint of magnetic resonances under theseconditions.

PRL 95, 203901 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending11 NOVEMBER 2005

203901-2


Metamaterials



The European Physical Journal Applied Physics

Fig. 3. (Color online) Summary of data on the analyzed particles. From left to right: S0, S1, S2, S3. From top to bottom:on-line HAADF image, relative thickness map (t/!), energy map for the low-energy LSP, intensity map for the low-energy LSP.The black line in the maps is taken from the on-line HAADF images. The white pixels in the maps indicate that the fittingprocedure was not valid; this was likely due to a poor SNR in the spectrum. A detailed description is given in the main text.

Only one main plasmon mode of energy ranging fromabout 2.0 eV to about 2.3 eV is detected in S0. The averageenergy of the plasmon resonance is 2.15 eV. In a small zoneof the particle, in a range of about 8 nm, the plasmonenergy reaches its minimum value of about 2.0 eV, thesame zone also shows the highest plasmon intensity. Bycomparing the energy and intensity maps (Fig. 3), onecan see that the regions of the particle where the energyis lower exhibit a higher intensity.

3.2 S1: quasi-star

Particle S1 has a degree of complexity greater than thatof S0. Three tips protrude from the spherical core, thelonger one lies on a thin mica substrate (visible only in therelative thickness map) whose thickness rapidly decreases.The core diameter is about 50 nm, the longer tip is about34 nm while the shorter tips measure about 20 nm.

Because of its quasi-spherical core with two short tipsand a longer one, particle S1 has been defined a “quasi-

star”. Despite its shape being still rather simple, the pres-ence of the tips gives rise to supplementary LSP modeswith respect to the case of the spheroid S0. The high-energy mode at the core of the particle lies at about 2.2 eV.Besides this mode, additional LSP resonances are detectedat each tip of the nanostar. The longer tip, that lies on athin mica substrate, has a resonance at 1.8 eV; the energyof the mode associated to the two shorter tips is instead2.1 eV. Also, the highest LSP intensity is measured at thetips, where the modes are 3 to 4 times stronger than thecore mode.

3.3 S2: multi-tipped star, first example

Particle S2 is a well-formed nanostar with five long tipsvisible in the image plane; each tip along the left-right di-rection of the HAADF image presents two supplementary“sub-tips”. Other tips might be present on the central corein the direction parallel to the electron beam. They could

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Bio sensors

Homola, Ph.D. Thesis Prague 2008

Selective Prostate Cancer Thermal Ablation With Laser Activated Gold Nanoshells

The Journal of Urology, Volume 179, Issue 2, February 2008, Pages 748-753

110 nm SiO2 spheres covered with a10 nm gold shell

IR 810 nm Laser200 μm optical fiber

4 W/cm2 3 minutes

Skin temperature at treated site : 65.4 C

21 days

SiO2

Au

Prostate cancer cells

Photothérapie

Surface enhanced Raman


Metamaterials




•Ballistic conductors•Two conduction channels•Conductance quantification

Electronic TransportStructure

1D - Density of States

G = 2 G0

R = 6.5 kOhm

• Van Hove singularities•Constant density of states near the Fermi level•Weak screening

Optical Properties

• Sharp transitions• Strong excitons

Carbon Nanotubes in a Nutshell

Semi-conductor(2/3 of the tubes)

(n - m) no multiple of 3

kx a0

∼0.5eV

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-1

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kx a0

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Optical properties of Nanotubes arise from excitons

orbit coupling in SWNTs, all optically activeexcitons are singlet states, with the allowedtransitions being governed by electric-dipoleselection rules. For the dominant transitionspolarized along the nanotube axis, one-photon(linear) excitation requires the final and initialstates to exhibit opposite symmetry. In con-trast, a two-photon transition is allowed onlywhen the final state has the same parity asthe initial state. Given the symmetry of theunderlying atomic-scale wave functions, one-photon excitation produces only excitons ofs-symmetry, whereas two-photon excitationleads only to excitons of p-symmetry (28).Thus, one-photon transitions access the low-est lying 1s exciton; two-photon transitionsaccess only the excited states of the exciton.

An experimental method to determine theenergies of the ground and excited excitonstates follows immediately from these sym-metry arguments: We measured the energiesneeded for one-photon and two-photon transi-tions in semiconducting nanotubes (Fig. 1A).A comparison of these energies yields theenergy difference between the ground andexcited exciton states and thereby directly in-dicates the exciton binding strength. Whenthe excitonic interactions were negligible, wereverted to a simple band picture in which theonset of two-photon absorption coincides withthe energy of one-photon absorption (Fig. 1B).The two-photon excitation spectra reflect thequalitative difference between these twopictures in an unambiguous fashion. In con-trast, conventional linear optical measurements,such as absorption and fluorescence spectros-copy, access only one-photon transitions, forwhich a van Hove singularity and a broadenedexcitonic resonance exhibit qualitatively similarfeatures. Because the one-photon absorptionand emission arise from the same electronictransition in SWNTs, there is no Stokes shiftbetween the two, as apparent in comparison ofabsorption and fluorescence spectra (8).

In our experiment, we used isolated SWNTsin a poly(maleic acid/octyl vinyl ether)(PMAOVE) matrix. SWNTs grown by high-pressure CO synthesis were dispersed in anaqueous solution of PMAOVE by a sonica-tion method (29). In order to minimize infra-red absorption of water, we formed a film ofSWNTs imbedded in polymer matrix by slow-ly drying a drop of the solution. The SWNTsamples obtained by this procedure showedfluorescence emission comparable to that ofthe SWNTs in aqueous solution.

Two-photon excitation is a nonlinear opticaleffect that requires the simultaneous absorptionof a pair of photons. Femtosecond laser pulsesprovided the high intensities of light necessaryto drive this process. The light source, acommercial optical parametrical amplifier(Spectra Physics OPA-800C), pumped by anamplified mode-locked Ti:sapphire laser,produced infrared pulses of 130-fs duration at

a 1-kHz repetition rate. Peak powers exceeding108 W were obtained over a photon energyrange from 0.6 to 1.0 eV. Because these pho-ton energies were well below the 1-photonabsorption threshold (91.2 eV) of the relevantSWNTs, no linear excitation occurred. A laserfluence of 5 J/m2 was typically chosen for themeasurements. At this fluence, we explicitlyverified the expected quadratic dependence ofthe excitation process on laser intensity.

To detect the two-photon excitation processin the SWNTs, we did not directly measure thedepletion of the pump beam. Rather, we usedthe more sensitive approach of monitoring theinduced light emission. The scheme can thusbe described as two-photon–induced fluores-cence excitation spectroscopy. Prior studieshave shown that rapid excited-state relaxa-tion processes in SWNTs (20) lead to fluores-cence emission exclusively from the 1s-excitonstate. Measurement of the two-photon–inducedfluorescence thus yielded (Fig. 1A) both two-photon absorption spectra (from the fluo-rescence strength as a function of the laserexcitation wavelength) and the one-photon1s-exciton spectra (from the fluorescence emis-sion wavelength). Further, because the fluores-cence peaks reflect the physical structure ofthe emitting nanotubes, we obtained structure-specific excitation spectroscopy even whenprobing an ensemble sample. We detected thefluorescence emission in a backscattering geom-etry, using a spectrometer with 8-nm spectralresolution and a 2D array charge-coupled de-

vice (CCD) detector. Our data sampled the in-frared excitation range in 10-meV steps.

Themeasured two-photon excitation spectra(Fig. 2) show the strength of fluorescence emis-sion as a function of both the (two-photon) ex-citation energy and the (one-photon) emissionenergy. From the 2D contour plot, distinct fluo-rescence emission features emerge at emissionenergies of 1.21, 1.26, 1.30, and 1.36 eV (Fig. 2,circles). These emission peaks have been as-signed, respectively, to SWNTs with chiral in-dices of (7,5), (6,5), (8,3), and (9,1) (7). It isapparent that none of the nanotubes were excit-ed when the two-photon excitation energy wasthe same as the emission energy (Fig. 2, solidline). Only when the excitation energy was sub-stantially greater than the emission energy didtwo-photon absorption occur. This behavior is asignature of the presence of excitons with sig-nificant binding energy and is incompatible witha simple band picture of the optical transitions.

The two-photon excitation spectra for nano-tubes of given chiral index can be obtained as ahorizontal cut in the contour plot of Fig. 2,taken at an energy corresponding to 1s-excitonemission of the relevant SWNT. To enhancethe quality of the data, we applied a fittingprocedure (30) to eliminate background con-tributions from the emission of other nanotubespecies. The resulting two-photon excitationspectra are shown for the (7,5), (6,5), and (8,3)SWNTs in Fig. 3. For each of the SWNTstructures, the energy of the 1s fluorescenceemission is indicated by an arrow.

Fig. 2. Contour plot of two-photon ex-citation spectra of SWNTs. The mea-sured fluorescence intensity is shownin a false-color representation as afunction of the (two-photon) excita-tion energy and the (one-photon) fluo-rescence emission energy. Fluorescencepeaks of different SWNT species [(7,5),(6,5), (8,3), and (9,1) with increasingemission energy] can be identified (blackcircles). The two-photon excitation peaksare shifted substantially above the en-ergy of the corresponding emission fea-ture, as is apparent by comparison withthe solid line describing equal excitationand emission energies. The large shiftarises from the excitonic nature of SWNToptical transitions.

Fig. 1. Schematic representation of thedensity of states for a SWNT, showingthe two-photon excitation (blue arrows)with photon energy hn and subsequentfluorescence emission (red arrows) in theexciton and band pictures. (A) In the ex-citon picture, the 1s exciton state is for-bidden under two-photon excitation. The2p exciton and continuum states are ex-cited. They relax to the 1s exciton stateand fluoresce through a one-photon pro-cess. (B) In the band picture, the thresh-old for two-photon excitation lies at theband edge, where the relaxed fluores-cence emission also takes place.

R E P O R T S

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The peaks in the two-photon excitationspectra can be assigned to the energy forcreation of the 2p exciton, the lowest lyingsymmetry-allowed state for the nonlinear exci-tation process. From a comparison of this ener-gy with that of the 1s-exciton emission feature,we obtained directly the relevant energy differ-ences for the ground and excited exciton states:E2p – E1s 0 280, 310, and 300 meV, respec-tively, for the (7,5), (6,5), and (8,3) SWNTs.

To determine the exciton binding energyand understand the nature of the two-photonspectra more fully, we considered the two-photon excitation process in greater detail. Inaddition to two-photon transitions to the 2pstate, higher lying bound excitons are alsoaccessible (such as 3p and 4p). The strength ofthese transitions was relatively small, and theydo not account for the main features of thespectrum. We also, however, have transitionsto the continuum or unbound exciton states.Including the influence of electron-hole inter-actions on the continuum transitions, we foundthat the expected shape of this contributionto the two-photon excitation spectrum couldbe approximated by a step function near theband edge (31). The experimental two-photonexcitation spectra can be fit quite satisfacto-rily to the sum of a Lorentzian 2p excitonresonance and the continuum transitions witha broadened onset.

A more quantitative description of the two-photon excitation spectra can be achieved witha specific model of the effective electron-holeinteraction within a SWNT. In the model, weconsider a truncated 1D Coulomb interactiongiven by the potential V(z) 0 –e2/Ee(|z| ! z0)^for electron-hole separation z. The value ofz0 0 0.30d is fixed to approximate the Coulombinteraction between two charges distributed asrings at a separation z on a cylindrical sur-face of diameter d (27); the effective dielectricscreening e is the only adjustable parameterin the analysis. This simple model provides agood fit to the experimental data for thedifferent nanotube species examined whenwe use an effective dielectric constant of 2.5(Fig. 3, solid line). The features predicted inthe model have been broadened by 80 meV(full width at half maximum). This broaden-ing is in part experimental, reflecting the spec-tral width of the short laser excitation pulses(30 meV). The main contribution, however,is the width of the excitonic transition itself.This width is ascribed to lifetime broadeningassociated with the rapid relaxation of the ex-cited states to the 1s exciton state (20). Fromthis analysis, we determined the energy of 2pfor the three SWNT species in Fig. 3 to beE2p , –120 meV with respect to the onset of thecontinuum states at the band gap energy Eg.

Combining the previously determined E2p –E1s energy difference with the position of the2p exciton relative to the continuum, weobtained an overall binding energy for theground-state (1s) exciton of Eex 0 (Eg – E1s) ,420 meV for the investigated SWNTs. Thisvalue is comparable to recent theoreticalpredictions of large exciton binding energies(13, 14). The exciton binding energy thus con-stitutes a substantial fraction of the gap energyEg , 1.3 eV for our 0.8-nm SWNTs. To putthis result in context, the exciton binding en-ergies in bulk semiconductors typically lie inthe range of several meV and represent a slightcorrection to the band gap. Furthermore, be-cause thermal energies at room temperatureexceed typical bulk exciton binding energies,excitonic effects in bulk materials can be large-ly neglected under ambient conditions. This sit-uation clearly does not prevail for SWNTs.

We can understand the strong increase inexcitonic effects in the SWNTs as the conse-quence of two factors. The first arises from ageneral property of reduced dimensionality: Inthree dimensions, the probability of having an

electron and hole separated by a displacementof r includes a phase space factor of r2, favor-ing larger separations over smaller ones. In onedimension, no such factor exists. Short separa-tions are thus of greater relative importance, andthe role of the Coulomb interactions is enhanc-ed. The second factor relates to the decreaseddielectric screening for a quasi-1D SWNT sys-tem. This effect arises because the electric fieldlines generated by the separated electron-holepair travel largely outside of the nanotube, wheredielectric screening is decreased. Because theseeffects are general features arsing from the 1Dcharacter, they should be widely present in 1Dsystems. Indeed, similar excitonic effects havebeen extensively studied in a large family of1D structures of conjugated polymers (24).

To help visualize the strongly bound ex-citons in SWNTs, we estimated the exciton_sspatial extent, i.e., the typical separation be-tween the electron and the hole in the corre-lated exciton state. Assuming an exciton kineticenergy comparable to its binding energy Eex,which applies precisely for 3D excitons, weobtain the relation Eex È I2/2mR2, where Iis Planck_s constant h divided by 2p, m isthe reduced electron-hole mass, and R is theexciton radius. For m 0 0.05 m0 (21), we de-duced from our experimental binding energya ground-state exciton radius of R 0 1.2 nm.This value is similar to that obtained by cal-culation within the truncated Coulomb modelspecified above. Figure 4 provides a represen-tation of the calculated density distribution ofthe exciton envelope wave function. The re-sult is a highly localized entity, with a spatialextent along the nanotube axis only slightlyexceeding the nanotube radius of 0.8 nm.

The importance of excitonic effects is clearfor the interpretation and assignment of the ob-served optical spectra, as discussed in the litera-ture on the relation of the E11 and E22 transitionenergies in SWNTs (7, 15, 17). The excitoniccharacter of the optically excited state alsohas immediate implications for optoelectronicdevices and phenomena. For example, photo-conductivity in SWNTs should have a strongdependence on the applied electric field, be-cause charge transport requires spatial sepa-ration of the electron-hole pair. The excitoniccharacter of optically excited SWNTs alsoraises the possibility of modifying the SWNTtransitions through external perturbations, thusfacilitating new electro-optical modulators andsensors. More broadly, the strong electron-holeinteraction demonstrated in our study high-lights the central role of many-body effects in1D materials.

References and Notes1. M. Bockrath et al., Science 275, 1922 (1997).2. S. J. Tans et al., Nature 386, 474 (1997).3. T. W. Odom, J. L. Huang, C. L. Cheung, C. M. Lieber,

Science 290, 1549 (2000).4. J. Nygard, D. H. Cobden, P. E. Lindelof, Nature 408,

342 (2000).5. M. Bockrath et al., Nature 397, 598 (1999).

Fig. 3. Two-photon excitation spectra of (7,5),(6,5), and (8,3) SWNTs. The traces, offset forclarity, show onset energies for two-photontransitions that are appreciably higher than thecorresponding fluorescence peaks (indicated bythe arrows). The solid lines are the fits to theexcitation spectrum obtained from our excitonmodel. For comparison, we show the single-particle band model prediction for an (8,3) nano-tube as the dashed line in the lower trace.

Fig. 4. Density of the 1s-exciton en-velope wave function for a (6,5) SWNT.The wave function has been calculatedusing the experimentally determinedexciton binding energy and the truncatedCoulomb electron-hole interaction. Thedensity represents the probability offinding the electron and hole composingthe exciton at the indicated relative separation. The half width of the exciton along the nanotubeis R 0 1.2 nm, compared to the 0.8-nm diameter of the nanotube.

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orbit coupling in SWNTs, all optically activeexcitons are singlet states, with the allowedtransitions being governed by electric-dipoleselection rules. For the dominant transitionspolarized along the nanotube axis, one-photon(linear) excitation requires the final and initialstates to exhibit opposite symmetry. In con-trast, a two-photon transition is allowed onlywhen the final state has the same parity asthe initial state. Given the symmetry of theunderlying atomic-scale wave functions, one-photon excitation produces only excitons ofs-symmetry, whereas two-photon excitationleads only to excitons of p-symmetry (28).Thus, one-photon transitions access the low-est lying 1s exciton; two-photon transitionsaccess only the excited states of the exciton.

An experimental method to determine theenergies of the ground and excited excitonstates follows immediately from these sym-metry arguments: We measured the energiesneeded for one-photon and two-photon transi-tions in semiconducting nanotubes (Fig. 1A).A comparison of these energies yields theenergy difference between the ground andexcited exciton states and thereby directly in-dicates the exciton binding strength. Whenthe excitonic interactions were negligible, wereverted to a simple band picture in which theonset of two-photon absorption coincides withthe energy of one-photon absorption (Fig. 1B).The two-photon excitation spectra reflect thequalitative difference between these twopictures in an unambiguous fashion. In con-trast, conventional linear optical measurements,such as absorption and fluorescence spectros-copy, access only one-photon transitions, forwhich a van Hove singularity and a broadenedexcitonic resonance exhibit qualitatively similarfeatures. Because the one-photon absorptionand emission arise from the same electronictransition in SWNTs, there is no Stokes shiftbetween the two, as apparent in comparison ofabsorption and fluorescence spectra (8).

In our experiment, we used isolated SWNTsin a poly(maleic acid/octyl vinyl ether)(PMAOVE) matrix. SWNTs grown by high-pressure CO synthesis were dispersed in anaqueous solution of PMAOVE by a sonica-tion method (29). In order to minimize infra-red absorption of water, we formed a film ofSWNTs imbedded in polymer matrix by slow-ly drying a drop of the solution. The SWNTsamples obtained by this procedure showedfluorescence emission comparable to that ofthe SWNTs in aqueous solution.

Two-photon excitation is a nonlinear opticaleffect that requires the simultaneous absorptionof a pair of photons. Femtosecond laser pulsesprovided the high intensities of light necessaryto drive this process. The light source, acommercial optical parametrical amplifier(Spectra Physics OPA-800C), pumped by anamplified mode-locked Ti:sapphire laser,produced infrared pulses of 130-fs duration at

a 1-kHz repetition rate. Peak powers exceeding108 W were obtained over a photon energyrange from 0.6 to 1.0 eV. Because these pho-ton energies were well below the 1-photonabsorption threshold (91.2 eV) of the relevantSWNTs, no linear excitation occurred. A laserfluence of 5 J/m2 was typically chosen for themeasurements. At this fluence, we explicitlyverified the expected quadratic dependence ofthe excitation process on laser intensity.

To detect the two-photon excitation processin the SWNTs, we did not directly measure thedepletion of the pump beam. Rather, we usedthe more sensitive approach of monitoring theinduced light emission. The scheme can thusbe described as two-photon–induced fluores-cence excitation spectroscopy. Prior studieshave shown that rapid excited-state relaxa-tion processes in SWNTs (20) lead to fluores-cence emission exclusively from the 1s-excitonstate. Measurement of the two-photon–inducedfluorescence thus yielded (Fig. 1A) both two-photon absorption spectra (from the fluo-rescence strength as a function of the laserexcitation wavelength) and the one-photon1s-exciton spectra (from the fluorescence emis-sion wavelength). Further, because the fluores-cence peaks reflect the physical structure ofthe emitting nanotubes, we obtained structure-specific excitation spectroscopy even whenprobing an ensemble sample. We detected thefluorescence emission in a backscattering geom-etry, using a spectrometer with 8-nm spectralresolution and a 2D array charge-coupled de-

vice (CCD) detector. Our data sampled the in-frared excitation range in 10-meV steps.

Themeasured two-photon excitation spectra(Fig. 2) show the strength of fluorescence emis-sion as a function of both the (two-photon) ex-citation energy and the (one-photon) emissionenergy. From the 2D contour plot, distinct fluo-rescence emission features emerge at emissionenergies of 1.21, 1.26, 1.30, and 1.36 eV (Fig. 2,circles). These emission peaks have been as-signed, respectively, to SWNTs with chiral in-dices of (7,5), (6,5), (8,3), and (9,1) (7). It isapparent that none of the nanotubes were excit-ed when the two-photon excitation energy wasthe same as the emission energy (Fig. 2, solidline). Only when the excitation energy was sub-stantially greater than the emission energy didtwo-photon absorption occur. This behavior is asignature of the presence of excitons with sig-nificant binding energy and is incompatible witha simple band picture of the optical transitions.

The two-photon excitation spectra for nano-tubes of given chiral index can be obtained as ahorizontal cut in the contour plot of Fig. 2,taken at an energy corresponding to 1s-excitonemission of the relevant SWNT. To enhancethe quality of the data, we applied a fittingprocedure (30) to eliminate background con-tributions from the emission of other nanotubespecies. The resulting two-photon excitationspectra are shown for the (7,5), (6,5), and (8,3)SWNTs in Fig. 3. For each of the SWNTstructures, the energy of the 1s fluorescenceemission is indicated by an arrow.

Fig. 2. Contour plot of two-photon ex-citation spectra of SWNTs. The mea-sured fluorescence intensity is shownin a false-color representation as afunction of the (two-photon) excita-tion energy and the (one-photon) fluo-rescence emission energy. Fluorescencepeaks of different SWNT species [(7,5),(6,5), (8,3), and (9,1) with increasingemission energy] can be identified (blackcircles). The two-photon excitation peaksare shifted substantially above the en-ergy of the corresponding emission fea-ture, as is apparent by comparison withthe solid line describing equal excitationand emission energies. The large shiftarises from the excitonic nature of SWNToptical transitions.

Fig. 1. Schematic representation of thedensity of states for a SWNT, showingthe two-photon excitation (blue arrows)with photon energy hn and subsequentfluorescence emission (red arrows) in theexciton and band pictures. (A) In the ex-citon picture, the 1s exciton state is for-bidden under two-photon excitation. The2p exciton and continuum states are ex-cited. They relax to the 1s exciton stateand fluoresce through a one-photon pro-cess. (B) In the band picture, the thresh-old for two-photon excitation lies at theband edge, where the relaxed fluores-cence emission also takes place.

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F. Wang, Science 308, 838 (2005).


Metamaterials



Rep. Prog. Phys. 74 (2011) 076501 I Aharonovich et al









5


Single photon emittersRep. Prog. Phys. 74 (2011) 076501 I Aharonovich et al









5

QD CdSe/CdS

Bunching and antibunching from single NV color centers in diamond 3

A CW frequency doubled Nd:YAG laser (! = 532nm) is focused onthe sample by a high numerical aperture (1.3) immersion objective. APZT-mounted mirror allows a x-y scan of the sample, and a fine z-scanis obtained using another PZT.

The sample is a 0.1!1.5!1.5mm3[110] crystal of synthetic Ib diamondfrom Drukker International. The Nitrogen-Vacancy centers consist in asubstitutional nitrogen with an adjacent vacancy, and are found with adensity of about 1 µm!3 in Ib diamond. The centers can be seen with asignal to background ratio of about 5 by scanning the sample as shownin figure 1, and a computer-controlled servo-loop allows to focus on onecenter for hours.

The fluorescence is collected by the same objective, and separatedfrom excitation light by a dichroic mirror. High rejection (1010) high-pass filters remove any leftover pump light. Spatial filtering is achievedby focusing on a 50µm pinhole. The fluorescence is then analyzed byan ordinary Hanbury-Brown and Twiss set-up. The time delay betweenthe two photons is converted by a time-to-amplitude converter (TAC)into a voltage which is digitalized by a computer board.

1.2

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Figure 2 Experimental data of g(2)(!) for di!erent values from 0.3 to 31 mW ofpumping power. The solid line represents the fit. The dashed (resp. thin) lines arecalculations of g(2)(!) for k23 and k32 (see figure 3 for definition) not depending (resp.depending) on pump power. Details are given in the text of section 2.

Applications ranging from bioimaging to quantum

cryptography A. Beveratos et al. Quantum Communication,

Computing, and Measurement 3 (Kluwer Academic Publishers, Boston, 2002), pp. 261–267.

B. Mahler et al. Nat Mater 7, 659 (2008).

NV centres in diamond

Manipulating nanoscale emission properties

Figure 2a shows the micro-photoluminescence (mPL) spectra of aphotonic nanowire S4P in the 911–919 nm wavelength range. Themeasurements were performed at 5 K, under non-resonant, pulsedoptical pumping (see Methods). The spectra exhibit an excitonicline (X) that peaks at 915.2 nm and a bi-excitonic line (XX)peaking at 914.1 nm. Figure 2b shows that their respective integratedintensities IX and IXX are approximately equal above saturation. Thisis expected for a single QD with a nearly perfect radiative yieldembedded in a source having a broadband collection efficiency. Inaddition, the nature of these two transitions is unambiguouslyconfirmed by the comparison of these data with the solid curves,calculated from the standard assumption that the probability ofcreating n excitons in a QD is Poissonian.

The photon statistics of the source were investigated throughmeasurement of the autocorrelation function g(2)(t)! kI(t)I(t" t)l/kI(t)l2 under pulsed optical excitation. Above saturation,which corresponds to the maximal source efficiency, the X line exhi-bits the signature of very pure single-photon emission, withg(2)(0) , 0.008 (Fig. 2c). In this regard, photonic nanowires havea key advantage over QD–cavity S4P, which systematically exhibita much larger g(2)(0) at saturation11,15,27. In a cavity, detunedtransitions of the same QD (for example, the XX one) can feedthe cavity mode through various mechanisms (dephasing28,coupling to a continuum of states29), which lead to the emissionof undesirable multiphoton pulses under non-resonantoptical pumping.

The source efficiency e is determined from comparison to asource emitting a known photon flux. To validate the calibrationprocedure detailed in the Methods, we first investigated a referenceS4P, a single InAs QD buried 120 nm under the surface of anunprocessed GaAs sample. With such a simple structure, e is calcu-lated for varying numerical aperture (NA) collection, usingan eigenmode expansion technique (solid line in Fig. 3b). At theX saturation, the efficiencies measured with two microscope objec-tives having NA! 0.4 and 0.75 are respectively (4.5+0.8)! 1023

and (1.2+0.19)! 1022, in close agreement with theoreticalpredictions (Fig. 3b).

The same measurements on the X line of the photonic nanowiresource with a 0.4 NA first lens lead to e ! 0.35+0.05 (Fig. 3a), veryclose to state-of-the-art microcavity-based S4Ps (0.44 (ref. 15) and0.38 (ref. 11)). However, unlike these microcavities, the far-fieldemission pattern of our photonic nanowires is not fully interceptedby a 0.4 NA collecting cone. Increasing further the collection NA to0.75 leads to e ! 0.72+0.09, which corresponds to a 55 MHzsingle-photon flux into the first lens and represents an improvement

by a factor of 1.6 compared to microcavity S4Ps. In addition, wemeasured several devices with e . 0.6 and reproducibly obtainede . 0.5 on a number of photonic nanowires with diametersranging from 200 to 260 nm.

The simple Fabry–Perot model developed in ref. 13 provides ananalytical expression of e given by

e"u# $ 12b"1% jrmj#

2

1% bjrmj#Ta"sin u# "1#

where Ta(sin u) is the taper transmission into free space within acone of opening angle 2u. The X decay rate extracted from autocor-relation measurements, equal to 0.42 ns21, is smaller that the 1 ns21

expected value for an ideal structure. This is likely due to an actualwire diameter d! 0.9dopt, which leads to a deconfinement of HE11.Fortunately, thanks to the strong inhibition of the SE in the otherelectromagnetic modes, b is robust against imperfections of thiskind, and remains about 0.9. In fact, the source efficiency ismainly limited by the upper taper geometry. Our data are welldescribed by a tapering angle a! 58 (solid line in Fig. 3a),leading to T58(0.75)! 0.77. Further fabrication improvement todecrease a may bring the efficiency closer to its theoretical limit,&0.95 for a taper having unity transmission13.

Together with a spectacular increase of e , replacing a high-Qcavity design by a monomode waveguide approach comes withanother crucial advantage: photonic nanowires offer an intrinsicallybroadband SE control, applicable to non-monochromatic emitters(colour centres in diamond, QDs operated at higher temperatures).Furthermore, the operating wavelength of the source can be tuned

!/2

!/2

rm

HE11

"

a2#

200 nm

2.5 µm

b

Au

SiO2

Figure 1 | Single-photon source geometry. a, An InAs QD (red triangle) isembedded in a GaAs photonic nanowire. The far-field emission collectionis optimized with an integrated modal mirror (gold and SiO2 spacer) and asmooth tapering of the wire tip (opening angle, a). b, Scanning electronmicroscopy image of a typical device.

10

XXX

XXX

Spectrally integrated counts (Hz)

103

104

105

Excitation power (µW)

3.62 µW0

APD

cou

nts (

104 H

z)

123456789

10a b

1.64 µW

570 nW

62 nW

10.10.01918916$ (nm)

914912

70

c

605040302010!10!20 00.0

0.1

Corre

latio

n co

unts

(Hz)

0.2

0.3

0.4

Delay (ns)

Figure 2 | Single-photon emission by a single QD in a photonic nanowire.a, mPL spectra of the photonic nanowire measured at 5 K for increasingvalues of the optical pump power P. b, Integrated counts of X and XX versusP and fits to the theory (solid lines). Below the saturation pump powerP0! 1.05 mW, they respectively exhibit linear and quadratic dependenceon P. c, Autocorrelation trace of the X transition (red) well above saturation(P/P0' 4), measured over a 0.5-nm spectral range (rectangle window in a).The fit to theory (black) demonstrates g(2)(0) , 0.008.

NATURE PHOTONICS DOI: 10.1038/NPHOTON.2009.287 LETTERS

NATURE PHOTONICS | VOL 4 | MARCH 2010 | www.nature.com/naturephotonics 175

Figure 2a shows the micro-photoluminescence (mPL) spectra of aphotonic nanowire S4P in the 911–919 nm wavelength range. Themeasurements were performed at 5 K, under non-resonant, pulsedoptical pumping (see Methods). The spectra exhibit an excitonicline (X) that peaks at 915.2 nm and a bi-excitonic line (XX)peaking at 914.1 nm. Figure 2b shows that their respective integratedintensities IX and IXX are approximately equal above saturation. Thisis expected for a single QD with a nearly perfect radiative yieldembedded in a source having a broadband collection efficiency. Inaddition, the nature of these two transitions is unambiguouslyconfirmed by the comparison of these data with the solid curves,calculated from the standard assumption that the probability ofcreating n excitons in a QD is Poissonian.

The photon statistics of the source were investigated throughmeasurement of the autocorrelation function g(2)(t)! kI(t)I(t" t)l/kI(t)l2 under pulsed optical excitation. Above saturation,which corresponds to the maximal source efficiency, the X line exhi-bits the signature of very pure single-photon emission, withg(2)(0) , 0.008 (Fig. 2c). In this regard, photonic nanowires havea key advantage over QD–cavity S4P, which systematically exhibita much larger g(2)(0) at saturation11,15,27. In a cavity, detunedtransitions of the same QD (for example, the XX one) can feedthe cavity mode through various mechanisms (dephasing28,coupling to a continuum of states29), which lead to the emissionof undesirable multiphoton pulses under non-resonantoptical pumping.

The source efficiency e is determined from comparison to asource emitting a known photon flux. To validate the calibrationprocedure detailed in the Methods, we first investigated a referenceS4P, a single InAs QD buried 120 nm under the surface of anunprocessed GaAs sample. With such a simple structure, e is calcu-lated for varying numerical aperture (NA) collection, usingan eigenmode expansion technique (solid line in Fig. 3b). At theX saturation, the efficiencies measured with two microscope objec-tives having NA! 0.4 and 0.75 are respectively (4.5+0.8)! 1023

and (1.2+0.19)! 1022, in close agreement with theoreticalpredictions (Fig. 3b).

The same measurements on the X line of the photonic nanowiresource with a 0.4 NA first lens lead to e ! 0.35+0.05 (Fig. 3a), veryclose to state-of-the-art microcavity-based S4Ps (0.44 (ref. 15) and0.38 (ref. 11)). However, unlike these microcavities, the far-fieldemission pattern of our photonic nanowires is not fully interceptedby a 0.4 NA collecting cone. Increasing further the collection NA to0.75 leads to e ! 0.72+0.09, which corresponds to a 55 MHzsingle-photon flux into the first lens and represents an improvement

by a factor of 1.6 compared to microcavity S4Ps. In addition, wemeasured several devices with e . 0.6 and reproducibly obtainede . 0.5 on a number of photonic nanowires with diametersranging from 200 to 260 nm.

The simple Fabry–Perot model developed in ref. 13 provides ananalytical expression of e given by

e"u# $ 12b"1% jrmj#

2

1% bjrmj#Ta"sin u# "1#

where Ta(sin u) is the taper transmission into free space within acone of opening angle 2u. The X decay rate extracted from autocor-relation measurements, equal to 0.42 ns21, is smaller that the 1 ns21

expected value for an ideal structure. This is likely due to an actualwire diameter d! 0.9dopt, which leads to a deconfinement of HE11.Fortunately, thanks to the strong inhibition of the SE in the otherelectromagnetic modes, b is robust against imperfections of thiskind, and remains about 0.9. In fact, the source efficiency ismainly limited by the upper taper geometry. Our data are welldescribed by a tapering angle a! 58 (solid line in Fig. 3a),leading to T58(0.75)! 0.77. Further fabrication improvement todecrease a may bring the efficiency closer to its theoretical limit,&0.95 for a taper having unity transmission13.

Together with a spectacular increase of e , replacing a high-Qcavity design by a monomode waveguide approach comes withanother crucial advantage: photonic nanowires offer an intrinsicallybroadband SE control, applicable to non-monochromatic emitters(colour centres in diamond, QDs operated at higher temperatures).Furthermore, the operating wavelength of the source can be tuned

!/2

!/2

rm

HE11

"

a2#

200 nm

2.5 µm

b

Au

SiO2

Figure 1 | Single-photon source geometry. a, An InAs QD (red triangle) isembedded in a GaAs photonic nanowire. The far-field emission collectionis optimized with an integrated modal mirror (gold and SiO2 spacer) and asmooth tapering of the wire tip (opening angle, a). b, Scanning electronmicroscopy image of a typical device.

10

XXX

XXX

Spectrally integrated counts (Hz)

103

104

105

Excitation power (µW)

3.62 µW0

APD

cou

nts (

104 H

z)

123456789

10a b

1.64 µW

570 nW

62 nW

10.10.01918916$ (nm)

914912

70

c

605040302010!10!20 00.0

0.1

Corre

latio

n co

unts

(Hz)

0.2

0.3

0.4

Delay (ns)

Figure 2 | Single-photon emission by a single QD in a photonic nanowire.a, mPL spectra of the photonic nanowire measured at 5 K for increasingvalues of the optical pump power P. b, Integrated counts of X and XX versusP and fits to the theory (solid lines). Below the saturation pump powerP0! 1.05 mW, they respectively exhibit linear and quadratic dependenceon P. c, Autocorrelation trace of the X transition (red) well above saturation(P/P0' 4), measured over a 0.5-nm spectral range (rectangle window in a).The fit to theory (black) demonstrates g(2)(0) , 0.008.

NATURE PHOTONICS DOI: 10.1038/NPHOTON.2009.287 LETTERS

NATURE PHOTONICS | VOL 4 | MARCH 2010 | www.nature.com/naturephotonics 175

InAs QD

J. Claudon et al., Nature Photon 4, 174 (2010).

More...

• Plasmons get quantified

• Plasmons get amplified

• Plasmons start lasing!

Where to find teams

• Nanooptics/nanophotonics is an extremely active field, especially in the Ile de France

• All the subjects and techniques (and much more!) I presented are represented

• Principal ressource: the web!!

Good starting points

• C’nano IdF: http://www.cnanoidf.org/-NanoPhotonique-NP-

• RTRA «triangle de la Physique»: http://triangledelaphysique.fr/Triangle_Physique_theme7

• Labex NanoSaclay:http://nanosaclay.extra.cea.fr/Phocea/Vie_des_labos/Ast/ast_theme.php?id_ast=5













nanoptics - École normale supérieure · 2014. 5. 5. · the photon statistics from a typical...

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