Finite element modeling of electromagnetic properties in photonic bianisotropic structures

doi:10.1007/s12200-021-1213-5

Front. Optoelectron.

2021, Vol. 14

Issue (2) : 148-153 https://doi.org/10.1007/s12200-021-1213-5

RESEARCH ARTICLE

Finite element modeling of electromagnetic properties in photonic bianisotropic structures

Zhongfei XIONG¹, Weijin CHEN^1,², Zhuoran WANG¹, Jing XU^1,³, Yuntian CHEN^1,³(

)

¹. School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China
². Department of Electrical and Computer Engineering (ECE), National University of Singapore, Singapore 117583, Singapore
³. Wuhan National Laboratory of Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is self-adjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropy-dependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarization-dependent optical insulator, are also consistent with the theoretical analyses.

Keywords bianisotropic finite element method adjoint

Corresponding Author(s): Yuntian CHEN

Just Accepted Date: 13 May 2021 Online First Date: 13 July 2021 Issue Date: 14 July 2021

Cite this article:

Zhongfei XIONG,Weijin CHEN,Zhuoran WANG, et al. Finite element modeling of electromagnetic properties in photonic bianisotropic structures[J]. Front. Optoelectron., 2021, 14(2): 148-153.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-021-1213-5
https://academic.hep.com.cn/foe/EN/Y2021/V14/I2/148

Fig.1 (a) Schematic diagram of simulating reflection and transmission spectrums of bianisotropic slab with normal incident light. A bianisotropic slab (dark gray) is surrounded by air (light gray), the boundaries are vertical with y-axis and light propagates along y direction. Horizontal (

p

) and vertical (

s

) polarized light are excited (received) at port 1 (2) and 3 (4) respectively. (b)−(e) Reflection (

r

) and transmission (

t

) spectrum of horizontal (

p

) and vertical (

s

) polarized light. The results from FEM and semi-analysis method are represented by blue circles and red lines respectively

Fig.2 (a) Bianisotropic honeycomb photonic crystal. The blue and purple circles represent two kinds of rods, and a unit cell is extracted as the green hexagon with

r = 0.25 a

ε / / = 8

ε prep = 1

κ = − 0.5

in rod 1 but

κ = 0.5

in rod 2. (b) Band structure on the high symmetry line. Red and blue points represent spin-down and spin-up sampled form literature, and blue circles is the result from COMSOL with modified weak form. The inset shows the Brillouin zone where

G 1

and

G 2

are reciprocal lattice vectors.

K

and

K'

are two kinds of vertex

Fig.3 Bianisotropic ring resonator behaves as polarization depended insulator. Bianisotropic slab waveguide (a) and bianisotropic ring resonator formed by rolling slab waveguide (b). Optical beam with polarization

E z + 1.72 i E y

propagates in the slab couples with ring from the left to the right (c) but propagates without coupling from the right to the left (d). Beam with polarization

E z − 1.72 i E y

goes through the slab in positive direction (e) but is insulated in reversal direction (f). The width of slab and ring is

0.15 ? μm

, the radius of ring is

2.3272 ? μm

ε r = μ r = 1

and

χ 11 = 2.7442

in bianisotropic ring,

ε r = μ r = 2.366

in slab. Vacuum wavelength is

1.0615 ? μm

and background medium is air

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