204 OPTICS LETTERS / Vol. 33, No. 3 / February 1, 2008

Surface waves between metallic films andtruncated photonic crystals observed with

reflectance spectroscopy

B. J. Lee,1 Y.-B. Chen,1,2 and Z. M. Zhang1,*1G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

2Present address, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan*Corresponding author: zhuomin.zhang@me.gatech.edu

Received October 22, 2007; accepted December 5, 2007;posted December 18, 2007 (Doc. ID 88858); published January 15, 2008

We have analyzed and demonstrated surface-wave excitations, by propagating waves in air, at the interfacebetween a truncated photonic crystal (PC) and a silver film in the near-infrared. The truncated PC was fab-ricated with several unit cells of alternating SiO2 and Si3N4 layers. The dispersion relation of surface waveswas calculated using the supercell method. A Fourier-transform infrared spectrometer measured the spec-tral reflectance of the fabricated sample at different incidence angles. An angle-resolved laser scatterometermeasured the reflectance as a function of the incidence angle at the wavelength of 891 nm. The agreementbetween the resonance conditions obtained from experiments and the calculated dispersion relation mani-fests that surface waves at the PC–Ag interface may be utilized to build coherent thermal-emission sources.© 2008 Optical Society of America

OCIS codes: 240.6690, 310.6860.

Surface polaritons or surface waves are electromag-netic waves that propagate along the interface be-tween different media and exponentially decay intoboth media [1–3]. The excitation of surface waves of-ten requires the parallel component of the incidentwave vector to exceed the magnitude of the wave vec-tor in vacuum; thus, an attenuated total reflection(ATR) configuration is commonly employed [1]. In ad-dition to prism couplers, surface relief gratings canalso excite surface waves due to diffraction. Surface-wave excitation can modify the thermal-emissioncharacteristics to achieve temporal and/or spatial co-herence from binary gratings constructed with ametal [2,4] or a polar material [3]. Thermal emissioncontrol has enormous applications in manufacturing,space thermal management, and energy conversion,and therefore, has received great attention lately[5–9].

Localized surface modes at the edge of a photoniccrystal (PC) have been extensively studied for bothone-dimensional (1D) [10,11] and two-dimensionalstructures [8]. The optical surface modes for trun-cated PCs are analogous to the localized electronicstates, at the surface of a crystalline solid, predictedby Tamm [12] in the 1930s. Yeh et al. [10] and Rob-ertson and May [11] experimentally demonstratedsurface waves on a 1D PC using an ATR configura-tion. More recently, Gaspar-Armenta and Villa [13]suggested that a metallic thin film deposited on asemi-infinite 1D PC could support surface wavescoupled with propagating waves in air. Lee et al.[14,15] extended the concept to constructing coherentthermal-emission sources from multilayer structures,whereas different layered structures have also beenconsidered for tailoring thermal emission [5–7]. Al-though surface waves at the interface between a PCand air and between two PCs have been extensivelyinvestigated [10,11,16,17], to our knowledge no ex-

perimental validation exists for surface waves at the

0146-9592/08/030204-3/$15.00 ©

interface between a PC and a metallic film. Here, wereport an experimental investigation of surface-waveexcitations at the interface between a truncated PCand a silver film in the near-infrared.

A PC-on-Ag structure was fabricated on a siliconsubstrate, and its cross-sectional image obtained byusing a focused ion beam (FIB) workstation is shownin Fig. 1. A Ti adhesive layer was first deposited on aSi substrate, followed by a Ag film, which is thickenough to be opaque (semi-infinite). The truncatedPC with six unit cells was formed on the Ag film us-ing plasma-enhanced chemical vapor deposition ofSiO2 and Si3N4 layers [15]. The refractive index atthe wavelength �=1 �m is approximately n1=1.45for SiO2 and n2=2.0 for Si3N4. The thicknesses wereobtained from fitting the reflectance dip wavelengthsto be d1=d2=153 nm, dt=100 nm.

Fig. 1. (Color online) Cross-sectional image of the fabri-cated PC-on-Ag structure. The Si3N4 layer adjacent to theAg film serves as a surface termination. The coordinatessystem is also shown for a plane wave with a wave vector k

at an angle of incidence �.

2008 Optical Society of America

February 1, 2008 / Vol. 33, No. 3 / OPTICS LETTERS 205

A Fourier-transform infrared (FTIR) spectrometerwas used to measure the specular reflectance. Figure2 shows the measured and predicted reflectance spec-tra of the fabricated sample near the region where areflectance dip occurs at the incidence angle �=30°and 45° for TE waves. The dashed curve indicates thecalculated spectrum using the fitted geometric pa-rameters and the tabulated optical constants from[18] for the two dielectrics and Ag. At the resonancewavelength (or frequency), the incident photon en-ergy is coupled to surface waves at the PC and Ag in-terface and eventually absorbed by the Ag layer. Thecalculated reflectance captures the essential featuresof the measured spectrum, although the measuredreflectance valley is not as deep and sharp. This maybe caused by partial coherence resulting from beamdivergence of the FTIR spectrometer. Surface rough-ness and nonuniformity of the layer thickness mayfurther reduce the coherence. The rms roughness ofthe fabricated sample was near 10 nm measuredwith an atomic force microscope.

Since the Ag layer is opaque, the emissivity of thePC-on-Ag structure is simply one minus the reflec-tance according to Kirchhoff ’s law [9]. A sharp dip inreflectance can be regarded as a peak in the emissiv-ity and, therefore, the concept of coherent thermalemission can be realized. For demonstration of theconcept of coherent emission by exciting surfacewaves at the truncated PC and metallic interface, theeffects of temperature and thermal stress are notconsidered. The quality factor Q=�c /�� is a measureof temporal coherence [14]. Here, �c is the center fre-quency of the emissivity peak (or reflectance dip) and�� is the full width at half-maximum (FWHM) (orminimum). At �=10°, our measurements suggestthat ��=158 cm−1 and Q=62.6. For TE waves, ��=196 cm−1 and 215 cm−1 at �=30° and 45°, and thecorresponding Q values are 52.3 and 50.6, respec-tively. The Q values obtained from spectral reflec-tance measurements are approximately half of thecalculated values [15] due to partial coherence.

Fig. 2. (Color online) Spectral reflectance of the fabricatedsample in the near-infrared at incidence angles �=30° and45° for TE waves. Reflectance at near-normal incidence ��

=10° � were also measured but not shown here.

The bidirectional reflectance of the fabricatedsample was measured with a custom-designed three-axis automated scatterometer at 891 nm wavelength[19]. Figure 3 compares the measured and calculatedreflectance for TE waves. Since the laser beam ishighly collimated, the measured reflectance exhibitsa very sharp dip at �=54° with a minimum less than0.05, which is even lower than that predicted, al-though the calculated width of the valley is some-what narrower. The absorption of Ag film depends onthe deposition conditions. The electron scatteringrate in the fabricated film may be greater than thetabulated handbook values. The additional loss mayresult in a line broadening of the reflectance dip aswell as a reduction of the reflectance at small inci-dence angles.

The emissivity, obtained from the measured reflec-tance, is plotted in the vicinity of the peak as an insetin Fig. 3. The right half represents the measurement,and the left half represents the prediction. The emis-sivity exhibits strong directional selectivity. The co-herence length given by Lcoh=� / ���� cos �� is a mea-sure of the spatial coherence [4], where �� is theFWHM of the emissivity peak. The estimated ��from the measurement is 2.2°, and the correspondingcoherence length is 14.1�. This value is slightlysmaller than those from gratings [3,4].

Due to the periodicity of constituent dielectrics, thesolution of Maxwell’s equations inside the PC mustsatisfy the Bloch condition. Consequently, PCs showband structures composed of passbands and stopbands in the �–kx plane, where � is the angular fre-quency and kx is the parallel wave-vector component.In the stop band, no energy can be transferredthrough the PC, and the field distribution is similarto that of an evanescent wave in a semi-infinite me-dium. Therefore, surface waves can be excited in thestop band of PCs. In general, it is inappropriate totreat a PC structure as a homogeneous medium withequivalent � and � that are independent of the space.For this reason, the dispersion relation for surfacewaves at the interface between homogenous media

Fig. 3. (Color online) Reflectance as a function of the inci-dence angles at 891 nm for the TE wave. The inset shows

the directional emissivity calculated from Kirchhoff ’s law.

206 OPTICS LETTERS / Vol. 33, No. 3 / February 1, 2008

[1] is not applicable to PCs. Nevertheless, thesurface-wave dispersion relation for 1D PCs can beobtained using the supercell method [20,21].

Figure 4 shows the calculated dispersion relationof surface waves at the PC-Ag interface for the TEwave. The light line in air is denoted by a dashed–dotted line, and the shaded areas represent the pass-bands of an infinitely extended PC. The dashed curverepresents the predicted dispersion relation that liesin the stop band of the PCs. In the calculation, thethicknesses of each dielectric were used as the fittedparameters of the reflectance measurements. The di-electric functions of Si3N4 and SiO2 layers were as-sumed to be �1=2.1 and �2=4.0, respectively [18]. ForAg, only the real part of the dielectric function (witha value of −41.3) was considered, as is commonlydone for calculating the dispersion relation of surfacepolaritons [1]. Sufficient Fourier coefficients wereused in constructing the Bloch wave to achieve a con-vergence within 0.1%.

The resonance conditions obtained from the mea-sured reflectance are compared with the surface-wave dispersion relation. The circles represent theresonance conditions in the spectral reflectance mea-surements, and the diamond mark indicates those ofthe angle-resolved reflectance measurements. It canbe seen that the experimentally obtained resonanceconditions agree well with the calculated surface-wave dispersion curve. The comparison confirms thatsurface waves are excited at the PC–Ag interface bypropagating waves in air. Although not shown here, ifthe surface termination dt increases for the consid-ered PC-on-Ag structure, the dispersion curves willshift to a lower frequency region, allowing tuning ofthe emissivity peak frequencies.

In summary, we have demonstrated the surface-wave excitations on the fabricated PC-on-Ag struc-ture by measuring the reflectance using an FTIRspectrometer as well as a laser scatterometer. The

Fig. 4. (Color online) Surface-wave dispersion relation,shown as a dashed curve for the TE wave. The resonanceconditions obtained from the spectrometer measurementsand from the scatterometer measurements are denoted by

the circular and diamond marks, respectively.

dispersion relations of surface waves are calculatedbased on the supercell method. It is found that fre-quencies and incidence angles where the measuredreflectance exhibits sharp dips agree very well withthe surface-wave dispersion relation. The presentwork experimentally demonstrates surface-wave ex-citation from a planar structure without employingan ATR configuration. The feasibility of constructingcoherent thermal-emission sources is also evidencedby examining spectral and directional selectivity inthe emissivity. The results will facilitate the develop-ment of coherent emission sources in energy conver-sion systems such as thermophotovoltaic devices.

This work was supported by the Department of En-ergy under contract number DE-FG02-06ER46343.The authors thank Georgia Tech’s MicroelectronicsResearch Center and Focused Ion Beam (FIB2) Cen-ter for us to fabricate the samples and to obtain thecross-sectional image.

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