Application to the design of guide-mode resonance grating filter with using simulated annealing method

Abstract

Although there are several well -known methods such as RCWA, FMM, for analyzing the diffraction properties of gratings, design of these optical elements with specified spectral properties is commonly a challenging problem. It is relatively not easy for the researchers to design narrow line-with diffraction filters based on guided mode resonance phenomenon with common diffraction algorithm. Simulated Annealing (SA) method is evolutionary, robust technique that has been widely utilized to design optical diffraction components. This method is inspired by the physical process of heating and controlled cooling of metal material to increase the size of its crystals and reduce their defects. The most distinctive features of this method lie in its powerful ability of convergence towards the global minimum in a reasonable computation time and the independence of the initial parameter values. In this paper, first, the physical basis of SA and its mathematical realization are introduced. Then, a Guided-Mode Resonant Grating (GMRG) filters with single layer is designed by using SA algorithm. The central wavelength of GMRG filter is locked at 532nm and its line-width is fixed at 1nm. The plane wave light radiates the grating from air cover with normal incidence. The optimized parameters are refractive indices and thicknesses of high and low material of grating, other parameters are grating period and fill factor of the grating. It is shown from our calculation that an excellent reflection spectrum with narrow line-width, high peak and low sideband can be obtained after optimizing the grating parameters. Next, a double layered GMRG filter with line-width of 4nm, which is relatively easy fabrication in experiment, is designed at central wavelength of 1064nm. The optimized parameters are grating period, groove depth, refractive index of waveguide layer and fill factor respectively. The grating substrate and waveguide layer are Sio2 and Hfo2 respectively, the grating structure is directly etched on the waveguide layer. The above grating values should be included in reasonable ranges in consideration of grating fabrication in our experiment condition. It is demonstrated from the calculations with the parameters obtained from SA optimization algorithm that the peak diffraction efficiency is more than 99% at central wavelength 1064nm and the sideband reflection is depressed at the level bellow 5% in a large wavelength range. Moreover, the parameters of a triple layer GMRG filter structure are also provided with this powerful method. Meanwhile, the results found by SA method are compared with RCWA theory.