### 基于杂化表面等离激元的多层波导布拉格光栅

Multilayer Waveguide Bragg Grating Based on Hybrid Surface Plasmon Polaritons

#### 桂林电子科技大学机电工程学院, 广西 桂林 541004

Abstract
According to the excitation mechanism of hybrid surface plasmon polaritons and the waveguide structure of traditional hybrid surface plasmon polaritons, a multilayer waveguide Bragg grating is proposed. Two low refractive index materials, SiO2 and NaF, are used as the core layer in the structure. At the communication wavelength of 1550 nm, the structure of the grating is studied and optimized for the transmission distance and the mode field limitation ability of the light wave. And the relationship between the grating period number and the reflectivity of light wave is further analyzed. Simulation results show that the transmission distance and the effective mode field area of the Bragg grating are 178.12 μm and 0.203 μm 2, respectively. The structure not only reduces the loss due to the light field limitation at the metal surface, but also reflects relatively strong mode field limitation. The reflectance can reach 71.9% when the grating period number is 60, and the structure has a good filtering characteristic.

## 2 端面结构的设计与优化

#### Fig. 1. End face structure of MWBG and electric field distribution. (a) Structure; (b) electric field distribution along z direction; (c) electric field distribution along y direction

$W(r)=12Red[ωε(r)]dωE(r)2+12μ0H(r)2,(1)$

#### Fig. 2. Relation of Re(neff) and Im(neff) with the thickness of NaF layer

$Aeff=∫∫W(r)dA/{max[W(r)]}。(2)$

## 3 杂化布拉格光栅的设计与分析

$Λ=mλc2neff=mλcneff1+neff2,(3)$

#### Fig. 4. (a) Structure of MWBG Bragg grating and (b) normalized electric field distribution in xz plane

$R=-iκsin(sL')γcosh(sL')+i(β-βc)sinh(sL')2,(4)s=κ2-(β-βc)2,(5)Δλ=λ2cπngκ2+(π/L')2,(6)$

00 11