含支节金属-介质-金属型等离激元波导的传输线计算模型

doi:10.19596/j.cnki.1001-246x.8629

摘要/Abstract

摘要：

为了揭示含支节金属-介质-金属(MIM)型表面等离激元(SPPs)波导透射率谱线的形成机理, 提升基于MIM波导支节结构的微纳光学器件结构设计与性能仿真的效率, 利用MIM波导与微波传输线之间导模特征的相似性, 基于菲涅耳反射公式提出MIM波导支节的修正传输线计算模型。该模型能够有效地计算SPP波在MIM波导支节末端反射产生的附加相位延迟, 从而更加精确地计算MIM波导侧向连接的支节腔对主波导中SPPs模式透射率的调制作用。采用修正传输线模型计算MIM波导侧向耦合单、双支节腔的透射率谱曲线, 并与有限元仿真结果进行对比。结果显示该修正解析模型与经典传输线模型相比, 在预测透射率极小值波长位置方面拥有更高的精度; 同时与数值仿真过程相比, 该模型又具有更高的计算效率。

关键词: 表面等离激元, 金属-介质-金属波导, 支节谐振腔, 传输线模型

Abstract:

Based on the well-known analogy of propagation modes between metal-insulator-metal (MIM) waveguides and microwave transmission lines, an improved transmission line model (ITLM) have been proposed to describe reflection coefficients of a MIM waveguide stub. The Fresnel formula have been employed to predict the phase shift resulting from the reflection of surface plasmon polaritons (SPP) from the stub's end, which allows the ITLM to describe the influence of the stub-shaped resonators arranged in the side-coupled configuration on the transmission spectrum of main waveguide more precisely. In this paper, the improved transmission line models of MIM waveguide side coupled to single stub and double-side symmetric stubs have been proposed, and the predicted transmission spectrum by the ITLM is well agreed with simulation results of the finite element method. Specifically, transmission minimum predicted by ITLM is more close to that calculated by numerical methods than the classical transmission line model. Moreover, it is verified that ITLM possess much higher efficiency in calculating the transmission spectrum of the MIM waveguide connected with stub-shaped resonators than the finite element method employed in this work.

Key words: surface plasmons polaritons, metal-insulator-metal waveguides, stub-shaped resonator, transmission line model

关建飞, 陈陶. 含支节金属-介质-金属型等离激元波导的传输线计算模型[J]. 计算物理, 2023, 40(4): 473-481.

Jianfei GUAN, Tao CHEN. Transmission Line Computation Model for Metal-Insulator-Metal Plasmonic Waveguide Connected with Stub-shaped Resonator[J]. Chinese Journal of Computational Physics, 2023, 40(4): 473-481.

图/表 8

图1 MIM型波导支节及其等效传输线模型(a)单端口MIM波导支节示意图；(b)等效的传输线支节模型；(c)带纯电抗负载的传输线支节模型；(d)引入长度增量的终端短路传输线支节模型

Fig.1 Schematic of a single-stub structure and equivalent transmission line model(TLM) (a) schematics of MIM waveguide stub; (b) equivalent TLM terminated by the impedance Zl; (c) approximate TLM terminated by the reactance Xl; (d) revised approximate TLM with an extend length Δd terminated by a short circuit

图2 MIM波导支节末端界面反射SPP波强度反射率及δϕ的变化曲线(a)强度反射率；(b)δϕ

Fig.2 Variation curves of intensity reflectivity and δϕ to the reflection of SPP on MIM stub end (a) intensity reflectivity; (b) δϕ

图3 Ag-air-Ag等离激元波导中SPP波传输常数随波长的变化规律(a)实部；(b)波导波长；(c)虚部；(d)传输距离

Fig.3 Varization of SPPs propagation constant with wavelength in Ag-air-Ag waveguide (a) real part of β; (b) waveguide wavelength; (c) imaginary part of β; (d) propagation length

图4 含单支节的MIM波导模型及其传输线示意图(a)含支节MIM波导；(b)等效传输线模型

Fig.4 Schematic of MIM waveguide with single-stub and its equivalent transmission line (a) MIM waveguide with single stub; (b) equivalent transmission line model

图5 含单支节MIM波导透射率随支节深度d1的变化曲线, 入射波长为(a)800 nm；(b)1550 nm

Fig.5 Transmissivity vs stub depths d1 for MIM waveguide with single stub (a) λ=800 nm; (b) λ=1550 nm

图6 含双支节的MIM波导模型及其等效传输线示意图(a)含双支节MIM波导；(b)等效传输线模型

Fig.6 Schematic of MIM waveguide with double stubs and its equivalent transmission line (a) MIM waveguide with double stubs; (b) equivalent transmission line model

图7 含双支节MIM波导透射率随支节深度的变化规律曲线，入射波长为(a)800 nm；(b)1 550 nm

Fig.7 Transmissivity vs stub depths for MIM waveguide with symmetric double stubs (a) λ=800 nm; (b) λ=1 550 nm

图8 含支节结构的MIM波导透射率谱(a) 单支节；(b)双支节

Fig.8 Transmission spectra of MIM waveguide with stub resonators (a) single side stub; (b) symmetric double-side stubs

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