计算脉冲在非线性耦合器中演化的Matlab 程序 3
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A og< % This Matlab script file solves the coupled nonlinear Schrodinger equations of
SVo:%mX % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_|`S9Nms % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
;5?$q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ak^g#^c* H9F\<5n]-l %fid=fopen('e21.dat','w');
5_9mA4gs@ N = 128; % Number of Fourier modes (Time domain sampling points)
L
slI!.( M1 =3000; % Total number of space steps
Wyd,7]'z)Z J =100; % Steps between output of space
FY@ErA7~ T =10; % length of time windows:T*T0
3a_~18W T0=0.1; % input pulse width
{ owK~ MN1=0; % initial value for the space output location
O'*KNJX dt = T/N; % time step
= a$7OV. n = [-N/2:1:N/2-1]'; % Index
s sUWr=mD t = n.*dt;
3{O^q/R u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
ZkSlztL)Tr u20=u10.*0.0; % input to waveguide 2
IZoS2^:yw u1=u10; u2=u20;
HM /2/
/ U1 = u1;
mfc\w' U2 = u2; % Compute initial condition; save it in U
bk44 qL;8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[< Bk% B 5 w=2*pi*n./T;
Y/?V%X g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
UOC>H%r~M? L=4; % length of evoluation to compare with S. Trillo's paper
^"STM'Zh dz=L/M1; % space step, make sure nonlinear<0.05
uS`XWn<CSD for m1 = 1:1:M1 % Start space evolution
7VduewKX8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
aEM2xrhy, u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4}E|CD/pZ ca1 = fftshift(fft(u1)); % Take Fourier transform
. zZee,kM ca2 = fftshift(fft(u2));
$aDAD4mmm c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
)!z<q}i5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
V{+'(<SV u2 = ifft(fftshift(c2)); % Return to physical space
V(3^ev/ u1 = ifft(fftshift(c1));
T)? : q if rem(m1,J) == 0 % Save output every J steps.
MH7 n@.t U1 = [U1 u1]; % put solutions in U array
""q76cx U2=[U2 u2];
=bgzl=A` MN1=[MN1 m1];
I7,5ID4pn z1=dz*MN1'; % output location
ammlUWl end
%/iD@2r end
f9ux+XQk 9 hg=abs(U1').*abs(U1'); % for data write to excel
iq*]CF ha=[z1 hg]; % for data write to excel
WR,MqM20 t1=[0 t'];
|C"(K-do hh=[t1' ha']; % for data write to excel file
(d mLEt %dlmwrite('aa',hh,'\t'); % save data in the excel format
&y_Ya%Z3*e figure(1)
"sh*,K5x| waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
`Y]t*`
e| figure(2)
[}:;B$, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
VZF; )}w2'(!X8 非线性超快脉冲耦合的数值方法的Matlab程序 ?TTtGbvU t$~CLq5a d 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
W'lejOiw Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%n?&#_G| %x{jmZ$} ,Y9bXC8+dU I Sa}Km>Q % This Matlab script file solves the nonlinear Schrodinger equations
v
*icoj % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
m-?hHd O % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gOb"-;Zw % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5?l8;xe`{f %[S-"k C=1;
&FrUj>i M1=120, % integer for amplitude
|Yb]@9 >vn M3=5000; % integer for length of coupler
oD<aWZ"Z N = 512; % Number of Fourier modes (Time domain sampling points)
YOOcHo.F dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
cvOCBg38BH T =40; % length of time:T*T0.
Aq 5CF`e{ dt = T/N; % time step
_ \&v A5- n = [-N/2:1:N/2-1]'; % Index
2 nra@ t = n.*dt;
wCQ.?*7-9Q ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GY`mF1b w=2*pi*n./T;
xQUskjv/ g1=-i*ww./2;
2P, %}Ms g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
]?S@g'Jd0Q g3=-i*ww./2;
O}s Mqh P1=0;
Dc@OrQu P2=0;
>:J7u*>$ ' P3=1;
S$N!Dj@e; P=0;
!( gMr1}w for m1=1:M1
'8w}m8{y p=0.032*m1; %input amplitude
Uv ) B s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
mP*Ct6628n s1=s10;
1u8 k} s20=0.*s10; %input in waveguide 2
$ U=j<^R}a s30=0.*s10; %input in waveguide 3
"f~*4g s2=s20;
;SgPF:T>Q s3=s30;
*q&^tn b p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Talmc|h %energy in waveguide 1
>\?RYy,s$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
L}=DC =E %energy in waveguide 2
@#r6->%W p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
S:lie*Aux* %energy in waveguide 3
sEymwpm9 for m3 = 1:1:M3 % Start space evolution
6%^A6U s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
<EKTFHJ! s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
1SF8D`3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
p!o-+@av a sca1 = fftshift(fft(s1)); % Take Fourier transform
z[Ah9tM% sca2 = fftshift(fft(s2));
A('o &H sca3 = fftshift(fft(s3));
70<{tjyc sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#H DP ha sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
w2H ^q3* sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9^+E$V1@ s3 = ifft(fftshift(sc3));
;#bDz}|\AN s2 = ifft(fftshift(sc2)); % Return to physical space
XEB eoOX/ s1 = ifft(fftshift(sc1));
G \z5Ue* end
dOT7;@ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
4 _P 6 P p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
<KX fh p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Skg}/Ek P1=[P1 p1/p10];
: al
,zxs P2=[P2 p2/p10];
;e{e
?,[ P3=[P3 p3/p10];
&gF9VY P=[P p*p];
MWv(/_b end
Q{| _"sf J figure(1)
p`2Q6 plot(P,P1, P,P2, P,P3);
L1#_ 704_ehrlE 转自：
http://blog.163.com/opto_wang/
