[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 {k)MC)%  
d E
Xw=u  
%  This Matlab script file solves the coupled nonlinear Schrodinger equations of $@<\$I2s  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9*x9sfCv9  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear duM>(y  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FkS{Z s  
)Y:CV,`  
%fid=fopen('e21.dat','w'); q
80?C.,`  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 
b :+ X3  
M1 =3000;              % Total number of space steps "
#OmmU<U  
J =100;                % Steps between output of space =l\D7s  
T =10;                  % length of time windows:T*T0 59)PJ0E  
T0=0.1;                 % input pulse width %URyGS]*  
MN1=0;                 % initial value for the space output location 5n"'M&Ce  
dt = T/N;                      % time step "'8$hV65.p  
n = [-N/2:1:N/2-1]';           % Index )h/fr|  
t = n.*dt;   3}vlj:L  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 4f>Vg$4  
u20=u10.*0.0;                  % input to waveguide 2 2 o.Mh/D0  
u1=u10; u2=u20;                 c1Hv^*Y  
U1 = u1;   +Gjy%JFp
 
U2 = u2;                       % Compute initial condition; save it in U P--#5W;^oB  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ei"FN3Rm  
w=2*pi*n./T; 1,/oS&?E  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T p'R}z|d)  
L=4;                           % length of evoluation to compare with S. Trillo's paper ^o{O5&i]  
dz=L/M1;                       % space step, make sure nonlinear<0.05 Coyop#q#"{  
for m1 = 1:1:M1                                    % Start space evolution K4 >d  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS lKa}Bcd  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; #\"5:.H Oz  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform 08twcY;&k  
   ca2 = fftshift(fft(u2)); LsmC/+7r$1  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation YlYTH_L>E  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   phNv^R+  
   u2 = ifft(fftshift(c2));                        % Return to physical space v3[ 2!UXq  
   u1 = ifft(fftshift(c1)); *v&g>Ni  
if rem(m1,J) == 0                                 % Save output every J steps. :JOF!Q  
    U1 = [U1 u1];                                  % put solutions in U array t
#d~gBe?V  
    U2=[U2 u2]; [3\}Ca1  
    MN1=[MN1 m1]; d6Z;\f7[  
    z1=dz*MN1';                                    % output location '91Ak,cWB  
  end HID;~Ne  
end uh GL1{  
hg=abs(U1').*abs(U1');                             % for data write to excel | 0&~fY  
ha=[z1 hg];                                        % for data write to excel vm Hf$rq  
t1=[0 t']; KI#hII[Q.  
hh=[t1' ha'];                                      % for data write to excel file OW6i2>Or  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format Va{`es)hky  
figure(1) 0R; ;ou  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn e}Db-7B_~  
figure(2) 9 Z4H5!:(  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn d-c+KV  
h<}4mo_$  
非线性超快脉冲耦合的数值方法的Matlab程序 Er%nSH^"  
O6m}#?Ai/@  
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。   HtXzMSGo7  
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 k6$.pCH6  
X${k  
+.zriiF]i  
Bf8 #&]O  
%  This Matlab script file solves the nonlinear Schrodinger equations tQ*5[F,fm  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of )K%AbKn  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear zHyM@*Gf(  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ] @IzJz"R  
Of-l<Ks\  
C=1;                           p6sXftk  
M1=120,                       % integer for amplitude \`x
$@s?  
M3=5000;                      % integer for length of coupler w%`7,du|  
N = 512;                      % Number of Fourier modes (Time domain sampling points) teET nz_L  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. uN'e~X6  
T =40;                        % length of time:T*T0. tLLP2^_&  
dt = T/N;                     % time step sv =6?uYW  
n = [-N/2:1:N/2-1]';          % Index X62GEqff  
t = n.*dt;   qL]!/}  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. /SjA;c!.  
w=2*pi*n./T; }+,;wj~  
g1=-i*ww./2; qA5tMZ^w  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; eAPGy-  
g3=-i*ww./2; '(~+ \  
P1=0; Y
Q;?N66  
P2=0; J](AJkGzK  
P3=1; Ij4oH  
P=0; iz&)FuOr  
for m1=1:M1                 Fq9AO~z  
p=0.032*m1;                %input amplitude =M>pL+#  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 fgq#Oi}  
s1=s10; }5u$/c@f1  
s20=0.*s10;                %input in waveguide 2 &pV'/  
s30=0.*s10;                %input in waveguide 3 7]62=p2R  
s2=s20; M2{{B^*$6  
s3=s30; 6gNsh  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   P @G2F:}  
%energy in waveguide 1 4Y;z46yM%  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   5v6*.e'p  
%energy in waveguide 2 up#W"`"  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]*D=^kA0[  
%energy in waveguide 3 1@egAo)  
for m3 = 1:1:M3                                    % Start space evolution (~#{{Ja  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 4Un(}P'  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ~#C7G\R  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; gQ6_]~4  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ^cn%]X#.  
   sca2 = fftshift(fft(s2)); %`?IY<  
   sca3 = fftshift(fft(s3)); <Y9%oJn%  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   TY"8.vd  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); a~>+I~^K5q  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); il|e5TD^  
   s3 = ifft(fftshift(sc3)); Uf4A9$R.G  
   s2 = ifft(fftshift(sc2));                       % Return to physical space fp^{612O?  
   s1 = ifft(fftshift(sc1)); TgoaEufS<  
end &s-iie$"@x  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 0Q`Dp;a5&  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); '1'De^%6W  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ibAZ=
RD  
   P1=[P1 p1/p10]; *j6KQZ"  
   P2=[P2 p2/p10]; uB_8P+h7  
   P3=[P3 p3/p10]; }>]V_}h  
   P=[P p*p]; H|JPqBNRh  
end ]?rVram;z  
figure(1) `tw[{Wb  
plot(P,P1, P,P2, P,P3); B]iPixA6  
n@[_lNa4GD  
转自：http://blog.163.com/opto_wang/

谢谢哈~！~