基于Matlab绘制二维光子晶体在恒定频率下的光子带

✅作者简介：热爱科研的Matlab仿真开发者，修心和技术同步精进，matlab项目合作可私信。

🍎个人主页：Matlab科研工作室

🍊个人信条：格物致知。

更多Matlab仿真内容点击👇

智能优化算法       神经网络预测       雷达通信       无线传感器        电力系统

信号处理              图像处理               路径规划       元胞自动机        无人机 

⛄ 内容介绍

光子晶体具有光子带隙特性的电介质结构,是一种能够操控光的人造物质.具有简便,廉价,高速,大容量和强抗干扰性能的更多光子晶体产品将在各个领域发挥重要作用.

⛄ 部分代码

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% this program calculates and plots the wave-vector diagram (i.e. photonic bands at constant frequency)

%%% for a 2D photonic crystal consisting of cylinders with circular cross-section and

%%% infinite height, arranged in a triangular lattice; oblique propagation is implicit, so 

%%% the polarization states cannot be separated in E-pol and H-pol; 'omega'is taken as input; 

%%% Fourier coefficients for the expansion of dielectric constant are calculated analytically; 

%%% the materials considered here are dielectric and dispersionless;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% the package contains the following programs:

%%%     pwem2Db.m - main program

%%%     epsgg.m - routine for calculating the matrix of Fourier coefficients

%%%                 of dielectric function

%%%     bz_irr2.m - routine for 2D discretization of irreducible Brillouin zone polygon;

%%%     kvect2.m - routine for calculating diagonal matrices with elements

%%%                 (kx+Gx) and (ky+Gy), where G=(Gx,Gy) is a reciprocal

%%%                 lattice vector

%%%     oblic_eigs.m - routine for solving the eigenvalue problem for

%%%                     H-field

close all

clear all

tic

omega=0.45; % normalized frequency "a/lambda"

r=0.43; % radius of cylindrical holes (normalized w.r.t. lattice constant "a")

na=1; nb=3.45; % refractive indices (cylinders-atoms, background) 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

No1=7; No2=No1; 

N1=2*No1+1; N2=2*No2+1;

N=N1*N2; % total number of plane waves used in Fourier expansions

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% primitive vectors of direct lattice (normalized w.r.t. lattice constant "a")

a1=[sqrt(3)/2, -1/2, 0]; a2=[sqrt(3)/2, 1/2, 0]; 

%%% area of primitive cell

ac=norm(cross(a1,a2)); 

%%% primitive vectors of direct lattice (normalized w.r.t. lattice constant "2*pi/a"): b1=[1/sqrt(3),-1]; b2=[1/sqrt(3),1]; 

b1=(1/ac)*[a2(2),-a2(1)]; b2=(1/ac)*[-a1(2), a1(1)]; 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% matrix of Fourier coefficients

eps1 = feval ('epsgg',r,na,nb,b1,b2,N1,N2); 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% 2D discretization of irreducible Brillouin zone polygon

Nr=20; % even number

[BZx,BZy]=feval('bz_irr2', Nr);

kx=[]; ky=[]; kz=[];

S=2.5; % point size for scatter plot

for j=1:length(BZx)

    %%% diagonal matrices with elements (kx+Gx) si (ky+Gy)

    [kGx, kGy] = feval('kvect2',BZx(j),BZy(j),b1,b2,N1,N2);

    [P, beta]=feval('oblic_eigs',omega,kGx,kGy,eps1,N);

    L=imag(beta)==0; 

    qp=sort(beta(L)); %%% keep only the propagative modes

    display(sprintf('Calculation for k[%d] is finished',j));

    for r=1:length(qp)

        kx(j,r)=BZx(j); ky(j,r)=BZy(j); kz(j,r)=qp(r);

    end  

end

M=length(BZx)*length(qp);

scatter3(reshape(kx,1,M), reshape(ky,1,M), reshape(kz,1,M), S,'r','filled'), view(65,10)

title(sprintf('Wavevector diagram for omega=%0.5g',omega)); 

xlabel('kx'); ylabel('ky'); zlabel('kz');

toc

⛄ 运行结果

⛄ 参考文献

[1]许江勇. 基于Matlab研究光子晶体的特性[J]. 兴义民族师范学院学报, 2012(4):4.

[2]吴炳坚, 沈廷根. 基于Matlab的光子晶体波导仿真研究[J]. 微计算机信息, 2007(01S):3.

⛄ 完整代码

❤️部分理论引用网络文献，若有侵权联系博主删除

❤️ 关注我领取海量matlab电子书和数学建模资料