计算脉冲在非线性耦合器中演化的Matlab 程序 cO,V8#H J\3} il
N % This Matlab script file solves the coupled nonlinear Schrodinger equations of
[+g@@\X4 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
5vf t} f % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hX m} d\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y.p 6%E_` LUck>l\l %fid=fopen('e21.dat','w');
S |>$0P4W( N = 128; % Number of Fourier modes (Time domain sampling points)
T-C#xmY( M1 =3000; % Total number of space steps
AwU c{h l< J =100; % Steps between output of space
^,lZ 58
2 T =10; % length of time windows:T*T0
87KrSZ T0=0.1; % input pulse width
4|N\Q=, MN1=0; % initial value for the space output location
GQ2Pm nV + dt = T/N; % time step
]<gCq/V # n = [-N/2:1:N/2-1]'; % Index
~AanU1U< t = n.*dt;
HhmVV"g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_A YC|R| u20=u10.*0.0; % input to waveguide 2
c%@~%IGF u1=u10; u2=u20;
k%}89glm U1 = u1;
2BDan^:-Av U2 = u2; % Compute initial condition; save it in U
$-P qs
^g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P4j 8`}&/ w=2*pi*n./T;
M J,ZXJXs g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
BD7@Mj*| L=4; % length of evoluation to compare with S. Trillo's paper
_]xt65TL dz=L/M1; % space step, make sure nonlinear<0.05
4i NbK~5j for m1 = 1:1:M1 % Start space evolution
.^lb LN^2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
3 ;MjO*- u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
+}Q BzG W` ca1 = fftshift(fft(u1)); % Take Fourier transform
NOr
<, ca2 = fftshift(fft(u2));
{R-82% X c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
yv)nW::D( c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BwJ^_:(p~ u2 = ifft(fftshift(c2)); % Return to physical space
Y^2Qxo3"3 u1 = ifft(fftshift(c1));
rN1U.FRe/ if rem(m1,J) == 0 % Save output every J steps.
LkGf|yd_ U1 = [U1 u1]; % put solutions in U array
Tz[?gF.Do U2=[U2 u2];
q^1aPz MN1=[MN1 m1];
0[:9 Hb6 z1=dz*MN1'; % output location
ml.;wB| end
4r[pMJi q end
MJ*]fC3/ hg=abs(U1').*abs(U1'); % for data write to excel
<D!c
~*[ ha=[z1 hg]; % for data write to excel
dA1
C)gLi t1=[0 t'];
;DD>k bd hh=[t1' ha']; % for data write to excel file
n2d8;B# %dlmwrite('aa',hh,'\t'); % save data in the excel format
{(Og/[ figure(1)
AB"1(PbG waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
d)0LVa( figure(2)
g T XW2S waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?o rh JS a, ~D+s;^ 非线性超快脉冲耦合的数值方法的Matlab程序 } B"|z'u +z |UpI 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
3G%wZ,)C Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
V+O0k: o TTZ['HP
oI _7lt(f[S Y:%m;b$] % This Matlab script file solves the nonlinear Schrodinger equations
hB?,7- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
kqD*TJA % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
1iJ0Hut}d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`u#;MUg q*[!>\ Z8 C=1;
A{z>D`d M1=120, % integer for amplitude
OG`|td M3=5000; % integer for length of coupler
#9D/jYK1X N = 512; % Number of Fourier modes (Time domain sampling points)
"[*S?QO(L dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
u3Usq=I j{ T =40; % length of time:T*T0.
"mPSA Z dt = T/N; % time step
w dGpt_ n = [-N/2:1:N/2-1]'; % Index
s] y-pZ t = n.*dt;
7deAr$?Wx ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7`IUMYl#~ w=2*pi*n./T;
-,QKTxwo> g1=-i*ww./2;
X!o[RJY g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
W?qpnPW g3=-i*ww./2;
7q%|4Z-~ P1=0;
C} b|2y P2=0;
5^i.;>(b P3=1;
=[]x\&@t P=0;
?}'N_n ys for m1=1:M1
7
9Qc`3a p=0.032*m1; %input amplitude
Nfv="t9e s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
m$fQ `XzU s1=s10;
0A#*4ap s20=0.*s10; %input in waveguide 2
7_9+=.
+X5 s30=0.*s10; %input in waveguide 3
UrO=!G k s2=s20;
_u r G_~q s3=s30;
o 'C~~Vg). p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
{y,nFxLq %energy in waveguide 1
+I|R k& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#^|| ]g/N %energy in waveguide 2
WD15pq l p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"^;#f+0 %energy in waveguide 3
CO-Iar for m3 = 1:1:M3 % Start space evolution
t< sp%zXZ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}m6f^fs} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
}@Xh xZu s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,*/Pg 52? sca1 = fftshift(fft(s1)); % Take Fourier transform
7MY)\aH sca2 = fftshift(fft(s2));
,{k<JA { sca3 = fftshift(fft(s3));
8h2D+1,PZC sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
vqq6B/r@Fu sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
WgE@8 9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
807al^s
x s3 = ifft(fftshift(sc3));
sffhPX\I s2 = ifft(fftshift(sc2)); % Return to physical space
jm+ V$YBP s1 = ifft(fftshift(sc1));
}@d>, 1DU end
`9/ 0J-7* p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
d 9O:,DKf p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
SOVj Eo4'3 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~gP7s_ qr{ P1=[P1 p1/p10];
R]Hz8 _X P2=[P2 p2/p10];
'X9AG6K1 P3=[P3 p3/p10];
Te# ]C n| P=[P p*p];
jDR')ascn end
_B)s =Snx figure(1)
G.E[6G3 plot(P,P1, P,P2, P,P3);
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8N% X2R )X/*($SuA 转自：
http://blog.163.com/opto_wang/
