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Abstract—A guided-mode resonance transmission filter is de- monstrated experimentally. A five-layer fiberglass/air structure with a waveguide-grating in the ...



Experimental Verification of Waveguide-Mode Resonant Transmission Filters S. Tibuleac, Student Member, IEEE, P. P. Young, Student Member, IEEE, R. Magnusson, Senior Member, IEEE, and T. R. Holzheimer, Senior Member, IEEE

Abstract—A guided-mode resonance transmission filter is demonstrated experimentally. A five-layer fiberglass/air structure with a waveguide-grating in the center layer is designed, fabricated, and tested. A close match between theoretical and experimental spectral characteristics is found over the spectral range of 4–20 GHz. Guided-mode resonance transmission peaks occur at frequency locations which are in excellent agreement with theoretical predictions. Index Terms— Bandpass filters, dielectric waveguides, frequency selective surfaces, gratings, guided-mode resonance effect, periodic structures, waveguide filters.



UIDED-MODE resonance (GMR) effects in dielectric waveguide gratings are attracting increasing interest due to their potential of generating high-efficiency reflection and transmission filters with unique properties [1]–[10]. In the optical spectral region, GMR reflection filters utilizing various materials, layer configurations, and fabrication techniques have been experimentally demonstrated exhibiting advantageous features such as peak reflectances exceeding 98% [3], narrow or large linewidths [4], low sidebands [5], extended filter ranges [3], and polarization sensitivity or independence [6]. Experiments on GMR reflection filters have also been reported in the microwave [7] and millimeter-wave spectral ranges [8]. The possibility of using GMR effects to generate transmission filters has been demonstrated theoretically utilizing structures with two gratings enclosing a number of homogeneous layers in a high-reflectance design [9]. More recently, it was shown that a GMR transmission filter can be realized in a simpler configuration with a single grating inserted in the center of a high-reflective stack of homogeneous layers [10]. However, to the best of our knowledge, GMR transmission filters have not yet been experimentally realized. The purpose of the present work is to design, build, and test a waveguide-grating device that exhibits transmission resonances in the frequency range of 4–20 GHz.

Manuscript received August 11, 1998. This work was supported in part by Raytheon Systems Company and by the Texas Advanced Technology Program under Grant 003656-042. S. Tibuleac, P. P. Young, and R. Magnusson are with the Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX 76019 USA. T. R. Holzheimer is with Raytheon Systems Company, Greenville, TX 75403 USA. Publisher Item Identifier S 1051-8207(99)02007-3.

Fig. 1. Theoretical spectral response of a five-layer guided-mode resonance transmission filter for a TE-polarized normally incident plane wave (a). A cross section of the device indicating the layer structure is shown in the inset. The parameters of the waveguide grating are: 3 = 2:0 cm, d = 0:3175 cm, f = 0:5; "H = 4:4944 (G10 fiberglass), "L = 1:0 (air). Curve (b) represents the transmittance of the same structure with the central (grating) layer replaced by a homogeneous layer with dielectric constant " = 2:7472:

II. DESIGN AND FABRICATION OF A GMR TRANSMISSION FILTER The guided-mode resonance effect occurring in waveguides containing diffractive structures generates sharp variations in the intensity of the observable propagating waves as the wavelength or angle of incidence is varied [1], [2]. To obtain high-efficiency resonance effects, subwavelength gratings are employed such that only zero-order forward- and backwarddiffracted waves are allowed to propagate. Structures with arbitrary layer thicknesses and dielectric constants typically exhibit resonance peaks with asymmetric lineshapes and high sidebands. Selecting the thicknesses and dielectric constants of the layers for antireflection (AR) or high reflection (HR) conditions yields high-efficiency reflection or transmission filters, respectively. A single-grating transmission filter can be obtained by superimposing the high-efficiency resonance transmittance peak on the low-transmittance region achieved by alternating homogeneous layers of high- and low-dielectric constant materials with quarter-wavelength thicknesses [10]. A transmission filter designed to operate in the 10–14 GHz frequency range was implemented with G10 fiberglass and air as presented schematically in the inset of Fig. 1. Low transmittance near the filter’s spectral peak is achieved by

1051–8207/99$10.00  1999 IEEE



Fig. 2. Experimental setup for transmittance measurements of GMR filters in an anechoic chamber with microwave lenses used to collimate the wave incident on the grating structure and to focus the diffracted wave on the receiver.

choosing the thicknesses of the layers to be approximately equal to quarter-wavelength at 12 GHz. The grating period cm) is selected to generate a guided-mode resonance ( that falls within the high-reflectance spectral range of the structure. The dimension of the waveguide grating is 76.2 cm (perpendicular to the grating vector) by 91.4 cm (parallel to the grating vector) thus containing 45 grating periods. The theoretical frequency response of the device with a TE-polarized (i.e., electric vector normal to the page) wave at normal incidence is illustrated in Fig. 1 for the spectral range 4–20 GHz. The calculations are performed with rigorous coupled-wave analysis [11] assuming plane waves incident on the structure and infinite lateral extent of the waveguide grating. Guided-mode resonance peaks with efficiencies approaching 100% are obtained for a lossless waveguide grating GHz and GHz. at frequencies Fig. 3. Measured spectral transmittance of the G10 fiberglass waveguide grating with the structure and theoretical response shown in Fig. 1.

III. EXPERIMENTAL RESULTS The experimental setup for spectral measurements of the waveguide-grating transmittance in an anechoic microwave chamber is illustrated in Fig. 2. The wavefront emitted by the transmitter horn antenna is collimated by a plano-convex teflon cm placed with the flat side lens with a diameter facing the source, at a distance from the transmitter equal to cm. Thus, an approximately the lens focal length, planar wavefront impinges on the GMR filter. The zeroorder forward-diffracted wave is focused on the receiver horn antenna by a second teflon lens identical to the first, located at its focal length away from the receiver. The transmittance of the filter is calculated by normalizing the microwave power measured with this setup (Fig. 2) with the power measured in the chamber without the filter. The measured filter transmittance is shown in Fig. 3. Guided-mode resonance peaks are found at frequencies GHz and GHz agreeing with the theoretical response of Fig. 1. The transmittance values at resonance are 22.9% ( 6.4 dB) and 60.3% ( 2.2 dB), respectively. The rapid oscillations in the measured transmittance spectrum are due to interference effects from multiple reflections between components that are placed in the path of the microwave beam.

Fig. 4. Experimental data of Fig. 3 with transmittance values averaged over 20 frequency points and theoretical response of the waveguide grating of Fig. 1 with the parameters: 3 = 2:03 cm, f = 0:5; d = 0:31 cm, "H = 4:4944; "L = 1:0; and tan  = 0:01:

A comparison between theoretical and experimental data is presented in Fig. 4. A smoother experimental response


curve is obtained by replacing each point of Fig. 3 with the average transmittance of the 20 neighboring frequency points. The reduced peak transmission in the measured data (Fig. 3) compared to the theoretical predictions (Fig. 1) is attributed mostly to bulk absorption and scattering losses in the fiberglass. Therefore, a value of the loss tangent tan is used in the theoretical calculations to yield the close fit between the experiment and theory presented in Fig. 4. The theoretical plot of Fig. 4 is generated with a layer thickness cm smaller by 0.0075 cm compared to the values used in Fig. 1, but well within the thickness tolerance of 0.03 cm specified by the manufacturer of the G10 plates. cm) was The grating period used in the calculation ( determined through measurement on the waveguide grating after assembly. The spectral measurements of the waveguide-grating structure indicate the presence of GMR transmission peaks at frequencies near those predicted by theory. The experimental transmittance spectra away from resonance are in excellent agreement with numerical results for the entire frequency range. At and near resonance, the parametric sensitivity is increased. In particular, if the structure is not perfectly flat, or if the wave has a small, nonzero angle of incidence, a splitpeak resonance arises; see Figs. 3 and 4. This is evident in the experimental data but is not shown by the theoretical curve at normal incidence [7]. The high resonance peak in Fig. 4 rides on the background Fabry–Perot response, as illustrated in Fig. 1. It is expected that higher peak transmittance can be obtained by utilizing materials with lower losses, higher degrees of homogeneity, and with improved thickness uniformity. Use of materials with higher dielectric constants can yield GMR filters with larger linewidths and lower sidebands.


ACKNOWLEDGMENT Measurement assistance by the Raytheon Systems Company and Garland Antenna Laboratory personnel, and technical assistance by M. I. Jones of Lockheed Martin, Fort Worth, TX, is gratefully acknowledged.

REFERENCES [1] R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett., vol. 61, no. 9, pp. 1022–1024, Aug. 1992. [2] S. S. Wang and R. Magnusson, “Theory and applications of guidedmode resonance filters,” Appl. Opt., vol. 32, no. 14, pp. 2606–2613, May 1993. [3] Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “Highefficiency guided-mode resonance filter,” Opt. Lett., vol. 23, no. 19, pp. 1556–1558, Oct. 1998. [4] D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: Design and experimental demonstration,” Opt. Lett., vol. 23, no. 9, pp. 700–702, May 1998. [5] R. Magnusson, D. Shin, and Z. S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett., vol. 23, no. 8, pp. 612–614, Apr. 1998. [6] S. Peng and G. M. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett., vol. 21, no. 8, pp. 549–551, Apr. 1996. [7] R. Magnusson, S. S. Wang, T. D. Black, and A. Sohn, “Resonance properties of dielectric waveguide gratings: Theory and experiments at 4-18 GHz,” IEEE Trans. Antennas Propagat., vol. 42, pp. 567–569, Apr. 1994. [8] V. V. Meriakri, I. P. Nikitin, and M. P. Parkhomenko, “Frequency characteristics of metal-dielectric gratings,” Radiotekhnika i Elektronika, no. 4, pp. 604–611, 1992. [9] R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt., vol. 34, no. 35, pp. 8106–8109, Dec. 1995. [10] S. Tibuleac and R. Magnusson, “Diffractive narrow-band transmission filters based on guided-mode resonance effects in thin-film multilayers,” Photon. Techol. Lett., vol. 9, pp. 464–466, Apr. 1997. [11] T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE, vol. 73, pp. 894–937, May 1985.

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