October 15, 2009 / Vol. 34, No. 20 / OPTICS LETTERS 3089

Characteristics of a waveguide mode in a trilayerAg/SiO2/Au plasmonic thermal emitter

Yu-Wei Jiang, Yi-Ting Wu, Ming-Wei Tsai, Pei-En Chang, Dah-Ching Tzuang, Yi-Hen Ye, and Si-Chen Lee*Department of Electrical Engineering, Graduate Institute of Electronics Engineering, National Taiwan University,

Taipei, Taiwan*Corresponding author: sclee@cc.ee.ntu.edu.tw

Received June 17, 2009; revised August 24, 2009; accepted September 1, 2009;posted September 10, 2009 (Doc. ID 112968); published October 6, 2009

A suitably designed trilayer Ag/SiO2/Au thermal emitter can be used as the narrow bandwidth infraredlight source. The thermal radiation generated in the SiO2 layer resonates between the two metal films andresults in not only the Ag/SiO2 surface plasmon polaritons but also the waveguide mode (WM) in theAg/SiO2/Au structure owing to the thick SiO2 layer. This study investigated the influence of dielectric thick-ness on energy dispersion relations and derived the theoretical dispersion relation, which fit well with ex-perimental results. This WM light source can be applied in the area of gas sensing and probing the responseof the animal cells and plants to infrared radiation. © 2009 Optical Society of America

OCIS codes: 230.7370, 240.6680, 230.4555, 290.6815.

Surface plasmon polaritons (SPPs) are electromag-netic excitations, propagating along a dielectric/metal interface, having the electric field componentsperpendicular to the surface and decaying exponen-tially into both neighboring media [1]. The trilayermetal/dielectric/metal structure can support spatiallight confinement owing to coupling with SPPs, withno light diffraction limitation, at both metal/dielectric interfaces [2–4]. The mechanism of themodes’ coupling changing from surface plasmon (SP)to waveguide resonance as a function of the dielectricmaterial thickness is investigated, and the strong in-teraction results in the formation of a waveguide-plasmon polariton [5–8]. Recently, optical field excita-tion through grating-induced SP and slab waveguidemodes (WMs) has been demonstrated theoretically[9,10]; it reveals more than a twofold enhancement ofoptical absorption and can be used to improve the de-vice efficiency in applications such as photovoltaics[11,12] and photodetectors [13]. A two-dimensionaltrilayer Ag/SiO2/Ag plasmonic thermal emitter hasdemonstrated the strong Ag/SiO2 SPP resonancethat can be converted to infrared light emission witha narrow bandwidth [14]. Comparing this work withprevious works of trilayer Ag/SiO2/Ag plasmonicthermal emitters with thinner SiO2 layers, this workproposes a trilayer emitter with a much thicker SiO2layer; therefore, the WM can be easily detected,whereas in previous works no WMs were detected.Then, this study characterizes the energy dispersionand emission spectra relations with respect to theSiO2 layer thickness and investigates the character-istic of modes’ coupling in the energy dispersion.

A 400-nm-thick Mo film was thermally depositedon the back of the double-polished Si substrate as aheating source. 20 nm Ti and 200 nm Au metal filmswere deposited on the front side of the Si substratefollowed by a SiO2 layer deposited with the plasma-enhanced chemical vapor deposition (PECVD). Thebottom Au layer is used as a reflection layer insteadof silver, because the SiO2 growth temperature is

350°C. The surface silver aggregates at 350°C, caus-

0146-9592/09/203089-3/$15.00 ©

ing the SiO2 layer to peel off. The thicknesses of theSiO2 layers in devices A–G were 0.7, 0.8, 0.9, 1.1, 1.6,2.1, and 2.6 �m, respectively. Then, a 100-nm-thicksilver film was deposited and lifted off on the SiO2layer to form a hexagonal hole array with a latticeconstant of 3 �m and a hole diameter of 1.5 �m. Theradiation area of the sample was 1 cm2. Figures 1(a)and 1(b) depict the schematics showing the side andtop views, respectively, of the device structure. ABruker IFS 66 v/s system was used to measure reflec-tion spectra. The sample was defined to lie in the�x ,y� plane rotating around the y axis in 1° incre-ments from �=12° to �=65°. The light was incident inthe z direction, allowing the dispersion relation in thekx ��K� direction to be measured. A Perkin Elmer2000 Fourier transform infrared (FTIR) spectrometersystem was adopted to measure the thermal radia-

Fig. 1. (Color online) Schematic of the (a) side and (b) topviews of the Ag/SiO2/Au plasmonic thermal emitter. The

top metal is perforated with a hexagonal hole array.

2009 Optical Society of America

3090 OPTICS LETTERS / Vol. 34, No. 20 / October 15, 2009

tion spectra. A dc was sent into the back Mo metal onthe Si substrate to heat the device, and a thermalcouple was put on the top of the device to measurethe temperature. When the sample is heated, thethermal radiation generated from the sample pen-etrates through the KBr window and is directed intothe FTIR via an off-axis mirror.

The energy dispersion relates as a function of k�x fordevices A, B, C, D, and G with various SiO2 thick-nesses, i.e., 0.7, 0.8, 0.9, 1.1, and 2.6 �m, respectively,and is shown in Figs. 2(a)–2(e). For device A witha SiO2 thickness of 0.7 �m, four dark lines represent-ing the reflection minimum and the excitation ofSPPs intersect with the y axis at 0.32 eV��3.88 �m�, which is composed of six degeneratemodes [i.e., �±1,0�, �0, ±1�, �−1,1�, and �1,−1�Ag/SiO2 modes denoted as (1,0) Ag/SiO2 mode]. Thedark area at higher energy represents the intense ab-sorption band. The absorption band narrowed andshifted to lower photon energy, blending with the �+1,0� Ag/SiO2 mode with an increasing SiO2 thick-ness from 0.8 (device B) to 0.9 �m (device C) asshown in Figs. 2(b) and 2(c), respectively. When theSiO2 thickness exceeded 1.1 �m as shown in Figs.2(d) and 2(e), the WM appeared and mixed with theAg/SiO2 mode. In particular, the dispersion curvesshown in

Fig. 2. (Color online) Measured energy dispersion relationas a function of k�x along �K direction for devices A, B, C, D,and G with different SiO2 thicknesses t of (a) 0.7, (b) 0.8, (c)0.9, (d) 1.1, and (e) 2.6 �m. The theoretical energy disper-sion relation (red curves) are shown to fit the experimentalresult of (e). WM is waveguide mode and WG is waveguide-

grating coupling mode.

Fig. 2(d) displayed anticrossinglike behavior of thetwo modes around 0.35 eV, which was attributed tocoupling between the propagating WM and its dif-fractive waves by Brillouin zone boundary in the mo-mentum space. From theoretical calculations, theWM with momentum kwg is given by

kwg = kx + iGx + jGy. �1�

Here, kx=� sin � /c, Gx and Gy are the reciprocal lat-tice vectors associated with the hexagonal array, � isthe incident photon frequency, � is the incident angle,c is the light velocity, and i and j are integers. For theparallel plate waveguide, the dispersion relation isgiven by

kwg =1

n���

cn�2

− �m�

t �2�1/2

, �2�

where m is the mode number and n and t are the re-fraction index and the thickness of the SiO2 layer, re-spectively. By solving Eqs. (1) and (2), Fig. 2(f) showsthe calculated dispersion curves (dotted red curves).Each curve is represented by the symbol �i , j ,m�,where i , j ,m are defined in Eqs. (1) and (2). They ap-pear in good agreement with the experimental re-sults when i= j=0; it is defined as the fundamentalWM [i.e., (0,0,1) WM in Figs. 2(d) and 2(e)]. Thehigher energy (shorter wavelength) zone shows aslight redshift, compared with the calculated result.This is because, at higher photon energy, the WMleaks out the top metal hole array easier, which leadsto an increase in the effective SiO2 layer thickness.Although the reflection spectra are dominated by theWM when the SiO2 thickness exceeds 1.1 �m, the SPresonance can still be readily seen. Even though theWM overlaps with the SP mode in the same energylevel, the reflection spectra are still dominated by theWM. This is because the WM resonance resultingfrom the overall SiO2 layer is stronger than the SPresonance from the top Ag/SiO2 interface.

The emission spectra of devices D, E, F, and G withincreasing SiO2 thickness (i.e., 1.1, 1.6, 2.1, and2.6 �m) were measured at normal incidence and dis-played in Figs. 3(a)–3(d), respectively. In Fig. 3(a), fordevice D, the peak at 4.11 �m (open square) is amixed mode, composed of Ag/SiO2 SP and (0,0,1) fun-damental WM. The small shoulder at 3.86 �m��0.32 eV� (open diamond) is the Ag/SiO2 SP modeas indicated in Fig. 2(d). The peak at 3.08 �m (opentriangle) is a waveguide-grating coupled mode com-posed of six degenerate modes [i.e., �±1,0�, �0, ±1�,�−1,1�, and �1,−1� modes], denoted as (1,0,1) WM.The peak positions of the (0,0,1) fundamental WMare found to redshift with increasing SiO2 thickness;however, the peak position at 3.86 �m associatedwith (1,0) Ag/SiO2 modes remain fixed when the SiO2thickness exceeds 1.1 �m, resulting from the weakcoupling between top and bottom Ag/SiO2 modes[15]. The measured emittance spectra displayed inFig. 3(b) for device E—the 4.92 �m peak—which is a(0,0,1) fundamental WM, exhibits a stronger inten-

sity between two metal slabs than that of the SP

October 15, 2009 / Vol. 34, No. 20 / OPTICS LETTERS 3091

does. The peak at 3.3 �m is the (1,0,1) waveguide-grating mode, showing a redshift with increasingSiO2 thickness. The peak at 3.65 �m (solid square)depicted in Fig. 3(c) for device F is a second-orderWM (0,0,2), which shifts to 4.01 �m and mixes withAg/SiO2 mode at 3.86 �m when SiO2 thickness is2.6 �m, shown in Fig. 3(d) for device G. The ratio��� /�� of the FWHM to the peak wavelength for thefundamental WM in devices E, F, and G is 0.04,0.028, and 0.018, respectively, demonstrating thatthe property of the narrow bandwidth WM is betterthan that of the SP for the application of thermalemitters [14]. In particular, a thermal emitter of theWM mode can provide a higher power intensity thanthat of the SP mode can at the same operated tem-perature (not shown) owing to the thicker SiO2 layerproviding much blackbody radiation energy in the de-vices.

The peak wavelength shown in Fig. 3 indicatesthat the fundamental WM (0,0,1) shifts to longerwavelengths at 4.11, 4.92, 5.69, and 6.61 �m for de-vice D, E, F, and G, respectively. This could be con-sidered as a Fabry–Perot type resonance generatedin the SiO2 layer between two parallel metal planescompared with the theoretical value ��c=2nt� withincreasing SiO2 layer thickness, where n and t arethe refractive index and the thickness of the SiO2

Fig. 3. Measured emission spectra of devices D, E, F, andG with different SiO2 layer thicknesses [i.e., t= �a� 1.1, (b)1.6, (c) 2.1, and (d) 2.6 �m, respectively]. The spectra showfundamental WM (0,0,1) (open square), (1,0) Ag/SiO2 SPPmode (open diamond), second-order WM (0,0,2) (solidsquare), and (1,0,1) waveguide-grating mode (open tri-angle). The devices with lattice constant a=3 �m and di-ameter d=1.5 �m were heated at a fixed temperature of140°C.

layer, respectively. The effective oxide thickness

should increase and shift the WM toward longerwavelengths because of the wave leaking via themetal film with a perforated hole array. With the in-creasing SiO2 layer thickness, the waveguide reso-nance and multidiffraction phenomena occur, makingthe dispersion relation intermix with those of theSPP modes.

In conclusion, this study successfully fabricatedthe ultranarrow bandwidth Ag/SiO2/Au infraredthermal emitters. When the SiO2 layer is thin, theAg/SiO2 SPP modes are clearly seen. As the SiO2layer becomes thicker than 1.1 �m, the WM deter-mined by the waveguide–waveguide cutoff frequencyappears on the energy dispersion and emission spec-tra. This work investigated the interaction betweenthe waveguide and the grating. The theoretical calcu-lation shows a good agreement with experimental re-sults. This infrared light source can be used in longwavelength optical communication and to explore theinteraction between the electromagnetic wave andplants in the mid-infrared region.

The authors would like to acknowledge the Na-tional Science Council of Taiwan (NSCT), for finan-cially supporting this research under contract NSC98-2221-E-002-242.

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