Example10.m

P = BPMmatlab.model;

% This example illustrates the adiabatic mode conversion and shedding of
% unguided modes illustrated in figure 4 of the article "BPM-Matlab - An
% open-source optical propagation simulation tool in MATLAB". The model
% starts with a fiber with core radius 5 µm. Based on the results from
% findModes, we can see that it supports 8 modes:
% {'LP01';'LP11o';'LP11e';'LP21o';'LP21e';'LP02';'LP31o';'LP31e'}. The
% fiber tapers down to a final width of 1.5 mum, where only the LP01 mode is
% guided. Initially, we excite the fiber with a superposition of all 8
% guided modes.
% 
% From theory, we expect that
% At r = 4.80 mum, the LP31 modes are no longer guided (z = 0.57e-3 m)
% At r = 3.64 mum, the LP02 mode is no longer guided (z = 3.9e-3 m)
% At r = 3.58 mum, the LP21 modes are no longer guided (z = 4.1e-3 m)
% At r = 2.25 mum, the LP11 modes are no longer guided (z = 7.9e-3 m)
% 
% However, the light is not immediately lost when the fiber radius passes
% the above thresholds, it takes some distance before the light exits the
% simulation window and is absorbed in the surrounding absorber layer. At
% the end of the simulations, we see that the remaining light is that of
% the fundamental mode, and it contains 1/8th of the initial power (12.5
% %), which fits with adiabatic mode conversion of the initial fundamental
% mode to the final fundamental mode.
% 
% This example also illustrates the plotting of xz and yz slices. Each
% segment stores its slice data in separate elements of the xzSlice and
% yzSlice cell arrays.


%% General and solver-related settings
P.name = mfilename;
P.useAllCPUs = true;
P.useGPU = false;

%% Visualization parameters
updateFrequency = 5e4; % [1/m]
P.saveVideo = false; % To save the field intensity and phase profiles at different transverse planes
P.plotZoom = 1;  % Zooms in on figures 1 & 3a,b. Set to 1 for no zooming.  
P.plotEmax = 1; % Max of color scale in the intensity plot, relative to the peak of initial intensity

%% Resolution-related parameters (check for convergence)
P.Lx_main = 25e-6;        % [m] x side length of main area
P.Ly_main = 25e-6;        % [m] y side length of main area
P.Nx_main = 201;          % x resolution of main area
P.Ny_main = 201;          % y resolution of main area
P.padfactor = 1.5;  % How much absorbing padding to add on the sides of the main area (1 means no padding, 2 means the absorbing padding on both sides is of thickness Lx_main/2)
P.dz_target = 1e-6; % [m] z step size to aim for
P.alpha = 6e14;             % [1/m^3] "Absorption coefficient" per squared unit length distance out from edge of main area

%% Problem definition
P.lambda = 1000e-9; % [m] Wavelength
P.n_background = 1.45; % [] (may be complex) Background refractive index, (in this case, the cladding)
P.n_0 = 1.46;
P.Lz = 10e-3; % [m] z propagation distances for this segment
P.updates = P.Lz*updateFrequency;            % Number of times to update plot. Must be at least 1, showing the final state.
P.taperScaling = 0.3;
P.figTitle = 'Segment 1';

P = initializeRIfromFunction(P,@calcRI);

P = findModes(P,10,'plotModes',false); % Find up to 10 modes, but don't plot them
randvec = [0.974931557198556 + 0.222504963491603i ,  0.583350562881419 - 0.812220487790066i ,  0.915224078253766 - 0.402945264998293i , -0.432956662664553 - 0.901414737096290i ,  0.048613506502203 - 0.998817664534203i , -0.043136586317590 - 0.999069184251454i , -0.779356851920114 + 0.626580319963187i , -0.559597395571616 - 0.828764595569493i]; % Randomly generated array of mode coefficients for use in the superposition
P.E = modeSuperposition(P,1:8,randvec); % Make a superposition of the first 8 modes with the above random coefficients

% Run solver
P = FD_BPM(P);

%% Next segment
P.figTitle = 'Segment 2';
P.Lz = 5e-3;
P.updates = P.Lz*updateFrequency;            % Number of times to update plot. Must be at least 1, showing the final state.
P.taperScaling = 1;

% Run solver
P = FD_BPM(P);

%% Plot xz and yz slices
figure(2);clf;
subplot(2,1,1);
imagesc(P.z,P.x,abs([P.xzSlice{1} P.xzSlice{2}]).^2);
axis xy;
xlabel('z [m]');
ylabel('x [m]');
subplot(2,1,2);
imagesc(P.z,P.y,abs([P.yzSlice{1} P.yzSlice{2}]).^2);
axis xy;
xlabel('z [m]');
ylabel('y [m]');

%% USER DEFINED RI FUNCTIONS
function n = calcRI(X,Y,n_background,nParameters)
% n may be complex
n = n_background*ones(size(X)); % Start by setting all pixels to n_background
n(X.^2 + Y.^2 < 5e-6^2) = 1.46;
end