Jon M. Bendickson

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.

Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses

Various integral diffraction methods are systematically unified into a single framework, clearly illustrating the interconnections among the numerous scalar and rigorous formulations. This hierarchical depiction of the integral methods makes clear the specific approximations inherent in each integral method. The scalar methods are compared in detail with a rigorous open-region formulation of the boundary element method (BEM). The rigorous BEM provides a reference method for accurately determining the diffracted fields for both TE and TM incidence. The rigorous BEM and the various scalar methods are then applied to the case of focusing of normally incident plane waves by diffractive cylindrical lenses with f-numbers ranging from f/2 to f/0.5. From the diffracted-field calculations, a number of performance metrics are determined including focal spot size, diffraction efficiency, reflected and transmitted powers, and focal-plane sidelobe power. The quantitative evaluation of the performance of the scalar methods with these metrics allows the establishment, for the first time, of the region of validity of the various scalar methods for this application. As expected, the accuracy of the scalar methods decreases as the f-number of the diffractive lenses is reduced. Additionally, some metrics, particularly the focal-plane sidelobe power, appear to be particularly sensitive to the approximations in the scalar methods, and as a result their accuracy is significantly degraded.

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.

Modeling considerations for rigorous boundary element method analysis of diffractive optical elements.

Critical modeling issues relating to rigorous boundary element method (BEM) analysis of diffractive optical elements (DOEs) are identified. Electric-field integral equation (EFIE) and combined-field integral equation (CFIE) formulations of the BEM are introduced and implemented. The nonphysical interior resonance phenomenon and thin-shape breakdown are illustrated in the context of a guided-mode resonant subwavelength grating. It is shown that modeling such structures by using an open geometric configuration eliminates these problems that are associated with the EFIE BEM. Necessary precautions in defining the incident fields are also presented for the analysis of multiple-layer DOEs.

Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods

The performance characteristics of focusing diffractive mirrors designed with various methods are evaluated by using the rigorous boundary element method. Quantitative results are presented for (1) conventional-zero-thickness mirror designs, (2) alternative-zero-thickness designs that incorporate an off-axis correction factor and (3) finite-thickness designs. For TM polarization, the mirrors designed by using the alternative-zero-thickness method perform considerably worse than those designed by using the conventional-zero-thickness method, which contradicts predictions made in an earlier paper.