700 OPTICS LETTERS / Vol. 23, No. 9 / May 1, 1998

Normal-incidence guided-mode resonant grating filters:design and experimental demonstration

David L. Brundrett, Elias N. Glytsis, and Thomas K. Gaylord

School of Electrical and Computer Engineering and Microelectronics Research Center, Georgia Institute of Technology,Atlanta, Georgia 30332

Received January 12, 1998

Guided-mode resonant grating filters have numerous applications. However, in weakly modulated gratingsdesigned for use at normal incidence, the filtering resonance of these subwavelength-period devices splits forangles of incidence that are even slightly off normal incidence. Strongly modulated gratings are designedthat essentially overcome this practical problem near normal incidence. In addition, these gratings canhave, by design, either broad or narrow spectral characteristics. An experimental demonstration (1.5 2.0-mmwavelength range) of such a normal-incidence guided-mode resonant silicon grating upon a sapphire substrateis presented. The measured ref lection resonance had a FWHM of 67–100 nm for angles of incidence of 0–8±

and peak efficiency of ,80%. 1998 Optical Society of AmericaOCIS codes: 050.0050, 050.2770, 260.5740, 120.2440.

The characteristics of guided-mode resonant gratingfilters make them significant candidates for a widevariety of applications, including narrow-band ref lec-tion f ilters,1 narrow-band transmission filters,2 modu-lators,3 and antennas. The observed resonances aredue to the excitation of leaky guided modes in the pe-riodic waveguide structure. Over a number of years,there has been a significant effort in the analysis ofboth one-dimensional4 and two-dimensional5 guided-mode resonant gratings but only a few experimentaldemonstrations. Mashev and Popov6 experimentallymeasured a narrow-band resonance exhibited by acoated one-dimensional grating. Magnusson et al.7

demonstrated narrow-band notches in the trans-mission spectrum of a one-dimensional grating atmicrowave frequencies. Recently, Sharon et al.8

demonstrated narrow spectral ref lectances fromweakly modulated semiconductor waveguide gratings(in the near infrared) and from dielectric waveguidegratings (in the visible). All these experimentswere done at an angle of incidence of 1±. Peng andMorris9 experimentally showed sharp peaks in theref lection spectrum of a two-dimensional grating atnear-infrared wavelengths at 2± angle of incidence.

In general, if weakly modulated (modulation index d

is defined below) guided-mode resonant gratings aredesigned for use at normal incidence, the resonancespectral peak is found to split into two peaks (above andbelow the wavelength of the normal-incidence peak)for small angles (a fraction of a degree) away fromnormal incidence. In addition, the spectral location ofthe narrow resonances is critically dependent on theangle of incidence, which may make devices based onsuch an effect diff icult to use in practice. However,it is shown in this Letter that strongly modulatedresonant gratings can overcome some or all of the aboveproblems. These guided-mode filters can exhibit arange of characteristics from narrow-band to widebandspectral responses. Also, strongly modulated gratingscan exhibit spectral responses that are stable withrespect to normal and near-normal incidence.

0146-9592/98/090700-03$15.00/0

In this Letter, an analysis of rectangular-groove(binary) strongly modulated gratings by the useof rigorous coupled-wave analysis (RCWA) is pre-sented.10 From this analysis, a guided-mode resonantgrating f ilter is designed to exhibit a stable spectralref lectance at normal and near-normal incidence.The grating is then fabricated and tested. The ex-perimentally measured spectral characteristics of thegrating are found to be stable with respect to angle ofincidence near normal incidence as predicted.

A typical resonant grating structure is composed ofa rectangular-groove grating with a ridge ref lective in-dex nr and a groove refractive index ng. The refrac-tive indices of the superstrate (cover) and the substrateare nc and ns, respectively. The grating period is L,and the fraction of the period occupied by the ridge ma-terial is the filling factor F . A guided-mode resonantsilicon grating is designed for a free-space wavelengthof l0 ­ 1.55 mm, with a superstrate of air snc ­ 1.0dand a substrate of sapphire sns ­ 1.746d. The ridgematerial of the grating is silicon snr ­ 3.48d, and thegroove is air sng ­ 1.0d. The ref lection resonance ofthe grating structure is associated with the excitationof the grating waveguide leaky modes. For this excita-tion to occur there are several requirements that mustbe met: (a) The effective refractive index of the grat-ing, nG (as defined in Ref. 11), must be higher thanthe refractive indices of the superstrate and the sub-strate media, that is, nG . ns . nc, for the gratinglayer to resemble a waveguide. (b) The grating periodmust be set so that the x wave-vector components ofthe 61-diffracted orders, kx, 61 (where x is the directionof the grating periodicity), satisfy either the inequality2k0nG , kx, 11 ­ k0nc sin u 2 K , 2k0ns or the in-equality k0ns , kx, 21 ­ k0nc sin u 1 K , k0nG , whereu is the angle of incidence from the cover, k0 ­ 2pyl0,and K ­ 2pyL. For normal incidence the previous in-equalities become k0ns , jkx, 61j ­ K , k0nG . (c) Thegroove depth of the grating must satisfy the transverseresonant condition of the 11 or the 21 diffracted orderinside the grating, kx, 11 or kx, 21 ­ bG , where bG is the

1998 Optical Society of America

May 1, 1998 / Vol. 23, No. 9 / OPTICS LETTERS 701

effective propagation constant of the waveguide thathas a film index equal to the grating effective indexnG , a film thickness equal to the grating groove depth,and the same cover and substrate indices.

The above design approach is described in Ref. 1.This approach works well for gratings that are weaklymodulated. That is, their modulation index d ­ snr 2

ngdysnr 1 ngd is small sd , 0.01d. For the silicon-on-sapphire grating with air as cover d ­ 0.55 .. 0.01,which results in a strongly modulated grating. Thesestructures have largely not been discussed in the lit-erature. By use of a f illing factor F . 0.5 (to achievea nG . ns), the above design procedure was employedfor a TE-incident polarization (polarization parallelto the grating grooves). However, after the perfor-mance of the resulting resonant grating was examinedwith RCWA, no resonance was observed in the wave-length range of interest! Therefore a parametric studyof the grating ref lectance (backward diffraction eff i-ciency of the 0-diffracted order, jR0j2) was performedwith RCWA. The calculated ref lectance of the silicon-on-sapphire resonant grating is shown in Fig. 1 as afunction of groove depth d and filling factor F . Theuse of grating period L ­ 0.8 mm satisfied the in-equalities (b) specif ied above. In Fig. 1 the ref lectanceis shown in gray scale; the dark areas correspond tohigh ref lectance. The darkest thin curves correspondto points of nearly 100% ref lectance sjR0j2 . 1d. Theleft edge of the plot corresponds to an unmodulatedlayer of groove material (air), and the right edge corre-sponds to unmodulated layers of silicon. In the lattercase the pure silicon f ilm waveguide can support oneto four pure guided TE modes when the groove depth(film thickness) varies from 0 to 1 mm. A wide rangeof ref lectance resonances (sometimes also referred toas scattering resonances) can be observed from Fig. 1.For example, a broad spectral resonance occurs whenF ­ 0.62 and d ­ 0.41 mm, whereas narrow spec-tral resonances occur at cusps such as F ­ 0.57 andd ­ 0.53 mm. The spectral characteristics of these ex-ample resonances are shown in Fig. 2 both for nor-mal incidence and for a 2± angle of incidence. Thestability of both the broad and the narrow resonanceswith respect to the angle of incidence is apparent. TheFWHM’s of the broad and the narrow resonances are,210 and ,2 nm, respectively. Other spectral reso-nances away from the normal-incidence design peakcan appear and, in general, vary with the angle ofincidence. The waveguiding behavior of the resonantgrating was examined by analysis of the leaky modesso that a better understanding of the physical basisof these ref lectance cusps could be gained. The com-plex propagation constants (of the TE0 and TE1 leakymodes that are associated with the resonances shownin Fig. 2) were calculated as the poles of the ref lec-tion coefficient12 in conjunction with RCWA. It wasfound that the strong modulation spectrally modifiedand mixed the grating stop bands in the correspondingBrillouin diagram. From numerical analysis of vari-ous gratings with the parameters shown in Fig. 1 it wasinferred that the insensitivity of the strongly modu-lated grating resonances to the angle of incidence isassociated with stop-band widening and mixing, which

is not observed in weakly modulated gratings. Moredetails about this analysis will be presented in a com-panion paper.

The grating that corresponds to the resonance shownin Fig. 2 for F ­ 0.57, d ­ 0.53 mm, and L ­ 0.8 mmwas fabricated and tested. The grating was fabri-cated with a sapphire wafer with ,560 nm of epitaxi-ally grown silicon by use of the procedure describedin Ref. 13. A scanning electron micrograph of the fab-ricated silicon-on-sapphire grating is shown in Fig. 3.From the micrograph, L . 0.82 mm and F . 0.57,which are close to the design values.

The fabricated silicon-on-sapphire guided-moderesonant grating was tested with a near-infrared au-tomated monochromator operating in the wavelength

Fig. 1. Calculated ref lectance (backward diffraction ef-ficiency, jR0j2) of a rectangular-groove silicon-on-sapphireguided-mode resonant grating sns ­ 1.746, nr ­ 3.48, ng ­nc ­ 1.00d as a function of groove depth and filling factor.

Fig. 2. Calculated ref lectance (backward diffraction eff i-ciency, jR0j2) of two rectangular-groove silicon-on-sapphireguided-mode resonant grating filters sns ­ 1.746, nr ­3.48, ng ­ nc ­ 1.00d for normal (0±) and 2± incidence. Thenarrow-band grating has d ­ 0.53 mm and F ­ 0.57. Thewideband grating has d ­ 0.41 mm and F ­ 0.62.

702 OPTICS LETTERS / Vol. 23, No. 9 / May 1, 1998

Fig. 3. Scanning electron micrograph of the fabri-cated silicon-on-sapphire grating. The grating hasL . 0.82 mm, d . 0.51 mm, and F . 0.57.

Fig. 4. Experimentally measured ref lectance (backwarddiffraction efficiency, jR0j2) of the fabricated silicon-on-sapphire guided-mode grating filter. Note that the spec-tral characteristic is stable with respect to a near-normalangle of incidence, as predicted by the analysis for thisstrongly modulated grating.

range 1.5 2.0 mm. The polarization that was incidentupon the grating was adjusted to be TE. The wave-length steps of the monochromator were 1 nm. The re-f lectance of the grating, jR0j2, was measured at normalincidence and at angles of incidence of u ­ 2±, 4±, 8±.The normalized ref lectance measurements are shownin Fig. 4 (an inset of the designed grating is alsoshown). Consistent with the design, the resonance isrelatively insensitive to the angle of incidence. Onlyfor u ­ 8± does the resonance show some splitting.The FWHM varies from ,67 to ,110 nm as the angleof incidence varies from 0 to 8±. This, according to theauthors’ knowledge, is the broadest guided-mode grat-ing resonance reported in the literature. The reso-nance occurs at l0 . 1.68 mm instead at the designvalue l0 ­ 1.55 mm owing to the deviation from thed ­ 0.53 mm design groove depth and to the residualhomogeneous silicon layer. Simulations showed thatthe position and the width of the resonance indeed varyas a function of the groove depth and the residual sili-con layer thickness. The deviation in the groove depthand the inclusion of the thin homogeneous silicon layer

are responsible for the experimental resonance’s be-ing broader than expected from the design. This ob-servation is supported by analysis (with RCWA) thatfits the normal-incidence resonance measured in Fig. 4for d . 0.51 mm and for a residual homogeneous siliconlayer thickness of ,0.045 mm. The theoretical resultsfor the nonzero angle of incidence predicted a second,much narrower resonance near 1.76 1.78 mm. The ef-fect of this second resonance is apparent in the splittingobserved in the experimental results for u ­ 8±. Forsmaller angles of incidence this second resonance wasnot observed, possibly because of the relatively low de-gree of coherence associated with the monochromator.This low coherence was also probably responsible forthe lower-than-theoretical efficiency of the experimen-tal resonances.

In summary, a rectangular-groove strongly modu-lated silicon-on-sapphire guided-mode resonant grat-ing was designed with RCWA. It was found that, incontrast to the weakly modulated gratings describedin the literature, this strongly modulated grating canhave either broad or narrow spectral resonances. Inaddition, the ref lectance resonance is stable as a func-tion of the angle of incidence and does not split fordeviations from the normal incidence as happens inthe weakly modulated resonant gratings. A stronglymodulated grating designed for normal incidence wasfabricated and experimentally tested. The resultingmeasurements clearly demonstrate a spectral reso-nance that is stable with the angle of incidence.

This research was supported in part by grant DAAH-04-96-1-0161 from the Joint Services Electronics Pro-gram and by grant ERC–94-02723 from the NationalScience Foundation.

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