A Rectangular Metal-Insulator-Metal basedNanoscale Plasmonic Resonator

Amir Hosseini and Yehia MassoudDepartment of Electrical and Computer Engineering

Rice University, Houston, TX, 77005(massoud@rice.edu)

Abstract—We present an optical range resonator based onsingle mode metal-insulator-metal plasmonic gap waveguides.Near lossless transmission at 90

◦ bends enables us to designrectangular structures with cross-section area less than 500 nm

2,which also leads to easing the fabrication process. The resonatorexhibits a free spectral range of 270 nm. We show that a smallbridge between the resonator and the input waveguide can beused to tune the resonance frequency. In addition, nanoscaleadd/drop directional couplers are realizable using the presentedring resonator structure.

I. INTRODUCTION

Electromagnetic waves coupled to propagating free electronoscillations at metal-dielectric interfaces, known as surfaceplasmon polaritons (SPPs), have been considered as energyand information carriers to overcome the diffraction limit oflight. Several plasmonic wave-guiding structures have beenproposed such as metallic strips and nanowires [1], V-grovesin metal substrates [2], and plasmon slots [3], [4]. Amongthese geometries, those which focus the light into the dielectriccore in a metal-insulator-metal (MIM) configuration, allowthe manipulation and transmission of light at the nanoscale.MIM-based plasmon slot waveguides have been shown toprovide both long-range propagation and subwavelength spa-tial confinement [3]. MIM waveguides are promising for thedesign of nanoscale all-optical devices as the numerical andexperimental investigations show strong localization, zero-bend losses as well as relatively simple fabrication [5], [6].

In this paper, we use a finite-difference time-domain(FDTD) method with the perfectly matched layer boundaryconditions [7] to investigate the performance of a surfaceplasmon based optical-range ring resonator. Ring resonatorsare generally configured with circular waveguides and havebeen used in several applications such as dispersion com-pensation systems, dropping/combining filters, band-pass fil-ters, wavelength multiplexers/demultiplexers, and all-opticalswitches [8].

In the case of circular dielectric ring resonators, such as therace-track resonator [9], a large bend radius is needed in orderto reduce the bend loss. Therefore, the overall size of the ringresonator increases to tens of microns, which in turn decreasesthe maximum free spectral range (FSR), the separation ofthe second resonance from the fundamental one(s). In orderto eliminate the limitation posed by the bending loss onring resonator size, hybrid photonic crystal and conventional

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1

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β(nm−1)E

nerg

y(eV

)

d=10nmd=100nm d=50nm

Ag,εm

Ag

dielectric,εd

β

x

z

d

Fig. 1. Dispersion relations for the fundamental TM mode of Ag/air/Ag(solid curve) and Ag/SiO2/Ag (dashed curve) MIM waveguides. The dottedcurve gives the dispersion relation for a single Ag/air interface. ωsp forAg/air and Ag/SiO2 interfaces is depicted by solid and dashed horizontallines, respectively. A MIM waveguide structure is shown in the inset.

waveguide structures were utilized to realize a rectangular ringresonator [10]. However, the overall size of the structure is stillin order of tens of microns due to the fact that the photoniccrystal needs at least 5 periods of the periodic structure at eachside to be able to exhibit forbidden frequency ranges.

MIM configuration can be used not only to reduce the sizeof the waveguides, but also to reduce the bend radius. We showthat 100% transmission at 90◦ bends allows the realizationof miniaturized rectangular ring resonators, which exhibit upto two fundamental resonance frequencies. The rectangularresonator can be utilized to make optical range filters withmore than 15 dB drop at the resonance wavelength (λr) withhigh FSR, In addition, directional couplers with high opticalefficiency are realizable based on the presented resonator.

II. 90◦ BENDS IN MIM WAVEGUIDES

Figure 1 shows the dispersion diagram, energy versus prop-agation constant (β), for the fundamental transverse magnetic(TM) mode of the plasmon-slot waveguide. Since the trans-verse field components of this mode are symmetric, they lendthemselves to end-fire excitations [5]. Figure 1 depicts thatthe fundamental TM mode does not exhibit a cut-off thick-ness. There is a cut-off frequency about the surface plasmonfrequency (ωsp). At this frequency εm(ωsp) = −εd, where εm

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Proceedings of the 7th IEEEInternational Conference on Nanotechnology

August 2 - 5, 2007, Hong Kong

and εd are the frequency-dependent dielectric functions of themetallic and dielectric materials, respectively.

The quasi-static approximation holds for plasmonic struc-tures that are much smaller compared to the operating wave-length. Under this condition, similar to a perfect conduc-tor parallel-plate waveguide bend, the bending behaves asa junction between two transmission lines with the samecharacteristic impedance [6]. Figure 1 shows that as thedielectric constant increases, or as the dielectric core becomesthiner, the effective index (neff = β/β0) increases, whereβ0 is the free space propagation constant. Consequently, theshortest wavelength at which the bending loss is still negligiblebecomes longer.

On the other hand, thinner dielectric cores and higher re-fractive index dielectric materials result in higher propagationlosses. Thus, for structures consisting of MIM plasmonicwaveguides with sharp bending, low refractive dielectric mate-rials should be used in order to increase the propagation lengthwhile maintaining a low bending loss using thin dielectriccores. We choose silver [11] and air for the surface plasmonbased resonators. A practical configuration for Ag/air/Agplasmonic waveguides is presented in [5]. Figure 2 showsthe transmission spectra of a 90◦ bend in MIM waveguidesfor different dielectric thicknesses and materials. A dielectricthickness of d = 50 nm allows for lossless bending forwavelengths longer than 760 nm [6]. It should be noted thatthe abovementioned waveguide is essentially single mode,because the propagation loss of the second mode is ordersof magnitude more than that of the fundamental mode [3].

III. RING RESONATOR STRUCTURE

A ring resonator consists of a reentrant waveguide in prox-imity to or in contact with a straight waveguide. At frequenciessuch that the length of the loop L = Nλg, where N , aninteger, is the mode number, the ring acts as a cavity andthe energy couples into the resonator, therefore, the output [b2

in Fig. 3(a)] drops. λg = λ0/neff is the guide-wavelength,where λ0 is the free space wavelength. Figure 3(a) showsthe schematic of a rectangular ring resonator. The couplingbetween the ring and the input waveguide depends on theseparation between them (s). The wave-guiding length in the

0.4 0.6 0.8 1 1.2 1.4 1.50

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λ(μm)

Tra

nsm

issi

on

d=50nm, aird=50nm, SiO

2

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dielectric d

Fig. 2. Transmission spectra of a MIM waveguide calculated using FDTD.

b2s

t

l(a)

(b)

a1

a1

b2

L

d

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silver

silver

dielectric

dielectric

a4

b3

Fig. 3. (a) Schematic of a MIM based rectangular resonator. (b) Schematicof a plasmonic add/drop filter structure.

� (�m)

Tra

nsm

issi

on (

dB)

(725,725)

(150,600)

(950,500)

(600,150)

(365,360)

(365,360), w/ bridge

Fig. 4. Transmission spectra |b2/a1|2 for different (l, t) values. Thetransmission values are normalized with respect to the output power of thestraight waveguide without the ring resonator.

ring is the average of the inner and outer perimeter, L =2(l + t), depicted by the dashed line in Fig. 3(a). We refer tothe resonator dimension by (l,t) with both values presented innanometers.

A schematic of an add/drop filter based on the rectangularring resonator is shown in Figure 3(b). At resonance frequen-cies, the electromagnetic energy from the input (a1) couplesinto the ring resonator from the lower straight waveguide andthen couples out to the output of the straight waveguide above(b2). In a similar way, if input a4 satisfies the resonancecondition, it couples into b3 output through the ring resonator.

IV. SIMULATION RESULTS

Starting with a (725, 725) resonator, due to neff =1.3788 and λg = 725 nm, a resonance is expected at λ0 =

82

(a)

(c)

(b)

(e)

(d)

(g) (h)

(f)

Fig. 5. 4: Field profile (|Hz|2) for different (l,t) values in nm, (a) (725,725),λr = 999 nm, (b) (725,725), λr = 1022 nm, (c) (365,360), λr =

1031 nm, (d) (365,360), λr = 978 nm, (e) (150,600), λr = 1041 nm,(f) (600,150), λr = 989 nm, (g) (950,500), λr = 996 nm, (h) (365,360),λr = 926 nm, with a 70 nm long bridge.

1000 nm. The transmission spectrum is depicted in Fig. 4,which shows two resonances at λr = 999 nm and λr =1022 nm. The field-profiles (|Hy|

2) corresponding to theseresonances are shown in Figs. 5(a) and (b). It might be notedthat the outer perimeter of the resonator is in fact 100 nmlonger than the dashed path shown in Fig. 3(a). Therefore, theeffective wave-guiding length can be more than L. For themode shown in Fig. 5(a), the standing waves forming in thering at resonance, have their maximum amplitude at the ringfaces. The standing waves are not affected by the ring corners,and thus resonance occurs at a wavelength very close to thepredicted value.

Figure 5(b) shows that the longer wavelength resonance cor-responds to a cavity mode concentrated at the ring corners. Asthe size of the ring resonator increases, the difference betweenthe face and the corner resonance frequencies decreases. Thisis because of the longer effective wave-guiding length sharedby a greater number of standing waves. In the case of therectangular ring resonator, we found that for mode numbersN > 6, the resonator becomes single frequency. It shouldbe noted that double resonance frequency does not happen inthe case of a circular resonator due to the geometry. Thus,this feature is specific to the nanoscale resonator and is onlyrealizable in systems based on a plasmonic waveguide.

Another interesting feature of the ultra small plasmonicrectangular resonator is that for odd values of N, the rectan-gular symmetry does not allow for an efficient coupling of theenergy from the input waveguide to the cavity at resonance.Therefore, L = 2λg is the shortest wave-guiding length thatresults in an efficient output drop at resonance. Figure 4shows that the transmission spectrum of the (365, 360) ringresonator exhibits two resonance wavelengths of about 70 nmdifference. For this resonator, L = 2λg holds at λ0 =

1000 nm. In fact, this geometry provides the largest differencein the fundamental resonance frequencies as a rectangular ring,since the corner mode has no standing waves at the faces, asshown in Fig. 5(c). Therefore, all the standing wave periodsare affected by the ring corners, and this explains why thecorner mode resonance is that far from the normal mode.

The existence of multiple resonance frequencies gives flex-ibility to design band stop filters with wider band-gaps. Inaddition, one of the resonances can be suppressed by changingthe aspect ratio (l/t), or the two modes can occur simulta-neously. As the electromagnetic energy couples through thelower horizontal face of the ring (Fig. 3), the field at this facecannot be zero at resonance. In the case of the (150, 600)resonator [Fig. 5(e)], the lower parallel face (150 nm) ismuch shorter than the guide wavelength at resonance (λg ∼725 nm). The standing wave period formed at this facefills the two lower corners. The other period fills the twoupper corners due to symmetry. The field profile, shown inFig. 5(e), has considerable amplitude at the corners, thus thegeometry dictates that only the corner mode resonance canexist. However, for the (600, 150) resonator, the length of thecoupling face is around 80% of λg at resonance. Again becauseof the coupling mechanism, the standing wave pattern formsin the coupling face, which only can fill one of the corners asshown in Fig. 5(f). Consequently, the energy is concentratedat only two out of the four ring corners. Instead of one hybridand one corner mode, there are two hybrid modes with almostthe same resonance frequencies, and the ring exhibits a widesingle resonance.

Similarly, the length of the coupling face in the (950, 500)resonator is roughly an odd integer multiple of half the guidewavelength. Therefore, there are again two hybrids modes.However, the corresponding resonance frequencies are closerto each other compared to those of the (600, 150) resonator.This is because of the more number of the standing waveperiods formed in the ring. The power (Pz) profiles of the(950, 500) resonator is depicted in Fig. 6. For the single-resonance shown in Fig. 5(g), FSR=268 nm, full width at halfmaximum ΔFWHM = 6 nm and the quality factor Q=166,where

FSR =λ2

r

neffL, Q = λr/ΔFWHM . (1)

We found that a small bridge between the input waveguideand the ring significantly changes the resonance frequency.Since the resonance mode [Fig. 5(h)] is dictated by theposition of the bridge, only one highly narrow resonanceoccurs as depicted in Fig. 4. This is in contrast with thecase of conventional circular resonators, where the resonancefrequency does not depend on the position of the contactbetween the ring and the straight waveguide. The presence of acontact bridge, changes the standing wave pattern in proximityof the bridge. For the conventional dielectric resonators, wheretens of standing wave periods form in the ring, a change inthe period at proximity of the bridge has a negligible effect onthe resonance frequency. However, for the resonator shown inFig. 5(h), there are only two periods of the standing wave, and

83

(b)

(a)

x(�m

)x(�m

)

z(�m)

z(�m)

Fig. 6. Power profile (Pz) for (950,500) ring resonator, s = 30 nm (a)λ = 996 nm, (b) λ = 1150 nm.

a change in one of them, dramatically affects the resonancebehavior of the structure.

The transmission (T = |b2/a1|2) through the input waveg-

uide is

T =α2 + |t|2 − 2α|t| cos (θ + φ)

1 + α2|t|2 − α|t| cos (θ + φ), (2)

where α and |t| represent the ring internal attenuation andthe coupling coefficient, respectively, i.e. α = 1 means nointernal loss, and θ = 2π

λg

L [12]. At resonance (φ+θ = 2Nπ),if α = |t|, the transmission drops to zero due to perfectdestructive interference in the input waveguide. This conditionalmost holds for all the ring resonators shown in Fig. 4, wherethe transmission drops over 10 dB in all cases. Equation 2indicates that in the case of smaller rings, where attenuationis less (α ≈ 1), the separation has to be shorter for bettercoupling in order to reduce transmission at resonance. Itshould be also noted that as l increases the coupling becomesstronger. In Fig. 4, s = 20 nm, s = 25 nm, s = 25 nmand s = 30 nm for (725, 725), (650, 100), (150, 600), and(950, 500) resonators, respectively. We found that a separationof s = 15 nm reduces the transmission to −24 dB for the(150, 600) ring resonator. As the bending loss is zero, only thepropagation loss inside the ring contributes to α. Thus, for anegligible transmission at resonance, the coupling coefficientcan be written as

|t| = α = exp

(−

2πIm(neff )

λ0

L

). (3)

Equation (3) provides us a means to calculate the couplingbetween MIM waveguides. In order to calculate the couplingcoefficient, the effective wave-guiding length should be con-sidered. It should be noted that the coupling coefficient alsodepends on the length of the waveguides.

We also investigated the possibility of realizing compactadd/drop directional couplers. One configuration for add/dropcouplers consists of two parallel waveguides that are coupledto each other through a ring resonator [Fig. 3(b)]. The power(Pz) profiles of the (950,500) add/drop directional coupler areshown in Fig. 7. At resonance, the structure efficiently couplesthe input power from the lower waveguide into the upper one.

(b)

(a)

x(�m

)x(�m

)

z(�m)

z(�m)

Fig. 7. Power profile (Pz) for (950,500) directional coupler, s = 30 nm(a) λ = 996 nm, (b) λ = 1150 nm.

V. CONCLUSION

This paper has reported the numerical analysis of surfaceplasmon based nanoscale rectangular ring resonators basedon the plasmon slot waveguides. The double- and single-resonance frequencies in the rectangular configuration havebeen investigated and high transmission drops at resonance arefound. We showed that the MIM-based ring resonator couldexhibit an high free spectral range of 270 nm.

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