计算脉冲在非线性耦合器中演化的Matlab 程序 [Z0e$ ^{w&&+#,q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
ew(6;}+^/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&eg,*K} ' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ld
$`5!Z % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
0e7!_/9 3{ci]h`:y8 %fid=fopen('e21.dat','w');
ciTQH (G N = 128; % Number of Fourier modes (Time domain sampling points)
.#n?^73 M1 =3000; % Total number of space steps
f_7p.H6\ J =100; % Steps between output of space
[Ue>KG62= T =10; % length of time windows:T*T0
z,9qAts?mh T0=0.1; % input pulse width
8^{BuUA MN1=0; % initial value for the space output location
N(9'U0z dt = T/N; % time step
a5'QL(IX n = [-N/2:1:N/2-1]'; % Index
ty78)XI
t = n.*dt;
d^w_rL u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
\o^+'4hq<5 u20=u10.*0.0; % input to waveguide 2
6"DvdJ0MB u1=u10; u2=u20;
#'T|,xIr-Q U1 = u1;
G>,rf
]N U2 = u2; % Compute initial condition; save it in U
3EyN"Lvp{o ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
E8xXr>j># w=2*pi*n./T;
"CaVT7L g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
v zn/waw L=4; % length of evoluation to compare with S. Trillo's paper
C>+UZ dz=L/M1; % space step, make sure nonlinear<0.05
x!< C0N>?z for m1 = 1:1:M1 % Start space evolution
4MM#\ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
eN$~@'w u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
B0Z@ Cf ca1 = fftshift(fft(u1)); % Take Fourier transform
_ehU:3L`s ca2 = fftshift(fft(u2));
eE&F1|8 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
rN}^^9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
6+It>mnR
u2 = ifft(fftshift(c2)); % Return to physical space
;02lmpBj u1 = ifft(fftshift(c1));
8]Pf:_e,+ if rem(m1,J) == 0 % Save output every J steps.
%=]{~5f> U1 = [U1 u1]; % put solutions in U array
1t)6wk
N U2=[U2 u2];
>$?Z&7Lv MN1=[MN1 m1];
rdK.*oT z1=dz*MN1'; % output location
[J^,_iN[. end
{>z.y1 end
u4S3NLG) hg=abs(U1').*abs(U1'); % for data write to excel
&8;mcM//4 ha=[z1 hg]; % for data write to excel
Rl,B !SF t1=[0 t'];
3oSQe" hh=[t1' ha']; % for data write to excel file
Ki' EO$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
+Kk6|+5u figure(1)
dWp4|r waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
YFW+l~[# figure(2)
toQn]MT waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
HsO=%bb F;zmq%rK 非线性超快脉冲耦合的数值方法的Matlab程序 9A6ly9DIS 89L-k%R 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。
ZK13[_@9 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
2Two|E 0{j>u` `Q{kiy Yux7kD\c % This Matlab script file solves the nonlinear Schrodinger equations
DF|qNX % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9oaq%Sf % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iBZ+gsSP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'aCnj8B }x%"Oq|2]x C=1;
c`iSe$eS M1=120, % integer for amplitude
o$Jk27 M3=5000; % integer for length of coupler
o?b"B+# N = 512; % Number of Fourier modes (Time domain sampling points)
#0mn_#-P) dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{!-w|&bF T =40; % length of time:T*T0.
[0 W^|=#K dt = T/N; % time step
qOng?(I n = [-N/2:1:N/2-1]'; % Index
P[Qr[74) t = n.*dt;
4gYP .h:, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s#d>yx_b w=2*pi*n./T;
:cOwTW?Fj g1=-i*ww./2;
's
e9|: g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
'-
Z4GcL g3=-i*ww./2;
QZDGk4GG P1=0;
g'mkhF( P2=0;
>8RIMW2 P3=1;
\TKv3N P=0;
N%^mR>.` for m1=1:M1
>CYg\vas! p=0.032*m1; %input amplitude
ok7DI s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n%ld*EgY s1=s10;
D$j`+` s20=0.*s10; %input in waveguide 2
*{C)o0D s30=0.*s10; %input in waveguide 3
YN\
QwV s2=s20;
oVLz7Y[JE s3=s30;
_/KW5 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
H#1/H@I# %energy in waveguide 1
YGxdYwBwf p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1Og9VG1^ %energy in waveguide 2
yqoi2J: p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
/R^!~J50 %energy in waveguide 3
SK-|O9Ki for m3 = 1:1:M3 % Start space evolution
3 \kT#nr s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
GA;E (a s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%.Mtn%:I* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
u]zb<)'_ sca1 = fftshift(fft(s1)); % Take Fourier transform
N`#v"f<~Q sca2 = fftshift(fft(s2));
)`g[k"yB3 sca3 = fftshift(fft(s3));
ka]n+"~==\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#BM *40tch sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Y \j &84 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
A]R"C:o s3 = ifft(fftshift(sc3));
PY` V]|J s2 = ifft(fftshift(sc2)); % Return to physical space
IPJs$PtKok s1 = ifft(fftshift(sc1));
(s}9N end
u0i
@. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
t[3Upe% p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
k5<lkC2z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]H.+=V;1 P1=[P1 p1/p10];
I2zSoQ1P P2=[P2 p2/p10];
XLM 9+L P3=[P3 p3/p10];
Ju:=-5r"' P=[P p*p];
uD. 0?*_ end
Q y15TJ figure(1)
$bD!./fl plot(P,P1, P,P2, P,P3);
h7o{l7`) lMP|$C 转自:
http://blog.163.com/opto_wang/