|Table of Contents|

Analyzing Gyroelectric Photonic Crystal Waveguides by Dirichlet-to-Neumann Maps(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2023年03期
Page:
12-19
Research Field:
数学
Publishing date:

Info

Title:
Analyzing Gyroelectric Photonic Crystal Waveguides by Dirichlet-to-Neumann Maps
Author(s):
Li ZhengHu Zhen
(College of Science,Hohai University,Nanjing 211100,China)
Keywords:
gyroelectric photonic crystal waveguides numerical methods eigenvalue problems Dirichlet-to-Neumann(DtN)maps
PACS:
O242
DOI:
10.3969/j.issn.1001-4616.2023.03.003
Abstract:
In this paper,we extend the Dirichlet-to-Neumann(DtN)map method to analyze two-dimensional gyroelectric photonic crystal(GPhC)waveguides. Based on DtN maps of GPhC unit cells,the DtN map of a supercell can be constructed. Then a linear eigenvalue problem is established on the boundaries of a supercell. Since we avoid discretizing inside the computational domain and only need to discretize on boundaries of unit cells,the matrices obtained in this method are relatively small. Numerical examples are used to illustrate the effectiveness of the proposed method.

References:

[1]JOANNOPOULOS J D,JOHNSON S G,WINN J N,et al. Photonic crystals:Molding the flow of light[M]. Second Edition. Princeton:Princeton University Press,1995.
[2]OGUSU K,TAKAYAMA K. Transmission characteristics of photonic crystal waveguides with stubs and their application to optical filters[J]. Optics letters,2007,32(15):2185-2187.
[3]MEKIS A,CHEN J C,KURLAND I,et al. High transmission through sharp bends in photonic waveguides[J]. Physical review letters,1996,77(18):3787-3790.
[4]KOSHIBA M,TSUJI Y,HIKARI M. Time-domain beam propagation method and its application to photonic crystal circuits[J]. Journal of lightwave technology,2002,18(1):102-110.
[5]OUYANG C,XIONG Z,ZHAO F,et al. Slow light with low group-velocity dispersion at the edge of photonic graphene[J]. Physical review A,2011,84(1):3442-3448.
[6]TASOLAMPROU A C,ZHANG L,ECONOMOU E N,et al. Supporting information:Surface states on photonic crystals as hybrid dielectric meta surface bound states of the termination layer[J]. American chemical society photonics,2020,7(10):2842-2849.
[7]SINGH B R,RAWAL S,SINHA R K. Chirped photonic crystal with different symmetries for asymmetric light propagation[J]. Applied physics A,2016,122(6):1-7.
[8]ZHOU T,TANG M,XIANG G,et al. Continuous-wave quantum dot photonic crystal lasers grown on on-axis Si(001)[J]. Nature communications,2020,11(1):147369.
[9]WU Y H,LI X X,FANG Y T. Evolution and Reversal of topological edge states in optical frequencies from two-dimensional photonic crystal[J]. Journal of optics,2020,22(10):102-105.
[10]WU X,YE F,MERLO J M,et al. Topologically protected photonic edge states in the visible in plasmo-gyroelectric metamaterials[J]. Advanced optical materials,2018,6(15):1800119.1-1800119.5.
[11]董圆圆. 电磁波在回旋介质中传播特性的研究[D]. 北京:北京交通大学,2016.
[12]LIU C Y. Efficient omnidirectional couplers achieved by anisotropic photonic crystal waveguides[J]. Physics letters A,2009,373(34):3061-3066.
[13]ZHANG Z,DAINESE M,WOSINSKI L,et al. Optical filter based on two-dimensional photonic crystal surface-mode cavity in amorphous silicon-on-silica structure[J]. Applied physics letters,2007,90(4):041108.
[14]CHAN C T,YU Q L,HO K M. Order-N spectral method for electromagnetic waves[J]. Physical review B,1995,51(23):16635-16642.
[15]LEUNG K M,LIU Y F. Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media[J]. Physical review letter,1990,65(21):2650-2653.
[16]OVIEDO I,MENDEZ R A,MANZANARES B. The plane wave expansion method applied to thin plates[J]. The journal of the acoustical society of America,2011,130(4):2346-2346.
[17]YANG H. Finite difference analysis of 2-D photonic crystals[J]. IEEE transactions on microwave theory and techniques,1996,44(12):2688-2695.
[18]YU C P,CHANG H C. Applications of the finite-difference frequency-domain mode solution method to photonic crystal structures[J]. Optical and quantum electronics,2004,36(1):145-163.
[19]AXMANN W,KUCHMENT P. An Efficient finite element method for computing spectra of photonic and acoustic band-gap materials:I. scalar case[J]. Journal of computational physics,1999,150(2):468-481.
[20]ZHANG Q,LI X. One-way rotating photonic crystal ring resonator with high quality factor[J]. IEEE photonics journal,2018,10(3):1-10.
[21]PENDRY J B. Calculating photonic band structure[J]. Journal of physics:condenced matter,1996,8(9):1085-1108.
[22]PENDRY J B,MACKINNON A. Calculation of photon dispersion relations[J]. Physical review letters,1992,69(19):2772-2775.
[23]DOOSOIU K B,BYRNE M A,BOTTEN L C,et al. Finite element computation of grating scattering matrices and application to photonic crystal band calculations[J]. Journal of computational physics,2006,219(1):120-143.
[24]BOTTEN L,NICOROVICI N,MCPHEDRAN R,et al. Photonic band structure calculations using scattering matrices[J]. Physical review E statistical nonlinear & soft matter physics,2001,64(4):046603.1-046603.18.
[25]HUANG Y,LU Y Y. Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps[J]. Journal of lightwave technology,2006,24(9):3448-3453.
[26]YUAN J,LU Y Y. Photonic bandgap calculations with Dirichlet-to-Neumann maps[J]. Journal of the optical society of America A optics image science & vision,2006,23(12):3217-3222.
[27]YE C,HU Z. Computing equifrequency contours of two-dimensional photonic crystals by Dirichlet-to-Neumann maps[J]. Journal of modern optics,2016,64(2):196-204.
[28]WANG M,HU Z. Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps[J]. Optical and quantum electronics,2019,51(6):194.1-194.14.
[29]LI S,LU Y Y. Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells[J]. Journal of the optical society of America A optics image science & vision,2007,24(8):2438-2442.
[30]HU Z,LU Y Y. Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps[J]. Optics express,2008,16(22):17383-17399.
[31]HU Z,LU Y Y. Propagating bound states in the continuum at the surface of a photonic crystal[J]. Journal of the optical society of America B,2017,34(9),1878-1883.
[32]HU Z,LU Y Y. Resonances and bound states in the continuum on periodic arrays of slightly noncircular cylinders[J]. Journal of physics B,2018,51(3):035402.

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Last Update: 2023-09-15