[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 e|y~q0Q$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of IW*.B6Hw8  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of &|*|  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8G<.5!f7`N  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \zyGJyy.  
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%fid=fopen('e21.dat','w'); ? GW3E  
N = 128;                       % Number of Fourier modes (Time domain sampling points) mJT m/C  
M1 =3000;              % Total number of space steps CB)#; |aDB  
J =100;                % Steps between output of space Mq$=zsj  
T =10;                  % length of time windows:T*T0 xy>mM"DOH  
T0=0.1;                 % input pulse width inrL'z
 
MN1=0;                 % initial value for the space output location nfB9M1Svn  
dt = T/N;                      % time step P*]g*&*Y +  
n = [-N/2:1:N/2-1]';           % Index [%:NR  
t = n.*dt;   :wm^04<i  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 na)ceN2h  
u20=u10.*0.0;                  % input to waveguide 2 N%yFL  
u1=u10; u2=u20;                 d0az#Yg!  
U1 = u1;   :{2$X|f 3  
U2 = u2;                       % Compute initial condition; save it in U ;'}xD5]  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. P]GGnT
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w=2*pi*n./T; ^\%%9jY  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T v>R.ou(  
L=4;                           % length of evoluation to compare with S. Trillo's paper ln7.>.F  
dz=L/M1;                       % space step, make sure nonlinear<0.05 XF6=xD  
for m1 = 1:1:M1                                    % Start space evolution #$E vybETx  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS
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   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; _i#Z'4?2E  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform o
k'1  
   ca2 = fftshift(fft(u2)); uv!/DX#  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation !$HWUxM;p  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   &-A7%"  
   u2 = ifft(fftshift(c2));                        % Return to physical space ~5b %~:  
   u1 = ifft(fftshift(c1)); {ar}.U  
if rem(m1,J) == 0                                 % Save output every J steps. :nt%z0_  
    U1 = [U1 u1];                                  % put solutions in U array ~MX@-Ff  
    U2=[U2 u2]; N8TO"`wdbs  
    MN1=[MN1 m1]; Mv3Ch'X[  
    z1=dz*MN1';                                    % output location zO,sq%vQn'  
  end xAflcY>Ozs  
end XA68H!I  
hg=abs(U1').*abs(U1');                             % for data write to excel I uDk9<[b:  
ha=[z1 hg];                                        % for data write to excel zD'gGxM1  
t1=[0 t']; A 3l1$t#w  
hh=[t1' ha'];                                      % for data write to excel file I$&/?ns@O  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format -~g3?!+Hb  
figure(1) Yu=^`I  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn >J1o@0tk  
figure(2) =zKp(_[D  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn TH-^tw  
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非线性超快脉冲耦合的数值方法的Matlab程序 \?ZdUY  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   5V0=-K  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 '"EOLr\Z,  
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%  This Matlab script file solves the nonlinear Schrodinger equations ntT|G0E  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of g6farLBF  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @fwU%S[v  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >cp9{+#f  
m`|Z1CT  
C=1;                           #3S/TBy,  
M1=120,                       % integer for amplitude fITml6mbE  
M3=5000;                      % integer for length of coupler C{D2mSS  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 'coqm8V[%  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. H_Yy.yi  
T =40;                        % length of time:T*T0. !l~
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dt = T/N;                     % time step SCo9[EJ  
n = [-N/2:1:N/2-1]';          % Index qrdI"  
t = n.*dt;   qhtc?A/0}  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. B@4#y9`5  
w=2*pi*n./T; z(xvt>  
g1=-i*ww./2; ]1K &U5p  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ;Cwn1N9S  
g3=-i*ww./2; C9z{8 ;  
P1=0; VYwaU^  
P2=0; E*%{Nn  
P3=1; QqDF_
  
P=0; [Xrq+O,  
for m1=1:M1                 dx~Wm1  
p=0.032*m1;                %input amplitude ;?rW`e2  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 TcC=_je460  
s1=s10; GH
kSU;})  
s20=0.*s10;                %input in waveguide 2 rk~/^(!  
s30=0.*s10;                %input in waveguide 3 H\^^p!^)  
s2=s20; KQqlM  
s3=s30;  u32<=Q[  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ]8^2(^3ct  
%energy in waveguide 1 y
U\|dL  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   AIeYy-f  
%energy in waveguide 2 \8pbPo=x  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   sOJ~PRA  
%energy in waveguide 3 myo/}58Nv  
for m3 = 1:1:M3                                    % Start space evolution B[$e;h*Aw[  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS iPIA&)x}  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ]Cj&C/(  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; B5cTzY.h-  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform qHj4`&  
   sca2 = fftshift(fft(s2)); #\jPBLc  
   sca3 = fftshift(fft(s3)); IJ0RHDod:  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   6?~pWZ&k_  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); dU\fC{1Z  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 1{wy%|H\  
   s3 = ifft(fftshift(sc3)); ~UnfS};
U  
   s2 = ifft(fftshift(sc2));                       % Return to physical space o 2DnkzpJ  
   s1 = ifft(fftshift(sc1)); B4b UcYk  
end GP[$&8\M  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ZpdM[\Q-  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); -&&mkK B!  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); cr!I"kTgD  
   P1=[P1 p1/p10]; 9> |rIw  
   P2=[P2 p2/p10]; hk=+t&Y<H  
   P3=[P3 p3/p10]; B)(A#&nrb  
   P=[P p*p]; 2@H~nw 0  
end s)C.e# xl  
figure(1) 3drgB;:g`  
plot(P,P1, P,P2, P,P3);  [W;14BD7  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~