计算脉冲在非线性耦合器中演化的Matlab 程序
|eoid ?= k<w(i
k1bi % This Matlab script file solves the coupled nonlinear Schrodinger equations of
qZ @0]"h % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
yTE%hHH]&[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
3>zN/ f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
QYXx:nIrg He0=-AR8 %fid=fopen('e21.dat','w');
aI
zv N = 128; % Number of Fourier modes (Time domain sampling points)
ZA~Z1Mro#" M1 =3000; % Total number of space steps
<0|9Tn2O J =100; % Steps between output of space
nM=e]qH T =10; % length of time windows:T*T0
M"q[ p T0=0.1; % input pulse width
f#%JSV"7 MN1=0; % initial value for the space output location
H Q!Xj .y dt = T/N; % time step
J MX6yV n = [-N/2:1:N/2-1]'; % Index
t<uYM t = n.*dt;
SEQ%'E5-' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
jD) {I u20=u10.*0.0; % input to waveguide 2
DG(7|`(aY u1=u10; u2=u20;
#Z =tJ U1 = u1;
kI*(V [i U2 = u2; % Compute initial condition; save it in U
J2GcBzRH ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<Y 4:'L6 w=2*pi*n./T;
g*\/N,"z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
h *0S$p<[1 L=4; % length of evoluation to compare with S. Trillo's paper
`|1M lRM9 dz=L/M1; % space step, make sure nonlinear<0.05
I4H`YOD% for m1 = 1:1:M1 % Start space evolution
I9$c F)zk u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
I^*'.z!4Q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
C`oa3B,z ca1 = fftshift(fft(u1)); % Take Fourier transform
oC*ees
g_ ca2 = fftshift(fft(u2));
%k f>&b,Mi c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~>G]_H]? c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
WV ;=@ v u2 = ifft(fftshift(c2)); % Return to physical space
O(2 cW Q u1 = ifft(fftshift(c1));
TGT$ >/w > if rem(m1,J) == 0 % Save output every J steps.
lw8"'0 U1 = [U1 u1]; % put solutions in U array
-y) ,Y
| U2=[U2 u2];
'6 Qy / R MN1=[MN1 m1];
RR1A65B z1=dz*MN1'; % output location
Hyk'c't_O end
~+D*:7Y_ end
h>S[^
-, hg=abs(U1').*abs(U1'); % for data write to excel
&'|B =7 ha=[z1 hg]; % for data write to excel
*#>F.#9 t1=[0 t'];
HCA{p R` hh=[t1' ha']; % for data write to excel file
!Gs} tiMH %dlmwrite('aa',hh,'\t'); % save data in the excel format
1.@vS&Y7OE figure(1)
wyc D>hc waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
!KS F3sz figure(2)
"yb WD Wu waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
4Tzd; P6_ }m]q}r 非线性超快脉冲耦合的数值方法的Matlab程序 `T*U]/zQ @
$cUNvI 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
YZ#V#[j'^ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"vF
MSY r2*<\ax 4Wel[] dLh6:Gh8_I % This Matlab script file solves the nonlinear Schrodinger equations
`qpc*en f0 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
";3*?/uM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
UgHf* m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4 |J[Jdj hP?fMW$V C=1;
rp!
LP#* M1=120, % integer for amplitude
s}x>J8hK M3=5000; % integer for length of coupler
bPD)D'Hs N = 512; % Number of Fourier modes (Time domain sampling points)
a^ nA Z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
JXQP T T =40; % length of time:T*T0.
)-P!Ae_.v dt = T/N; % time step
B l.u=I:Y4 n = [-N/2:1:N/2-1]'; % Index
U)jUq_LX t = n.*dt;
*3{J#Q6fk3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
+`en{$%% w=2*pi*n./T;
0 Vv9BL{ g1=-i*ww./2;
~ 2 }Pl) g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
<dR,' g3=-i*ww./2;
y%B X ]~ P1=0;
g#^|oYuH6 P2=0;
6k0^ x Q P3=1;
r((T avn P=0;
0A$SYF$O+[ for m1=1:M1
B+VuUt{S p=0.032*m1; %input amplitude
z MdC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
SBKeb|H8 s1=s10;
?qH F}k| s20=0.*s10; %input in waveguide 2
TYS\95< s30=0.*s10; %input in waveguide 3
E:A!wS`" s2=s20;
cf8-]G?tK s3=s30;
s3t!<9[m p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
;_JH:}j %energy in waveguide 1
W|c.l{A5Q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=G>(~+EA %energy in waveguide 2
d+2daKi p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`7Ug/R< %energy in waveguide 3
Agy
<j
for m3 = 1:1:M3 % Start space evolution
L/r{xS s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
xxX/y2\ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
x'`"iZO.t s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
r2eQ{u{nX sca1 = fftshift(fft(s1)); % Take Fourier transform
a8uYs DS sca2 = fftshift(fft(s2));
Bku' H sca3 = fftshift(fft(s3));
u}jrf Kd E sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
SE `l(-t L sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
X-Ycz 5? sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
(!z M\sF s3 = ifft(fftshift(sc3));
9; f|EGwZ s2 = ifft(fftshift(sc2)); % Return to physical space
A3UQJ s1 = ifft(fftshift(sc1));
_vrWj<wyf end
'Ji+c p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
cH"@d^"+q| p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
C ?7X"~ ~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
}B)jq`a?|\ P1=[P1 p1/p10];
} p'8 w\C$ P2=[P2 p2/p10];
&4kM8Qh P3=[P3 p3/p10];
-J$g(sikt P=[P p*p];
Eb@MfL end
#)74X% 4( figure(1)
gue(C(~.k_ plot(P,P1, P,P2, P,P3);
+WF.wP?y B=zMY i 转自：
http://blog.163.com/opto_wang/
