Optical Response to Submicron Digital Elements Simulated by FDTD Wavelets with Refractive Impulse

Accurate simulation from digital, submicron, optical elements is obtained by finite difference time domain (FDTD) results that are phase analyzed as sources for Huygens wavelets on fine scales much shorter than the wavelength used. Results, from the MIT electromagnetic evaluation program, are renormalized by a method here called “refractive impulse.” This is valid for polarized responses from digital diffractive and focusing optics. The method is employed with plane wave incidence at any angle or with diverging or converging beams. It is more systematic, more versatile, and more accurate than commercial substitutes. 1. Introduction Modern optical components train submicron wavelengths through yet smaller optical diffractive and imaging elements [1]. Meanwhile, digitized optics enables novel applications with asymmetric diffractive and focusing components and with holographic systems. Classical wave theory can indicate only coarse descriptions of the response, though several techniques have been described that address the problem. For example, attempts at coupled-wave approaches [2–4] are typically limited in configuration and approximate in application. Generally, the solution requires integrations or summations in three dimensions, including the profile of an optical component. Commercial software, typically, attempts simulation of the optics of microelements by adapting dynamical diffraction [2–4]. This adaptation involves treating a two-dimensional grating as if it were a three-dimensional crystal. However the method is inappropriate for many reasons and the predictions for diffracted intensities cannot be better than 50% accurate. The law of diffraction of light, having wavelength , from a plane grating, of spacing , is given by [5] where is the order and is the scattering angle. Diffraction from three-dimensional crystals is quite different. Bragg’s law gives which approximates to when as in transmission electron microscopy. However, the interplanar spacing in Bragg diffraction becomes multivalued and is peculiar for each diffracted beam following the method of indexation, , , [4]. Moreover, the scattering angle is approximately twice the Bragg angle. Unlike diffraction from gratings, Bragg diffraction requires the angle of incidence to change when high orders are measured. There are yet further fundamental differences that are overlooked in the commercial software. Bragg diffraction is not refracted since there is only one zero order beam and it lies in the direction of incidence; all Bragg diffraction is specular, while each diffracted beam has