Numerical modeling and electromagnetic resonant modes in complex grating structures and optoelectronic device applications

An extended surface impedance boundary condition algorithm is developed that allows for the optical properties of a wide variety of complex one-dimensional periodic grating structures to be modeled. Wood-Rayleigh anomalies, diffraction, and electromagnetic resonance modes including horizontally oriented surface plasmons and vertical surface resonances are identified and described as well as analyzing their structural and geometrical dependencies. Methods to combine these modes to produce hybrid modes that channel and localize light are described. Application of these modes to metal-semiconductor-metal photodetectors (MSM-PD) is discussed and an example silicon-based MSM-PD with over 30 GHz bandwidth and 0.3 A/W responsivity is described.

I. Introduction

Electromagnetic resonances with dramatic characteristics have been observed and analyzed in lamellar gratings and other periodically patterned structures by many researchers for quite some time. Research into the phenomenon of “anomalous” transmission and electromagnetic resonances in periodic structures increased after Ebbesen et al. reported that a two-dimensional periodic array of holes can transmit a higher proportion of light at certain wavelengths and angles of incident than the ratio of the area of the holes relative to the total area of the film. In other words, the incident light seems to be “channeled” through the holes [1], [2]. Anomalous transmission, absorption and other effects caused by electromagnetic resonance modes and diffraction have also been observed in one–dimensional (1-D) periodic grating structures including reflection and transmission gratings [3] [4]–[13]. Surface plasmons (SPs) have been suggested as playing a dominant role in these resonances but there is still considerable disagreement within the research community and several theories have recently been put forth suggesting alternative views [14]. One increasingly accepted view of the mechanism responsible for enhanced transmission is the coupling of Wood–Rayleigh (WR) anomalies on the (top layer)/contact and contact/(bottom layer) interfaces via a vertical surface resonant mode in the grooves of the grating [14], [15]. This view also states that horizontal SP modes with momentum parallel to the (top layer)/contact and contact/(bottom layer) interfaces actually inhibit transmission [14]. Even though there is not a consensus on the physical mechanism responsible for enhanced transmission, there are several numerical modeling techniques that calculate the optical characteristics of these structures, without regard to the proper identification of the excited optical modes. These techniques include rigorous coupled plane wave (RCPW) techniques [8]–[13], integral techniques [17]–[19], finite difference time domain techniques [20], an exact modal method [21], [22], and a modal method [3] [4]–[7] that uses a surface impedance boundary condition assumption (SIBC).