some questions about the code

[Yaozengsw]

Dear Mr. Michael Ekstrom,
Thank you for taking the time to read my message amidst your busy schedule.
I am a graduate student at Wuhan University, and I have been studying the Lugiato-Lefever equation (LLE). Fortunately, I recently read your article, “Modeling of optical microresonator frequency combs,” which helped me understand how to apply the split-step Fourier method to solve the LLE. However, I am facing challenges with the equation presented in the paper “Topological dissipative Kerr soliton combs in a valley photonic crystal resonator,” particularly with handling the pump term.
I have attached the code I developed, and I would greatly appreciate it if you could take a moment to review it and help me identify any issues. Additionally, if you have any insights or code related to the time series diagram (Fig. 7.2 in your thesis), I would be grateful for your guidance.
Thank you once again for your time and assistance. I apologize for any inconvenience my inquiry may cause.
Wishing you good health and all the best.
Warm regards,
Yao Zeng
School of Electronic Information
Wuhan University
Wuhan 430072, China

clear all;
clc;
kappa=10000;
Pin=2.2;
dispersion2=0.1e9;
delta_w=30e12;
%%
FSR=450e9;
a=300e-9;
l=180a;
L=3l;
omega0=370.67e12;
n2=2.5e-19;
c=3e8;
A_eff=2.1e-14;
gamma=(omega0n2)/(cA_eff);
eta=0.5;
hbar=1.05e-34;
Omega=omega0-delta_w;
%%
nt=1000; Tmax=300; % FFT points and window size
step_num=200; % No. of z steps
deltaz=L/step_num; % step size in z
dtau=(2Tmax)/nt; % step size in tau
tau=(-nt/2:nt/2-1)dtau; % temporal grid
omega=fftshift((2pi/Tmax)(-nt/2:nt/2-1)); % frequency grid
%% 输入场
psi=sech(tau);
% Plot input time series
figure;
subplot(3,1,1)
plot (tau, abs(psi).abs(psi), '-r'); hold on;
%% Split Step LLE
P_hat=fft(sqrt(Pin)ones(1, nt));
D1=-kappa/2-1idelta_w-1ipiFSRdispersion2omega.omega;
D2=exp(D1deltaz);
alpha=(kappaeta)/(hbarOmega);
% Initial linear half-step
psi=ifft(fft(psi).sqrt(D2)+(sqrt(alpha)P_hat./D1).(sqrt(D2) - 1));
for q=1:1
% Nonlinear step
psi=psi.exp(1ideltazLFSRgammaabs(psi).^2);
% Linear step
psi=ifft(fft(psi).*D2+(sqrt(alpha)P_hat./D1).(D2 - 1));
end
% Inverse linear half-step
psi=ifft(fft(psi).*1./sqrt(D2)+(sqrt(alpha)P_hat./D1).(1./sqrt(D2)-1));
% Plot output time series
subplot(3,1,2)
plot (tau, abs(psi).*abs(psi), '-b')
%% 频谱
E_t=psi;
P_t=E_t.*conj(E_t);
x_complex=P_t;
dt=dtau;
Nf = length(x_complex);
Fs=1/dt;
df=Fs/Nf;
freq_span = (-floor(Nf/2):floor((Nf-1)/2))df;
fft_mag_laser_Ax = abs(fftshift(fft(x_complex)));
subplot(3,1,3)
plot(freq_span,10log10(fft_mag_laser_Ax),'k')
xlabel('Frequency (GHz)')
ylabel('Microwave Power (dB)')

[miceks]

Hello Yao, Apologies for the late answer to your email. I'm afraid my ability to help you with your code is limited due to no longer having a MATLAB license and also being out of practice in the field, but I can offer some general advice about the code I wrote and lessons learned. All the code used in the thesis can be found at https://github.com/miceks/kerr_comb_simulator. There should be a file named 'split_step_LLE.m' implementing an LLE solver. The first thing to keep in mind is that all code (and figures in the results) uses a form of normalized/scaled variables which is documented in section 2.3 of the thesis. These were picked to make the problem I was working on simpler and may not be suitable for your work. In my experience, there are a lot of different conventions used to express these equations. The second thing to remember is that critical coupling is assumed, so there is no corresponding parameter for that. Finally, a tricky issue in general is to find suitable simulation parameters to avoid numerical instability and also good initial conditions to get the field to converge to something interesting (solitons, Turing patterns, etc.). The only advice I have here is trial and error. The app at the github repo might be useful if you want to play around with different values to get a feel for what numerical instability looks like. With regards to initial values you can either try parameter sweeps or use some analytical approximation, which I think are available in the app as well (again, I can't run it myself anymore to check). Best of luck! Regards, Michael Ekström Den mån 4 nov. 2024 kl 15:47 skrev Yaozengsw ***@***.***>:

…

Dear Mr. Michael Ekstrom, Thank you for taking the time to read my message amidst your busy schedule. I am a graduate student at Wuhan University, and I have been studying the Lugiato-Lefever equation (LLE). Fortunately, I recently read your article, “Modeling of optical microresonator frequency combs,” which helped me understand how to apply the split-step Fourier method to solve the LLE. However, I am facing challenges with the equation presented in the paper “Topological dissipative Kerr soliton combs in a valley photonic crystal resonator,” particularly with handling the pump term. I have attached the code I developed, and I would greatly appreciate it if you could take a moment to review it and help me identify any issues. Additionally, if you have any insights or code related to the time series diagram (Fig. 7.2 in your thesis), I would be grateful for your guidance. Thank you once again for your time and assistance. I apologize for any inconvenience my inquiry may cause. Wishing you good health and all the best. Warm regards, Yao Zeng School of Electronic Information Wuhan University Wuhan 430072, China clear all; clc; kappa=10000; Pin=2.2; dispersion2=0.1e9; delta_w=30e12; %% FSR=450e9; a=300e-9; l=180 *a; L=3*l; omega0=370.67e12; n2=2.5e-19; c=3e8; A_eff=2.1e-14; gamma=(omega0*n2)/(c*A_eff); eta=0.5; hbar=1.05e-34; Omega=omega0-delta_w; %% nt=1000; Tmax=300; % FFT points and window size step_num=200; % No. of z steps deltaz=L/step_num; % step size in z dtau=(2 *Tmax)/nt; % step size in tau tau=(-nt/2:nt/2-1)dtau; % temporal grid omega=fftshift((2pi/Tmax)*(-nt/2:nt/2-1)); % frequency grid %% 输入场 psi=sech(tau); % Plot input time series figure; subplot(3,1,1) plot (tau, abs(psi). *abs(psi), '-r'); hold on; %% Split Step LLE P_hat=fft(sqrt(Pin)ones(1, nt)); D1=-kappa/2-1idelta_w-1i*pi*FSR*dispersion2 *omega.omega; D2=exp(D1deltaz); alpha=(kappa*eta)/(hbar *Omega); % Initial linear half-step psi=ifft(fft(psi).sqrt(D2)+(sqrt(alpha)P_hat./D1).(sqrt(D2) - 1)); for q=1:1 % Nonlinear step psi=psi.exp(1ideltazL*FSR*gamma*abs(psi).^2); % Linear step psi=ifft(fft(psi).*D2+(sqrt(alpha)*P_hat./D1).*(D2 - 1)); end % Inverse linear half-step psi=ifft(fft(psi).*1./sqrt(D2)+(sqrt(alpha)*P_hat./D1).*(1./sqrt(D2)-1)); % Plot output time series subplot(3,1,2) plot (tau, abs(psi).*abs(psi), '-b') %% 频谱 E_t=psi; P_t=E_t.*conj(E_t); x_complex=P_t; dt=dtau; Nf = length(x_complex); Fs=1/dt; df=Fs/Nf; freq_span = (-floor(Nf/2):floor((Nf-1)/2)) *df; fft_mag_laser_Ax = abs(fftshift(fft(x_complex))); subplot(3,1,3) plot(freq_span,10*log10(fft_mag_laser_Ax),'k') xlabel('Frequency (GHz)') ylabel('Microwave Power (dB)') — Reply to this email directly, view it on GitHub <#3>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AR7F3YXVBFYFQCLP6I4OMZ3Z66CI5AVCNFSM6AAAAABRENRYOCVHI2DSMVQWIX3LMV43ASLTON2WKOZSGYZTGMBSGA3TOMQ> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>