Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements

Abstract

We present an optimization-based synthesis algorithm for the design of diffractive optical elements (DOE's) that are finite in extent, have subwavelength features, and are aperiodic. The subwavelength nature of the DOE's precludes the use of scalar diffraction theory, and their finite extent and aperiodic nature prevents the use of coupled-wave analysis. To overcome these limitations, we apply the boundary element method (BEM) as the propagation model in the synthesis algorithm. However, the computational costs associated with the conventional implementation of the BEM prevent the design of realistic DOE's in reasonable time frames. Consequently, an alternative formulation of the BEM that exploits DOE symmetry is developed and implemented on a parallel computer. Designs of finite extent, subwavelength, and aperiodic DOE's, such as a lens and a focusing beam splitter, are presented.

Diffractive micro-optical elements for implementing hollow beam and bi-focus simultaneously

“…Instead, vectorical diffraction theory should be employed to analyze the DMOEs with sub-micrometer-sized structure [12]. Considerable investigations [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] into the design [22], the analysis [12][13][14][15][16][17][18][19][20][21][23][24][25][26][27][28][29][30][31][32], and the fabrication [33] of various DMOEs have been presented recently. In this paper, we design a diffractive micro-optical element with sub-micrometer-sized structure by introducing a half-p-phase shifting scheme to achieve bi-focus and hollow beam simultaneously.…”

Optimal Design and Fabrication of Fine Diffractive Optical Elements Using Proximity Correction with Electron-Beam Lithography

“…Prather et al showed that a multilevel diffractive lens with a small F-number (<1.5) should be analyzed by rigorous electromagnetic wave analysis. (Prather et al, 2001) In some reports, an optimizing design for highly efficient diffractive lenses with a small F-number by simulated quenching (Prather et al, 1998) and Gerchberg-Saxton algorithm (Di et al, 2003) is described. Moreover, a diffractive lens consisting of a subwavelength grating structure is suggested.…”

“…Moreover, a diffractive lens consisting of a subwavelength grating structure is suggested. (Prather et al, 1998) These optical design methods are based on only an electromagnetic analysis without restrictions on fabrication limits; thus, it may be difficult to fabricate the designed grating profile, particularly for short-period gratings. In this chapter, we demonstrate a unified design method optimizes the electron dose and grating profiles simultaneously to obtain the desired diffraction efficiency under the restriction of the proximity effect.…”

Application of the boundary-element method to the interaction of light with single and coupled metallic nanoparticles

“…The present implementation is based on some pioneering work conducted by Prather et al, 12,13 who applied the method to Fresnel lenses.…”