| tianmen |
2011-06-12 18:33 |
求解光孤子或超短脉冲耦合方程的Matlab程序
计算脉冲在非线性耦合器中演化的Matlab 程序 n4}e!
/;1O9HJa % This Matlab script file solves the coupled nonlinear Schrodinger equations of }&2,!;"">3 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `<|<1, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NuUiW*|`7 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >kmgYWG B
I3fk %fid=fopen('e21.dat','w'); !"Q%I#8uh N = 128; % Number of Fourier modes (Time domain sampling points) )& Oxp&x M1 =3000; % Total number of space steps .]JIo&>5 J =100; % Steps between output of space NJ-Ji> w T =10; % length of time windows:T*T0 B'`25u_e< T0=0.1; % input pulse width $N;J) MN1=0; % initial value for the space output location 4m"0R\ dt = T/N; % time step
kN8B, n = [-N/2:1:N/2-1]'; % Index r)K5<[\r t = n.*dt; _2{_W9k u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 5;XYF0 u20=u10.*0.0; % input to waveguide 2
_<Ij)#Rq7 u1=u10; u2=u20; H{S+^'5Y. U1 = u1; %N`_g' r! U2 = u2; % Compute initial condition; save it in U 8e,F{>N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. sK&kp=zu w=2*pi*n./T; |0}7/^ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T (6:.u.b L=4; % length of evoluation to compare with S. Trillo's paper CYwV]lq:s dz=L/M1; % space step, make sure nonlinear<0.05 3(,m(+J[S for m1 = 1:1:M1 % Start space evolution 8TP~=qU u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS ]vn*eqd u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; S4{vS?>j ca1 = fftshift(fft(u1)); % Take Fourier transform Gau@RX:O ca2 = fftshift(fft(u2)); lBs-u h c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation \)wch P_0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift j u"?b2f u2 = ifft(fftshift(c2)); % Return to physical space oSkQ/5hg. u1 = ifft(fftshift(c1)); r `n|fD. if rem(m1,J) == 0 % Save output every J steps. -o`K/f}d U1 = [U1 u1]; % put solutions in U array u~Po5W/i U2=[U2 u2]; [6JDS;MIN MN1=[MN1 m1]; [)GRP z1=dz*MN1'; % output location y %61xA`# end D M+MBK
end e!gNd>b { hg=abs(U1').*abs(U1'); % for data write to excel Fw{@RQf8 ha=[z1 hg]; % for data write to excel j%-Ems*H t1=[0 t']; pUF JQ* hh=[t1' ha']; % for data write to excel file *i:8g( %dlmwrite('aa',hh,'\t'); % save data in the excel format 3\
Mt+!1{ figure(1) 2y!aXk\#C waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn KB :JVK^ < figure(2) E QU@';~8 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn <jF&+[*iT 9lR6:}L7 非线性超快脉冲耦合的数值方法的Matlab程序 }5(_gYr A%F8w'8( 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。 "RK"Pn+ 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 -Fn/= V4ePYud;^ .PVYYhrt gT$WG$^i % This Matlab script file solves the nonlinear Schrodinger equations lnyq%T[^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of d v[.u{#tP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear T&>65`L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O TlqJ Xy 4k;+ C=1; W,Q>3y* M1=120, % integer for amplitude xZ;eV76 M3=5000; % integer for length of coupler 0=6mb]VUi= N = 512; % Number of Fourier modes (Time domain sampling points) wbKJ:eWgt dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. ^\Q,ACkZb T =40; % length of time:T*T0. 0|tyKP|J dt = T/N; % time step IE996
n = [-N/2:1:N/2-1]'; % Index 2\k!DF t = n.*dt; X=)L$Kd7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. a6./;OC w=2*pi*n./T; bO/r1W g1=-i*ww./2; m[2[9bQ0 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ||pOiR5 g3=-i*ww./2; qp6'n&^& P1=0; e.DN,rhqI P2=0; wZ\93W-} P3=1;
=5B5 P=0; '[F`!X for m1=1:M1 S}U_uZ$b p=0.032*m1; %input amplitude
f&^}yqmuE s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 *qSvSY* s1=s10; wdBBx\FP s20=0.*s10; %input in waveguide 2 ojf6@p_ s30=0.*s10; %input in waveguide 3 U+B"$yBR s2=s20; ~zac.:a8 s3=s30; p qpsa' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); D3dh,&KO\ %energy in waveguide 1 \M@IKE p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); u;rmqo1 %energy in waveguide 2 T3
ie-G@< p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); _zM?"16I} %energy in waveguide 3 UMd.=HC L for m3 = 1:1:M3 % Start space evolution 6IT6EkiT s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS kjV>\e s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ">1wPq& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; iZdl0;16[ sca1 = fftshift(fft(s1)); % Take Fourier transform "'Fvt-<^S7 sca2 = fftshift(fft(s2)); 1<#D3CXK sca3 = fftshift(fft(s3)); 9ETdO,L)f sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift h'h8Mm sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); (EWGX |QA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); O^-QqCZE s3 = ifft(fftshift(sc3)); 5p!{#r6m s2 = ifft(fftshift(sc2)); % Return to physical space (VN'1a ( s1 = ifft(fftshift(sc1)); t/O^7)% end WK*tXc_[b p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); hkb\GcOj p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); PP'5ANK p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Vfy@?x=
& P1=[P1 p1/p10]; 13v`rK`7o P2=[P2 p2/p10]; t6KKfb P3=[P3 p3/p10]; +<xQF P=[P p*p]; 3Q62H+MC end H9TeMY figure(1) !]uB4 plot(P,P1, P,P2, P,P3); [Ca''JqrA vmkiw1 转自:http://blog.163.com/opto_wang/
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