计算脉冲在非线性耦合器中演化的Matlab 程序 `2N&{( +@*}_%^l" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
zY_xJ"/9 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
QcQQQM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
0qP&hybL[( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
XJJdCv^ uG<VQ2LM %fid=fopen('e21.dat','w');
r*?rwtFtg N = 128; % Number of Fourier modes (Time domain sampling points)
& D@/_m $ M1 =3000; % Total number of space steps
GP=i6I6C J =100; % Steps between output of space
l{q$[/J~) T =10; % length of time windows:T*T0
v `& T0=0.1; % input pulse width
_
nF sC MN1=0; % initial value for the space output location
"9F]Wv/ dt = T/N; % time step
)Dn~e #
n = [-N/2:1:N/2-1]'; % Index
L(Ww6oj t = n.*dt;
CUJP"u>8M u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~q0g7?}& u20=u10.*0.0; % input to waveguide 2
) D_ZZPq_ u1=u10; u2=u20;
1K(a=o[Ce U1 = u1;
r*$$82s U2 = u2; % Compute initial condition; save it in U
ttQX3rmF01 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
MtE18 m "z w=2*pi*n./T;
C- 25\ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
[f`^+, U L=4; % length of evoluation to compare with S. Trillo's paper
ifA=qn0=} dz=L/M1; % space step, make sure nonlinear<0.05
Q depzo>E for m1 = 1:1:M1 % Start space evolution
j5hM |\] u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
tF:'Y ~3 p u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
!%w#h0(b ca1 = fftshift(fft(u1)); % Take Fourier transform
jC_7cAsl ca2 = fftshift(fft(u2));
3Ee8_(E\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/r Mxl(wD' c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
\=n0@ 1Q=> u2 = ifft(fftshift(c2)); % Return to physical space
aJh =4j~. u1 = ifft(fftshift(c1));
*Nfn6lVB if rem(m1,J) == 0 % Save output every J steps.
_PTo !aJL U1 = [U1 u1]; % put solutions in U array
b1X.#pz7F U2=[U2 u2];
.-kq t^Gc MN1=[MN1 m1];
$ #Mew:J z1=dz*MN1'; % output location
}qf9ra end
$^&SEz end
Znl&.,c) hg=abs(U1').*abs(U1'); % for data write to excel
&uLxA w ha=[z1 hg]; % for data write to excel
,.#
SEv5 t1=[0 t'];
XBJ 9"G5 hh=[t1' ha']; % for data write to excel file
B_f0-nKP %dlmwrite('aa',hh,'\t'); % save data in the excel format
qg7]
YT& figure(1)
i&cH waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
{HgW9N( figure(2)
|. b p waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
G5^ gwG+ "| 1MJuY_6 非线性超快脉冲耦合的数值方法的Matlab程序 @G/':N .aRL'1xHl 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
+{%@kX<V_ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%}z/_QZ 7ko7)"N tE)%*z@<Lt ?nm:e.S+? % This Matlab script file solves the nonlinear Schrodinger equations
+B*8$^,V) % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~;ink % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
j/zD`yd j % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Kuh! b`9 47Y| 1 C=1;
Z &mV1dxR M1=120, % integer for amplitude
Pn{yk`6E M3=5000; % integer for length of coupler
lYd#pN N N = 512; % Number of Fourier modes (Time domain sampling points)
#unE>#DW dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
b0a'Y"oef4 T =40; % length of time:T*T0.
rT`D@
I dt = T/N; % time step
y$)gj4k/D n = [-N/2:1:N/2-1]'; % Index
uo1G t = n.*dt;
' :,6s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l<<G". ? w=2*pi*n./T;
2|k*rv}l g1=-i*ww./2;
c$f|a$$b g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
i '!M<>7 g3=-i*ww./2;
W7N Hr5RC P1=0;
^H+j;K{5, P2=0;
bw*@0; P3=1;
-X@;"0v P=0;
QN(f8t( for m1=1:M1
TJtW?c7 p=0.032*m1; %input amplitude
m[^;HwJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
i_GE9A=h s1=s10;
syh0E= If_ s20=0.*s10; %input in waveguide 2
z(<
E % s30=0.*s10; %input in waveguide 3
)Jx!VJ^Y s2=s20;
VGcl)fIqw? s3=s30;
#e%.z+7I p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
oWyg/{M %energy in waveguide 1
;U<) $5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
_lQ+J=J$.R %energy in waveguide 2
@"9y\1u p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
gb:Cc,F, % %energy in waveguide 3
, IUMH]D for m3 = 1:1:M3 % Start space evolution
3w )S=4lB s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
cFLu+4.jsG s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
hE:P'O1 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
o*n""m sca1 = fftshift(fft(s1)); % Take Fourier transform
_}] o~ sca2 = fftshift(fft(s2));
rOY^w9! sca3 = fftshift(fft(s3));
Tu_dkif' sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
P's <M sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
K! /E0G& sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9BANCW" s3 = ifft(fftshift(sc3));
Oe9{`~ s2 = ifft(fftshift(sc2)); % Return to physical space
nGW
wXySq s1 = ifft(fftshift(sc1));
V`69%35*@ end
?l,i(I p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
@6*<Xs
= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
iy
tSC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]CC=
\ < P1=[P1 p1/p10];
hl~(& D1^ P2=[P2 p2/p10];
9r1pdG_C@ P3=[P3 p3/p10];
-lL*WA ` P=[P p*p];
9+QLc b end
Cu;X{F'H figure(1)
! #
tRl plot(P,P1, P,P2, P,P3);
n 2#uH glHag"( 转自：
http://blog.163.com/opto_wang/
