David L. Brundrett

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

Guided-mode resonant grating filters have numerous applications. However, in weakly modulated gratings designed for use at normal incidence, the filtering resonance of these subwavelength-period devices splits for angles of incidence that are even slightly off normal incidence. Strongly modulated gratings are designed that essentially overcome this practical problem near normal incidence. In addition, these gratings can have, by design, either broad or narrow spectral characteristics. An experimental demonstration (1.5-2.0-mu m wavelength range) of such a normal-incidence guided-mode resonant silicon grating upon a sapphire substrate is presented. The measured reflection resonance had a FWHM of 67-100 nm for angles of incidence of 0-8 degrees and peak efficiency of ~80% .

HOMOGENEOUS LAYER MODELS FOR HIGH-SPATIAL-FREQUENCY DIELECTRIC SURFACE-RELIEF GRATINGS : CONICAL DIFFRACTION AND ANTIREFLECTION DESIGNS

The validity of various homogeneous layer models for high-spatial-frequency rectangular-groove (binary) dielectric surface-relief gratings is examined for both nonconical and conical diffraction. In each model the grating is described by a slab of uniaxial material with its optic axis parallel to the grating vector. The ordinary and principal extraordinary indices of the slab depend on the grating filling factor, the substrate and cover refractive indices, and the ratio of the wavelength to the grating period. These indices can be determined by solving two transcendental equations. Higher-order indices are defined as the exact solution to these equations. Second-order indices (second-order dependence on the wavelengthto- period ratio) and first-order indices (no dependence on the wavelength-to-period ratio) are defined by approximate solutions to these equations. Layer models using higher-order and second-order indices are shown to be accurate for high-spatial-frequency gratings, even at wavelength-to-period ratios near the onset of higher-order propagating diffracted waves. These models are used to design example antireflecting gratings on silicon substrates, including designs for conical incidence. All designs are evaluated and optimized by exact rigorous coupled-wave analysis.

Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence

A comparative study of the reflection spectral resonances in weakly and strongly modulated subwavelength gratings is presented. The effects of strong modulation in resonant subwavelength gratings have been largely ignored in the literature. We show that the spectral stability of resonances as a function of angle of incidence around normal can be greatly enhanced with strongly modulated gratings while the desirable narrow line-width associated with weakly modulated gratings is still maintained.

Polarizing mirror/absorber for visible wavelengths based on a silicon subwavelength grating: design and fabrication

A one-dimensional 280-nm period silicon grating designed to exhibitpolarization-dependent reflection or antireflection behavior at visiblewavelengths has been fabricated and tested. For normally incident575-nm light, this grating reflects less than 3% of the incidentradiation polarized perpendicular to the grating grooves andapproximately 23% of the orthogonal polarization. To demonstratethe gratings broadband characteristics, reflectance measurements arepresented over the free-space wavelength range 475 nm < lambda(0) < 800 nm, for angles of incidence in the range 0 degrees < theta < 40 degrees , for polarization parallel and perpendicular to thegrating grooves, and for planes of incidence parallel and perpendicularto the grooves. A description of the fabrication process is alsogiven.

Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings

The effects of finite beams and finite gratings on the performance of guided-mode resonant subwavelength gratings are characterized by using the rigorous boundary element method. The gratings are strongly modulated, have a finite number of periods, and are illuminated by normally incident Gaussian beams. Quantitative results are presented for silicon-on-sapphire resonant gratings and gallium arsenide-aluminum arsenide resonant gratings.

Subwavelength transmission grating retarders for use at 10.6 μm

Designs are given for gallium-arsenide subwavelength grating retarders operating at 10.6 μm. A design procedure is detailed that takes into account the reflections at all surfaces and that uses numerical optimization to improve the transmittance of the retarders to nearly 100%. It is shown that the homogeneous uniaxial layer model for subwavelength gratings can be used to provide starting points for the Nelder-Mead simplex optimization, obviating the need for stochastic optimization techniques such as simulated annealing. An analysis of the designs with respect to wavelength, angle of incidence, and fabrication tolerances indicates that such grating retarders will perform favorably compared with commercial alternatives.

Rigorous coupled-wave analysis and applications of grating diffraction

A review of the rigorous coupled-wave analysis (RCWA) as applied to the diffraction of electromagnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and for conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy and loss can be incorporated under the same formalism. Volume and surface-relief gratings can be analyzed. Convergence analysis is presented for rectangular-groove surface-relief dielectric and metallic gratings. The role of multilevel surface-relief and holographic gratings in the substrate-mode photonic interconnect configuration is investigated. Results obtained using the RCWA are presented for 1-, 2-, 4-, 8-, and 16-level surface-relief gratings and are compared with the predictions of the simple scalar model. Two practical configurations are analyzed: (a) a silicon substrate at a freespace wavelength of 1.3 microns and (b) a glass substrate at a freespace wavelength of 0.84 microns. Equivalent holographic gratings are also designed and compared. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the grating filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. It is shown how these models result from the eigenvalue equation of the boundary-value rectangular-groove grating problem. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared.