Local density of optical states of an asymmetric waveguide grating at photonic band gap resonant wavelength

Abstract

ABSTRACT We have investigated the characteristics of local density of optical states (LDOS) at photonic band gap resonant wavelength of an asymmetric waveguide grating based on Green’ s function formulation. It is found that the LDOS of the considered structure exhibits different characteristics in its localization between the upper and lower resonant wavelengths of the corresponding photonic band gap edges. Keywords: Local density of optical states, waveguide grating, Green’s function method, resonant state. 1. INTRODUCTION In recent years, the asymmetric waveguid e grating (WG) structure in the form of asymmetric corrugated slab waveguide has been intensively used in integrated optical device for sensor application [1]. The existence of photonic band gap (PBG) in an asymmetric WG, where light in certain range of wavelength cannot propagates, has been well studied [2]. The wavelength variation of resonant wavelengths at PBG edges are usually considered in sensor device due to its ability to detect the change of refractive index of the surrounding material. Recently also, it was reported the characteris tics of energy confinement, scattering loss and group velocity of asymmetric WG at resonant states of the correspond ing PBG [3]. It was shown that for increasing number of teeth, the group velocity and energy confinement can be enhanced significantly without affecting the scattering loss on both upper and lower resonant states. In the meantime, groove depth variation exhibited different characteristics between both resonant states. It is well known that the number of teeth as well as groove depth that lead to the variation of the corresponding parameters affect significantly its sensitivity. On the other hand, it is well known that one of the important properties of optical structure is its ability to accommodate photon eigenmodes at specific location inside the asymmetric WG. This property is represented by the so called local density of optical states or LDOS. There are several ways to calculate LDOS e.g. [4, 5, 6]. One of them is through Green’s function method in the form of Dyson formulation [6]. In this method the corresponding LDOS can be calculated directly without calculating the electromagnetic field first as needed in the method given in ref. [4,5]. Unlike finite-difference scheme, this met hod does not need boundary condition. Following the results of ref. [3], in this report we discuss the characteristics of LDOS of the associated asymmetric WG structure. Similar to that report, we employ the same Green’s function method to calculate the related LDOS. We will discuss the dynamical characteristics of LD OS of the considered asymmetric WG w ith respect to the variation of number of teeth and groove depth showing the different behavior between the upper and lower resonant states.