We report here on the theoretical performance of blazed binary diffractive elements composed of pillars carefully arranged on a two-dimensional grid whose period is smaller than the structural cutoff. These diffractive elements operate under unpolarized light. For a given grating geometry, the structural cutoff is a period value above which the grating no longer behaves like a homogeneous thin film. Because the grid period is smaller than this value, effective-medium theories can be fully exploited for the design, and straightforward procedures are obtained. The theoretical performance of the blazed binary elements is investigated through electromagnetic theories. It is found that these elements substantially outperform standard blazed echelette diffractive elements in the resonance domain. The increase in efficiency is explained by a decrease of the shadowing effect and by an unexpected sampling effect. The theoretical analysis is confirmed by experimental evidence obtained for a 3λ-period prismlike grating operating at 633 nm and for a 20°-off-axis diffractive lens operating at 860 nm.

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Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff

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.

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

We have successfully demonstrated an integrated optical system for collecting the fluorescence from a trapped ion. The system, consisting of an array of transmissive, dielectric micro-optics and an optical fiber array, has been intimately incorporated into the ion-trapping chip without negatively impacting trapping performance. Epoxies, vacuum feedthrough, and optical component materials were carefully chosen so that they did not degrade the vacuum environment, and we have demonstrated light detection as well as ion trapping and shuttling behavior comparable to trapping chips without integrated optics, with no modification to the control voltages of the trapping chip.

Integration of fluorescence collection optics with a microfabricated surface electrode ion trap

Publisher Summary This chapter discusses the electromagnetic approach for the diffractive optics. The chapter focuses on the domain of diffractive optics in which rigorous electromagnetic theory is necessary or useful. The chapter describes one approach to rigorous analysis of gratings. The chapter discusses the linear gratings, which employ the first and zeroth diffraction orders. Diffractive elements obtained by modulating these gratings are also discussed in the chapter.. The chapter describes the linear diffraction gratings, which produce two transmitted or reflected orders, the zeroth and (minus) first orders. Together with improved fabrication technology, the use of rigorous theory has pushed diffractive optics beyond the limitations of the paraxial approximation, and therefore significantly broadened its applicability in optical engineering.

V Diffractive optics: Electromagnetic approach

We describe a local linear grating model that permits estimation of the diffraction efficiency of high-numerical-aperture two-dimensional circular lenses with one-dimensional rigorous coupled-wave analysis. The model is self-consistent and is consistent with the scalar theory that results for low-numerical-aperture lenses. The accuracy of the model increases with the number of Fresnel zones of the lens. On the basis of this model we optimize the discrete phase profile of the lens for the maximum diffraction efficiency, using the random search method. The TE and the TM modes are optimized simultaneously. Their phase variations as functions of local grating periods are removed by cyclic shifts of the grating profiles, resulting in constructive summation at the focus and high diffraction efficiency.

Dazeng Feng

Papers

Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled-wave theory