计算脉冲在非线性耦合器中演化的Matlab 程序 ZgN*m\l +1e*>jE % This Matlab script file solves the coupled nonlinear Schrodinger equations of
I(<1-3~ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
|s| RJA1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j+ s8V-7( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
K":- zS b%AYYk)d? %fid=fopen('e21.dat','w');
Dt8eVWkN ~ N = 128; % Number of Fourier modes (Time domain sampling points)
Oi7|R7NE M1 =3000; % Total number of space steps
`,TPd ~#~ J =100; % Steps between output of space
2H4+D) T =10; % length of time windows:T*T0
|i1z47jN6P T0=0.1; % input pulse width
G.L4l|%W MN1=0; % initial value for the space output location
ucTkWqG dt = T/N; % time step
0(teplo&P n = [-N/2:1:N/2-1]'; % Index
594$X@ !v t = n.*dt;
1298&C@ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
)5&Wt@7Kj` u20=u10.*0.0; % input to waveguide 2
W.>yIA% u1=u10; u2=u20;
InRn!~_N U1 = u1;
K{HdqmxL.I U2 = u2; % Compute initial condition; save it in U
x}72jJe` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
O>H4hp w=2*pi*n./T;
^
.>)*P g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
@@}A\wA- L=4; % length of evoluation to compare with S. Trillo's paper
;b(/PH!O dz=L/M1; % space step, make sure nonlinear<0.05
~ 5`Ngpp for m1 = 1:1:M1 % Start space evolution
)TG\P ,H9 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~KEnZa 0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_)lK. 5 ca1 = fftshift(fft(u1)); % Take Fourier transform
sd
Z=3) ca2 = fftshift(fft(u2));
df}B:?Ew. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
vrh}X[JEw' c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$yRbo '- u2 = ifft(fftshift(c2)); % Return to physical space
|)1"*` z u1 = ifft(fftshift(c1));
i9w xP i if rem(m1,J) == 0 % Save output every J steps.
>[ywrB ?T U1 = [U1 u1]; % put solutions in U array
-K+gr sb
g U2=[U2 u2];
R0 {+Xd MN1=[MN1 m1];
3
nb3rHQ z1=dz*MN1'; % output location
0s= GM|y end
PE+N5n2Tl end
Z$Qlr:7 hg=abs(U1').*abs(U1'); % for data write to excel
H~&9xtuH N ha=[z1 hg]; % for data write to excel
F^KoEWj[H t1=[0 t'];
5Gg`+o hh=[t1' ha']; % for data write to excel file
f H}` %dlmwrite('aa',hh,'\t'); % save data in the excel format
rXvvJIbi figure(1)
Onby=Y
o6 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
=v1s@5 ;~ figure(2)
$O7>E!uVD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
>L)Xy q 1,BtOzuRo 非线性超快脉冲耦合的数值方法的Matlab程序 Z3"f7 l6 [BmondOx 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。
w ~Es,@ 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
XW`&1qx [G4#DP\t>p [R6du*P
`<q{8 % This Matlab script file solves the nonlinear Schrodinger equations
O3B\K <l % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
7S),:Uy[\ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7RTp+FC] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*m 2J$9q z_CBOJl#C! C=1;
GXJJOy1"! M1=120, % integer for amplitude
bQEQH qY5 M3=5000; % integer for length of coupler
rn U2EL N = 512; % Number of Fourier modes (Time domain sampling points)
ad }^Dj/ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
`[/BG)4 T =40; % length of time:T*T0.
f`P%aX'cBQ dt = T/N; % time step
B4_0+K H n = [-N/2:1:N/2-1]'; % Index
+*~?JT t = n.*dt;
8BC}D +q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
|_
E)2b:h w=2*pi*n./T;
\*1pFX# g1=-i*ww./2;
G) i V g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Q_qc_IcM y g3=-i*ww./2;
-i7W|X" P1=0;
^~8l|d_ P2=0;
@R(6w {h9 P3=1;
Sh}AGNE' P=0;
T'0Ot3m` for m1=1:M1
s 3Y
\,9\ p=0.032*m1; %input amplitude
!$f@j6. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
$yHlkd`Y s1=s10;
YjoN: z`b s20=0.*s10; %input in waveguide 2
#*1\h=bzmW s30=0.*s10; %input in waveguide 3
)nTOIfP2 s2=s20;
R/A 40i s3=s30;
>Ix)jSNLgo p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ZSU;>&>%v %energy in waveguide 1
Ri " 3o p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
]7fqVOi Ou %energy in waveguide 2
N@)tU;U3O p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
% )?$82=2 %energy in waveguide 3
83Bp_K2\ for m3 = 1:1:M3 % Start space evolution
;HgV(d#X s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
r[J gCj+$& s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
[#$z.BoEo s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ie= tM'fb sca1 = fftshift(fft(s1)); % Take Fourier transform
b _z;^y~ sca2 = fftshift(fft(s2));
>jq~5HN sca3 = fftshift(fft(s3));
$:t;WXc.< sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
V2V^*9(wu@ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4JT9EKo sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|*e
>hk s3 = ifft(fftshift(sc3));
GadQ \> s2 = ifft(fftshift(sc2)); % Return to physical space
9Psy$ s1 = ifft(fftshift(sc1));
Yhb=^)@)) end
\:'=ccf p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
P}KyT?X: p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
}pTy mAN p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ZB B^?FF P1=[P1 p1/p10];
= pF 6 P2=[P2 p2/p10];
5NZob<< P3=[P3 p3/p10];
OGzth$7A P=[P p*p];
K\`L>B. 1 end
8~u#?xs6 figure(1)
Ir_K8 3VM plot(P,P1, P,P2, P,P3);
?Xx,[Z& kViX FPW 转自：
http://blog.163.com/opto_wang/
