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Resonant leaky-mode spectral-band engineering and device applications

Y. Ding and R. Magnusson

Open Access Open Access

Abstract

Single-layer subwavelength periodic waveguide films with binary profiles are applied to design numerous passive guided-mode resonance elements. It is shown that the grating profile critically influences the spectral characteristics of such devices. In particular, the symmetry of the profile controls the resonance spectral density. Symmetric profiles generate a single resonance on either side of the second stopband whereas two resonances arise, one on each side of the band, for asymmetric structures. Moreover, the profile’s Fourier harmonic content, along with the absolute value of the grating modulation strength, affects the resonance linewidths and their relative locations. Computed Brillouin diagrams are presented to illustrate many key properties of the resonant leaky-mode spectra in relation to modulation strength and profile symmetry at the second stopband. Associated mode plots elucidate the spatial distribution of the leaky-mode field amplitude at resonance and show that, for small modulation, the mode shape may be simple whereas at higher modulation, the shape appears as a complex mixture of modes. By computing device spectra as function of the modulation strength, the buildup of the final spectral properties is illustrated and the contributions of the various leaky modes clarified. The results presented include wavelength and angular spectra for several example devices including narrow linewidth bandpass filters with extended low sidebands for TE and TM polarization, wideband reflectors for TE and TM polarization, polarizer, polarization-independent element, and a wideband antireflector, all with only a single binary layer with one-dimensional periodicity. These results demonstrate new dimensions in optical device design and may provide complementary capability with the field of thin-film optics.

©2004 Optical Society of America

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Figures (16)
Fig. 1.
Fig. 1. Brillouin diagram illustrating the second stopband for a single-layer waveguide grating with an asymmetric profile. Structural parameters for one period are shown in the inserted schematic where Λ denotes the period, d is the thickness, and n is the refractive index in the various regions (c=cover, s=substrate, l=low, h=high). The fill factors for the grating materials are shown beneath the layer. In the figure, k0=2π/λ where λ is the wavelength in free space, K=2π/Λ, and βR (βI) is the real (imaginary) part of the propagation constant of the leaky mode. The dispersion curve is associated with the TE0 mode and has been transferred to the first Brillouin zone. The dashed curves show the resonance spectrum at normal incidence (not to scale).

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Fig. 2.
Fig. 2. Numerically computed derivative of the propagation constant in Fig. 1.

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Fig. 3.
Fig. 3. Second stop band for a structure with two different modulations. (a) βR and βI for structure with nh=2.8. Only half of the first Brillouin zone is shown; (b) |∂k0/∂βR| and reflectance at normal incidence for structure with nh=2.8 (not to scale). (c) βR and βI for structure with nh=3.3. Only half of the first Brillouin zone is shown; (d) |∂k0/∂βR| and reflectance at normal incidence for structure with nh=3.3 (not to scale). The parameters are: d=0.67µm, Λ=1µm, nc=1, ns=1.48, navg=2.445, and modulation profile nh/nl/nh/nl of 0.397/0.103/0.051/0.449.

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Fig. 4.
Fig. 4. Standing-wave pattern (electric-field amplitude) of the leaky mode at resonance when the field is close to maximum. (a) GMR#3 in Fig. 3(d); (b) GMR#2 in Fig. 3(d). The size of region is ~1.5µm×2µm. The excitation wave has unit amplitude and is incident from the left as shown.

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Fig. 5.
Fig. 5. Spectra of a single-layer bandpass filter for TE polarization. (a) Reflectance of the filter with the parameters shown in the inserted schematic. (b) Angular spectra at the central wavelength.

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Fig. 6.
Fig. 6. Spectra of the bandpass filter for TE polarization. (a) Reflectance spectra for different modulations with the effective index of the waveguide kept constant. (b) Transmittance of the filter on a logarithmic scale.

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Fig. 7.
Fig. 7. Standing-wave pattern (electric-field amplitude) of the leaky mode at resonance when the field is close to maximum. (a) GMR TE1,1 at short wavelength (upper bandedge) for nh=2.8; (b) GMR TE1,1 at long wavelength (lower bandedge) for nh=2.8. (c) GMR TE1,1 at short wavelength for nh=3.48; (d) GMR TE1,1 at long wavelength for nh=3.48. The size of region is ~2.5µm×2µm.

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Fig. 8.
Fig. 8. Spectra of a bandpass filter for TM polarization. (a) Reflectance of the filter. Profile parameters are shown in the inserted schematic. (b) Angular spectra at central wavelength.

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Fig. 9.
Fig. 9. Standing-wave pattern (magnetic-field amplitude) of the leaky mode at resonance when the field is close to maximum. (a) GMR TM1,1 at short wavelength; (b) GMR TM1,1 at long wavelength. The size of region is ~2.5µm×2µm. The incident beam with unit amplitude approaches from the left side.

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Fig. 10.
Fig. 10. Spectra of a wideband reflector for TE polarization. (a) Reflectance of the filter. Profile parameters are shown in the inserted schematic. (b) Angular spectra at central wavelength. (c) Reflectance spectra for differing modulation strengths with the effective index of the waveguide kept constant. (d) Transmittance of the filter on a log scale.

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Fig. 11.
Fig. 11. Spectra of a wideband reflector for TM polarization. (a) Reflectance of the filter. Profile parameters are shown in the inserted schematic. (b) Angular spectra at central wavelength. (c) Reflectance spectra for different modulation with the effective index of the waveguide kept constant. (d) Transmittance of the filter on a log scale.

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Fig. 12.
Fig. 12. Magnetic field patterns of the leaky modes at resonance. (a) Pattern of TM1,1&2, short wavelength side (b) Pattern of TM1,2, long wavelength side (c) Pattern of TM1,1 (d) Pattern of TM1,0.

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Fig. 13.
Fig. 13. Spectra of a wideband polarizer. (a) Reflectance of the polarizer. Profile parameters are shown in the inserted schematic. (b) Angular spectra at central wavelength. (c) TE reflectance spectra for different modulation with the effective index of the waveguide kept constant. (d) TM transmittance of the polarizer on a log scale.

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Fig. 14.
Fig. 14. Resonant leaky-mode magnetic field pattern at resonance. (a) Pattern for TM1,1, short wavelength side (b) Pattern for TM1,1, long wavelength side.

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Fig. 15.
Fig. 15. Spectra of a polarization-independent reflector with asymmetric grating profile. (a) Reflectance with TE and TM incidence with nh=3.48. (b) Transmittance for TE and TM incidence with nh=3.48. (c) TE spectrum with nh=2.8. (d) TM spectrum with nh=2.8.

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Fig. 16.
Fig. 16. Spectra of a wideband antireflector for TM polarization. (a) Reflectance of the element. Profile parameters are shown in the inserted schematic. (b) Angular spectra at central wavelength. (c) Reflectance of the filter on a log scale. (d) Angular spectra on a log scale

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