| 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 {<Xl57w-Q W 7w*VD| % This Matlab script file solves the coupled nonlinear Schrodinger equations of IeB^BD+j % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of /KhY,G'Z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear v>5TTL~? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [pz1f!Wn ?$=Ml$ %fid=fopen('e21.dat','w'); 5Z[HlN|-! N = 128; % Number of Fourier modes (Time domain sampling points) @"afEMd M1 =3000; % Total number of space steps W\O.[7JP J =100; % Steps between output of space rji<g>GQ T =10; % length of time windows:T*T0 A6#v6 iT T0=0.1; % input pulse width Hm_&``=' MN1=0; % initial value for the space output location 3#idXc dt = T/N; % time step gh%Q9Ni- n = [-N/2:1:N/2-1]'; % Index D"P<;@ef t = n.*dt; ;MW=F9U* u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 Sv[+~co<l u20=u10.*0.0; % input to waveguide 2
QLZ%m $Z u1=u10; u2=u20; -IL' (vx U1 = u1; =64Ju Wvo U2 = u2; % Compute initial condition; save it in U V QbKrnX ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. @XH@i+{B w=2*pi*n./T; _J0(GuG=~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T *-s':('R L=4; % length of evoluation to compare with S. Trillo's paper KXcE@q9 dz=L/M1; % space step, make sure nonlinear<0.05 Zc=#Y for m1 = 1:1:M1 % Start space evolution hho\e
8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS <#lNi.?. u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 2l +t- ca1 = fftshift(fft(u1)); % Take Fourier transform U-#vssJhk ca2 = fftshift(fft(u2)); PBAQ
KQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation `Wu.wx c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift [UB]vPXm$ u2 = ifft(fftshift(c2)); % Return to physical space &IFXU2t} u1 = ifft(fftshift(c1)); >x${I`2w if rem(m1,J) == 0 % Save output every J steps. )>!y7/3 U1 = [U1 u1]; % put solutions in U array sl*&.F,v= U2=[U2 u2]; ~\Udl MN1=[MN1 m1]; f1I/aR V:+ z1=dz*MN1'; % output location
bRx}ih end $lF\FC end !8o;~PPVl hg=abs(U1').*abs(U1'); % for data write to excel 8b $e) ha=[z1 hg]; % for data write to excel \5F
{MBx ! t1=[0 t']; /z4n?&tM hh=[t1' ha']; % for data write to excel file @eRv`O" %dlmwrite('aa',hh,'\t'); % save data in the excel format (E \lLlN figure(1) a7e.Z9k! waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn (?z"_\^n/ figure(2) YF13&E2`\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn 7/FF}d &DWSu`z 非线性超快脉冲耦合的数值方法的Matlab程序 ,h'omU7 SoB6F9 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 Yu|L6#[E Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 I(+%`{Wv Ml+O -
3T bYy7Ul6]
-to 3I % This Matlab script file solves the nonlinear Schrodinger equations }z_7?dn/ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of kDWvjT % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <nF1f(ky % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 n#)kvr g y1i% C=1; Cx
;n#dn* M1=120, % integer for amplitude >>0c)uC|W M3=5000; % integer for length of coupler 5}`e"X N = 512; % Number of Fourier modes (Time domain sampling points) iIU>:)i dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. oY7 eVu z T =40; % length of time:T*T0. eed!SmP dt = T/N; % time step 7R>Pk9J n = [-N/2:1:N/2-1]'; % Index \> t = n.*dt; 0/zgjT|fe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ]s~%1bd
w=2*pi*n./T; axdRV1+s g1=-i*ww./2; yUu+68Z6 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; xu*dPG)v g3=-i*ww./2; M l9 P1=0; F6-U{+KU$! P2=0; q@Sj$ P3=1; go5l<:9 P=0; _eMY? for m1=1:M1 *gN)a%9 p=0.032*m1; %input amplitude s
F3M= uz s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 };]f 3 s1=s10; &BQ%df<y\ s20=0.*s10; %input in waveguide 2 f}+8m .g2 s30=0.*s10; %input in waveguide 3 |BA<> WE s2=s20; z|i2M8 s3=s30; \FjY;rqfKe p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); FY <77i %energy in waveguide 1 +AL(K: p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); y`-5/4 %energy in waveguide 2 N1u2=puJY p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); &!O~ f %energy in waveguide 3 oH kjMqju for m3 = 1:1:M3 % Start space evolution S$Fq1 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 3dC;B@ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Q)}z$h55 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; /&G )IY]g sca1 = fftshift(fft(s1)); % Take Fourier transform 6O'6,%# sca2 = fftshift(fft(s2)); 2V =bE- sca3 = fftshift(fft(s3)); R%^AW2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift ob"yz } sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); %R LGO& sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); nN!R!tJPa s3 = ifft(fftshift(sc3)); j-wz7B s2 = ifft(fftshift(sc2)); % Return to physical space {-)*.l= s1 = ifft(fftshift(sc1)); \o{rw0w0 end 6T{SRN{ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Shb"Jc_i p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); {]dH+J7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); };@J)} P1=[P1 p1/p10]; odC}RdN P2=[P2 p2/p10]; P0XVR_TJf P3=[P3 p3/p10]; 4+15` P=[P p*p]; f3HleA&& end ,]|*~dd>G figure(1) ~TfQuIvQB plot(P,P1, P,P2, P,P3); @mId{w z .q9wyVi7GI 转自:http://blog.163.com/opto_wang/
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