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 sCAWrbOe> y-:d`>b>\ % This Matlab script file solves the coupled nonlinear Schrodinger equations of R?kyJ4S % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of K~\Ocl % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @(e/Y/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #Ic-?2Gn4< ^pvnUODW[ %fid=fopen('e21.dat','w'); ?7aeY5p N = 128; % Number of Fourier modes (Time domain sampling points) Qnv)\M1 M1 =3000; % Total number of space steps Ykj+D7rA: J =100; % Steps between output of space )>^!X$`3 T =10; % length of time windows:T*T0 V)Y#m/$` T0=0.1; % input pulse width i}LVBx"K( MN1=0; % initial value for the space output location 8<X;
8R dt = T/N; % time step ,S=ur% n = [-N/2:1:N/2-1]'; % Index n]WVT@ t = n.*dt; nTPq|=C u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 s\
YHT.O? u20=u10.*0.0; % input to waveguide 2 [`|gj u1=u10; u2=u20; ft4(^|~ U1 = u1; *Ag,/Cm] U2 = u2; % Compute initial condition; save it in U A>J,Bi ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. [Xo[J?w],2 w=2*pi*n./T; g,5Tr_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #?RT$L>n L=4; % length of evoluation to compare with S. Trillo's paper Zm/I & dz=L/M1; % space step, make sure nonlinear<0.05 |jTRIMj%,_ for m1 = 1:1:M1 % Start space evolution [#C(^J*@c u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS @L5s.]vg= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; HO9w"){d$ ca1 = fftshift(fft(u1)); % Take Fourier transform </jTWc'} ca2 = fftshift(fft(u2)); Z(a,$__ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation j.7BoV c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift D1f}g u2 = ifft(fftshift(c2)); % Return to physical space QNgfvy u1 = ifft(fftshift(c1)); 5TS&NefM if rem(m1,J) == 0 % Save output every J steps. L+2<J,
U1 = [U1 u1]; % put solutions in U array y^hCO:`l3 U2=[U2 u2]; #Q61c MN1=[MN1 m1]; 5Z*6,P0 z1=dz*MN1'; % output location Hn!13+fS end 4,qhWe`/ end FWDAG$K@0 hg=abs(U1').*abs(U1'); % for data write to excel #>dj!33 ha=[z1 hg]; % for data write to excel Z+G/==%3#, t1=[0 t']; k^*S3#" hh=[t1' ha']; % for data write to excel file f#b;s<G %dlmwrite('aa',hh,'\t'); % save data in the excel format MPD<MaW$ figure(1) ,\=,,1_ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn L/2,r*LNx$ figure(2) o==:e waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn jdAjCy; s! \d}>@@U& 非线性超快脉冲耦合的数值方法的Matlab程序 I7e.pm zM2_z 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。 X6SWcJtSw 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 6_kv~`"t Z )@[##F2 E]dmXH8A M.?[Xpa % This Matlab script file solves the nonlinear Schrodinger equations 6#(==}Sm+ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of }*s`R;B|, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2c1L[]h' % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 &Na,D7A:3I H[D<G9: C=1; yttaZhK^u M1=120, % integer for amplitude <S68UN(Ke M3=5000; % integer for length of coupler xSy`VuSl N = 512; % Number of Fourier modes (Time domain sampling points) :.aMhyh#* dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. Bvsxn5z+: T =40; % length of time:T*T0. N`et]'_A} dt = T/N; % time step t4v@d n = [-N/2:1:N/2-1]'; % Index zy(NJ t = n.*dt; 2xK v; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. #Ic)]0L w=2*pi*n./T; 85?;\5%- g1=-i*ww./2; fs\A(]`$ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; w;;9YFBdM g3=-i*ww./2; !QSj*)V# P1=0; 7BkY0_KK P2=0; |wINb~trz P3=1; #g= P=0; `Vl9/IEk for m1=1:M1 1V.oR`&2E p=0.032*m1; %input amplitude 5yk#(i7C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 o2~P
vef s1=s10; c*.-mS~Z` s20=0.*s10; %input in waveguide 2 LS]0 p# s30=0.*s10; %input in waveguide 3 %z~=Jz^ s2=s20; -}(2}~{e( s3=s30; GRh430V[ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 6GA+xr= %energy in waveguide 1 [h63* & p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 5Mz:$5Tm %energy in waveguide 2 Q$(Fma 4a p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); rld8hFj %energy in waveguide 3 )M><09 for m3 = 1:1:M3 % Start space evolution gCq'#G\Z s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS i&YWutG s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; U0U y
C s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; LwYWgT\e sca1 = fftshift(fft(s1)); % Take Fourier transform `I.pwst8i- sca2 = fftshift(fft(s2)); JED\"(d( sca3 = fftshift(fft(s3)); Z@(KZ| sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift EpH_v` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $[UUf}7L sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 6EeO\Qj{ s3 = ifft(fftshift(sc3)); GZ^Qt*5 { s2 = ifft(fftshift(sc2)); % Return to physical space -Xx4:S s1 = ifft(fftshift(sc1)); 0X3yfrim end RqX^$C8M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); tI)|y?q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); gxx#<=` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 5th?m> P1=[P1 p1/p10]; hd6O+i
Y4 P2=[P2 p2/p10]; !2h ZtX P3=[P3 p3/p10]; MU%7'J :_ P=[P p*p]; 2+_a<5l~ end Ol~M
BQs figure(1) Q(36RX%@ plot(P,P1, P,P2, P,P3); Wy%FF\D.Y *YSRZvD<\ 转自:http://blog.163.com/opto_wang/
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