[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 [Z0e$  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of ew(6;}+^/  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of &eg,*K}'  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ld $`5!Z  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 0e7!_/9  
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%fid=fopen('e21.dat','w'); ciTQH
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N = 128;                       % Number of Fourier modes (Time domain sampling points) .#n?^73  
M1 =3000;              % Total number of space steps f_7p.H6\  
J =100;                % Steps between output of space [Ue>KG62=  
T =10;                  % length of time windows:T*T0 z,9qAts?mh  
T0=0.1;                 % input pulse width 8^{BuUA  
MN1=0;                 % initial value for the space output location N(9'U0z  
dt = T/N;                      % time step a5'QL(IX  
n = [-N/2:1:N/2-1]';           % Index ty78)XI  
t = n.*dt;   d^w_rL  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 \o^+'4hq<5  
u20=u10.*0.0;                  % input to waveguide 2 6"DvdJ0MB  
u1=u10; u2=u20;                 #'T|,xIr-Q  
U1 = u1;   G>,rf ]N  
U2 = u2;                       % Compute initial condition; save it in U 3EyN"Lvp{o  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. E8xXr>j>#  
w=2*pi*n./T; "CaVT7L  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T v zn/waw  
L=4;                           % length of evoluation to compare with S. Trillo's paper C>+U
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dz=L/M1;                       % space step, make sure nonlinear<0.05 x!< C0N>?z  
for m1 = 1:1:M1                                    % Start space evolution 4
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   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS eN$~@'w  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; B0Z@ Cf  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform _ehU:3L`s  
   ca2 = fftshift(fft(u2)); eE&
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation rN}^^9  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   6+It>mnR  
   u2 = ifft(fftshift(c2));                        % Return to physical space ;02lmpBj  
   u1 = ifft(fftshift(c1)); 8]Pf:_e,+  
if rem(m1,J) == 0                                 % Save output every J steps. %=]{~5f>  
    U1 = [U1 u1];                                  % put solutions in U array 1t)6wk N  
    U2=[U2 u2]; >$?Z&7Lv  
    MN1=[MN1 m1]; rdK.*oT  
    z1=dz*MN1';                                    % output location [J^,_iN[.  
  end {>z.y1  
end u4S3NLG)  
hg=abs(U1').*abs(U1');                             % for data write to excel &8;mcM//4  
ha=[z1 hg];                                        % for data write to excel Rl,B !SF  
t1=[0 t']; 3oSQe"  
hh=[t1' ha'];                                      % for data write to excel file Ki'EO$  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format +Kk6|+5u  
figure(1) dWp4|r  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn YFW+l~[#  
figure(2) toQn]MT  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn HsO=%bb  
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非线性超快脉冲耦合的数值方法的Matlab程序 9A6ly9DIS  
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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。   ZK13[_@9  
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 
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%  This Matlab script file solves the nonlinear Schrodinger equations DF|qNX  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 9oaq%Sf  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear iBZ+gsSP  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'aCnj8B  
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C=1;                           c`i
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M1=120,                       % integer for amplitude o$Jk27  
M3=5000;                      % integer for length of coupler o?b"B+#  
N = 512;                      % Number of Fourier modes (Time domain sampling points) #0mn_#-P)  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {!-w|&bF  
T =40;                        % length of time:T*T0. [0 W^|=#K  
dt = T/N;                     % time step qOng?(I  
n = [-N/2:1:N/2-1]';          % Index P[Qr[74)  
t = n.*dt;   4gYP .h:,  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. s#d>yx_b  
w=2*pi*n./T; :cOwTW?Fj  
g1=-i*ww./2; 's e9|:  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; '- Z4GcL  
g3=-i*ww./2; QZDGk4GG  
P1=0; g'mkhF(  
P2=0; >8RIMW2  
P3=1; \TKv3N  
P=0; N%^mR>.`  
for m1=1:M1                 >CYg\vas!  
p=0.032*m1;                %input amplitude ok7DI  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 n
%ld*EgY  
s1=s10; D$j`+`  
s20=0.*s10;                %input in waveguide 2 *{C)o0D  
s30=0.*s10;                %input in waveguide 3 YN\ QwV  
s2=s20; oVLz7Y[JE  
s3=s30; _/KW5  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   H#1/H@I#  
%energy in waveguide 1 YGxdYwBwf  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   1Og9VG1^  
%energy in waveguide 2 yqoi2J:  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   /R^!~J50  
%energy in waveguide 3 SK-|O9Ki  
for m3 = 1:1:M3                                    % Start space evolution 3 \kT#nr  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS GA;E (a  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %.Mtn%:I*  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; u]zb<)'_  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform N`#v"f<~Q  
   sca2 = fftshift(fft(s2)); )`g[k"yB3  
   sca3 = fftshift(fft(s3)); ka]n+"~==\  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   #BM *40tch  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); Y\j &84  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); A]R"C:o  
   s3 = ifft(fftshift(sc3)); PY`V]|J  
   s2 = ifft(fftshift(sc2));                       % Return to physical space IPJs$PtKok  
   s1 = ifft(fftshift(sc1)); (s}9N  
end u0i @.  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); t[3Upe%  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); k5<lkC2z  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ]H.+=V;1  
   P1=[P1 p1/p10]; I2zSoQ1P  
   P2=[P2 p2/p10]; XLM 9+L  
   P3=[P3 p3/p10]; Ju:=-5r"'  
   P=[P p*p]; uD. 0?*_  
end Qy15TJ  
figure(1) $bD!./fl  
plot(P,P1, P,P2, P,P3); h7o{l7`)  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~