## Inverse diffraction grating of Maxwell’s equations in biperiodic structures |

Optics Express, Vol. 22, Issue 4, pp. 4799-4816 (2014)

http://dx.doi.org/10.1364/OE.22.004799

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### Abstract

Consider a time-harmonic electromagnetic plane wave incident on a perfectly conducting biperiodic surface (crossed grating). The diffraction is modeled as a boundary value problem for the three-dimensional Maxwell equation. The surface is assumed to be a small and smooth deformation of a planar surface. In this paper, a novel approach is developed to solve the inverse diffraction grating problem in the near-field regime, which is to reconstruct the surface with resolution beyond Rayleigh’s criterion. The method requires only a single incident field with one polarization, one frequency, and one incident direction, and is realized by using the fast Fourier transform. Numerical results show that the method is simple, efficient, and stable to reconstruct biperiodic surfaces with subwavelength resolution.

© 2014 Optical Society of America

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(290.3200) Scattering : Inverse scattering

(180.4243) Microscopy : Near-field microscopy

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: January 3, 2014

Revised Manuscript: February 5, 2014

Manuscript Accepted: February 6, 2014

Published: February 21, 2014

**Citation**

Gang Bao, Tao Cui, and Peijun Li, "Inverse diffraction grating of Maxwell’s equations in biperiodic structures," Opt. Express **22**, 4799-4816 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4799

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