计算脉冲在非线性耦合器中演化的Matlab 程序 %MZP)k,&U ^s&W>hTX: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
VfSj E.| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
^C/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5G[x }4U % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|mhKI is U &<3&'*ueW %fid=fopen('e21.dat','w');
"
.4,." N = 128; % Number of Fourier modes (Time domain sampling points)
Apj; M1 =3000; % Total number of space steps
+bA% J =100; % Steps between output of space
j.m(ltGh T =10; % length of time windows:T*T0
aJhx c<"e T0=0.1; % input pulse width
}rq9I"/L MN1=0; % initial value for the space output location
B(_WZa! dt = T/N; % time step
AiP!hw/V$ n = [-N/2:1:N/2-1]'; % Index
tGjhHp8}c t = n.*dt;
r^0F"9eOL u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Ag9?C* u20=u10.*0.0; % input to waveguide 2
> Lft9e u1=u10; u2=u20;
),(V6@Z? U1 = u1;
}!p`1]gem U2 = u2; % Compute initial condition; save it in U
t~``md4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
IgIYguQ w=2*pi*n./T;
XJ1=m g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
cA)[XpQ:+W L=4; % length of evoluation to compare with S. Trillo's paper
nhT-Ido dz=L/M1; % space step, make sure nonlinear<0.05
H1/?+ N}( for m1 = 1:1:M1 % Start space evolution
UAn&\ 8g_ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
E{E0Z9t7& u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
k^\pU\J ca1 = fftshift(fft(u1)); % Take Fourier transform
i#/]Ks Sp ca2 = fftshift(fft(u2));
- +> 1r c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
:| +Qe e c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
S >yLqPp u2 = ifft(fftshift(c2)); % Return to physical space
$q$7^ r@ u1 = ifft(fftshift(c1));
JH8}Ru%Z if rem(m1,J) == 0 % Save output every J steps.
`= UWqb(K_ U1 = [U1 u1]; % put solutions in U array
GZip\S4Y U2=[U2 u2];
_oG&OJ@ MN1=[MN1 m1];
FAsFjRS z1=dz*MN1'; % output location
W,XTF end
Fv74bC % end
q_kdCO{:df hg=abs(U1').*abs(U1'); % for data write to excel
ZfrVjUB ha=[z1 hg]; % for data write to excel
"ZwKk
G t1=[0 t'];
n_?tN\M hh=[t1' ha']; % for data write to excel file
vi.w8 >CE %dlmwrite('aa',hh,'\t'); % save data in the excel format
?W>qUrZ figure(1)
w[tmCn+ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
F + m }#p figure(2)
x'<K\qp{{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
+{<#(} Dre2J<QL 非线性超快脉冲耦合的数值方法的Matlab程序 YNwp/Y b~=0[Rv 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。
_g%TSumvq< 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
yAL[[
]^'@ [< gzoEUp =s @+3kb.P%7 % This Matlab script file solves the nonlinear Schrodinger equations
h/?l4iR* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
*Kdda}
J+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;AO#xv+# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8NyJc"T<. I:K"'R^ C=1;
^[:p|U2mA M1=120, % integer for amplitude
!;?+>R)h M3=5000; % integer for length of coupler
cufH?Xg< N = 512; % Number of Fourier modes (Time domain sampling points)
M5gWD==uP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
sMu]
/'7 T =40; % length of time:T*T0.
C74a(Bk}H dt = T/N; % time step
:oJ=iB'Zc n = [-N/2:1:N/2-1]'; % Index
0lhVqy}:}o t = n.*dt;
: q#Xq;Wp ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"[y-+)WTG w=2*pi*n./T;
ZK >WW g1=-i*ww./2;
`
,SiA-3* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
}Y;K~J g3=-i*ww./2;
/!c${W!sY P1=0;
X5 j1`t, P2=0;
y UpgoX( 6 P3=1;
Q ]} Hd- P=0;
M5 <@~V/[ for m1=1:M1
+E{|63~q p=0.032*m1; %input amplitude
C.FI~Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
gLOEh6 s1=s10;
4O35 "1 s20=0.*s10; %input in waveguide 2
v%q0OX>9X" s30=0.*s10; %input in waveguide 3
gHo?[pS%y s2=s20;
gP;&e: /3 s3=s30;
"1%5, p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Evedc*z~P %energy in waveguide 1
'Iw NTM p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
dw*_(ys %energy in waveguide 2
~{jcH p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"thdPZ %energy in waveguide 3
Dy:|g1> for m3 = 1:1:M3 % Start space evolution
|a Vn&qK s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(jAg_$6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
?vbvBu{a s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
` Tv[DIVW sca1 = fftshift(fft(s1)); % Take Fourier transform
njputEG X sca2 = fftshift(fft(s2));
T( U_ sca3 = fftshift(fft(s3));
vkri+:S3 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
++`0rY% sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
5:KQg
sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
' F9 jq s3 = ifft(fftshift(sc3));
@X#F3; s2 = ifft(fftshift(sc2)); % Return to physical space
'Wm x)0) s1 = ifft(fftshift(sc1));
?gt l )q end
VgZsB$Ori p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
9, :l8 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
X:nN0p # p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]1#e#M]# P1=[P1 p1/p10];
D$I5z. a P2=[P2 p2/p10];
JehrDC 2N P3=[P3 p3/p10];
rWR}Stc@] P=[P p*p];
>JFO@O5 end
:LW4E9O=H figure(1)
+ |n*b plot(P,P1, P,P2, P,P3);
?kbiMs1;u KUlp"{a`,K 转自：
http://blog.163.com/opto_wang/
