Example11.m

P = BPMmatlab.model;

% This example shows that refractive indices can be complex, leading to
% losses during propagation. The imaginary part of the refractive index is
% called the extinction coefficient (kappa) and is related to the
% absorption coefficient (alpha) by alpha = 4*pi*kappa/lambda. Both
% n_background and the refractive indices of the individual shapes can be
% complex.

% Here, light is launched into two cores. The cladding and the bottom core
% absorb strongly. As a result, the intensity can be seen to decrease
% rapidly in the bottom core, but also gradually in the top core. This is
% because the evanescent field of the top core mode extends into the
% cladding.

% The example also illustrates that the mode solver can be set to solve for
% modes of each core individually using the singleCoreModes flag. This
% makes no difference in the case where one core absorbs differently than
% the other, but if the cores' absorptions are the same then the mode
% solver will otherwise find symmetric and antisymmetric modes that extend
% into both cores.

%% General and solver-related settings
P.name = mfilename;
P.useAllCPUs = false; % If false, BPM-Matlab will leave one processor unused. Useful for doing other work on the PC while simulations are running.
P.useGPU = false; % (Default: false) Use CUDA acceleration for NVIDIA GPUs

%% Visualization parameters
P.updates = 100;            % Number of times to update plot. Must be at least 1, showing the final state.
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 = 50e-6;        % [m] x side length of main area
P.Ly_main = 50e-6;        % [m] y side length of main area
P.Nx_main = 200;          % x resolution of main area
P.Ny_main = 200;          % 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 = 3e14;             % [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 + 1e-3i; % [] (may be complex) Background refractive index, (in this case, the cladding)
P.n_0 = 1.46; % [] reference refractive index
P.Lz = 2e-3; % [m] z propagation distances for this segment

P = initializeRIfromFunction(P,@calcRI);

P = findModes(P,2,'singleCoreModes',true,'sortByLoss',true); % Find 2 modes, one for each core by itself. Sort them so that lowest loss mode is first.

P.E = modeSuperposition(P,[1 2]);

% Run solver
P = FD_BPM(P);

%% USER DEFINED E-FIELD INITIALIZATION FUNCTION
function E = calcInitialE(X,Y,Eparameters) % Function to determine the initial E field. Eparameters is a cell array of additional parameters such as beam size
w_0 = 2.5e-6;
offset = 2.5e-6;
amplitude = exp(-((X-offset).^2+Y.^2)/w_0^2);
phase = zeros(size(X));
E = amplitude.*exp(1i*phase); % Electric field
end

%% USER DEFINED RI INITIALIZATION FUNCTION
function n = calcRI(X,Y,n_background,nParameters)
n = n_background*ones(size(X));
n((X.^2 + (Y + 10e-6).^2 < 5e-6^2)) = 1.46 + 1e-3i;
n((X.^2 + (Y - 10e-6).^2 < 5e-6^2)) = 1.46;
end