import importlib import numpy from numpy.linalg import norm import meanas from meanas import fdtd from meanas.fdmath import vec, unvec from meanas.fdfd import waveguide_3d, functional, scpml, operators from meanas.fdfd.solvers import generic as generic_solver import gridlock from matplotlib import pyplot import logging logging.basicConfig(level=logging.DEBUG) logging.getLogger('matplotlib').setLevel(logging.WARNING) __author__ = 'Jan Petykiewicz' def test0(solver=generic_solver): dx = 50 # discretization (nm/cell) pml_thickness = 10 # (number of cells) wl = 1550 # Excitation wavelength omega = 2 * numpy.pi / wl # Device design parameters radii = (1, 0.6) th = 220 center = [0, 0, 0] # refractive indices n_ring = numpy.sqrt(12.6) # ~Si n_air = 4.0 # air # Half-dimensions of the simulation grid xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx # Coordinates of the edges of the cells. half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max] edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] # #### Create the grid, mask, and draw the device #### grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3) grid.draw_cylinder(surface_normal=gridlock.Direction.z, center=center, radius=max(radii), thickness=th, eps=n_ring**2, num_points=24) grid.draw_cylinder(surface_normal=gridlock.Direction.z, center=center, radius=min(radii), thickness=th*1.1, eps=n_air ** 2, num_points=24) dxes = [grid.dxyz, grid.autoshifted_dxyz()] for a in (0, 1, 2): for p in (-1, 1): dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega, thickness=pml_thickness) J = [numpy.zeros_like(grid.grids[0], dtype=complex) for _ in range(3)] J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1 ''' Solve! ''' sim_args = { 'omega': omega, 'dxes': dxes, 'epsilon': vec(grid.grids), } x = solver(J=vec(J), **sim_args) A = operators.e_full(omega, dxes, vec(grid.grids)).tocsr() b = -1j * omega * vec(J) print('Norm of the residual is ', norm(A @ x - b)) E = unvec(x, grid.shape) ''' Plot results ''' pyplot.figure() pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic') pyplot.axis('equal') pyplot.show() def test1(solver=generic_solver): dx = 40 # discretization (nm/cell) pml_thickness = 10 # (number of cells) wl = 1550 # Excitation wavelength omega = 2 * numpy.pi / wl # Device design parameters w = 600 th = 220 center = [0, 0, 0] # refractive indices n_wg = numpy.sqrt(12.6) # ~Si n_air = 1.0 # air # Half-dimensions of the simulation grid xyz_max = numpy.array([0.8, 0.9, 0.6]) * 1000 + (pml_thickness + 2) * dx # Coordinates of the edges of the cells. half_edge_coords = [numpy.arange(dx/2, m + dx/2, step=dx) for m in xyz_max] edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords] # #### Create the grid and draw the device #### grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3) grid.draw_cuboid(center=center, dimensions=[8e3, w, th], eps=n_wg**2) dxes = [grid.dxyz, grid.autoshifted_dxyz()] for a in (0, 1, 2): for p in (-1, 1): dxes = scpml.stretch_with_scpml(dxes,omega=omega, axis=a, polarity=p, thickness=pml_thickness) half_dims = numpy.array([10, 20, 15]) * dx dims = [-half_dims, half_dims] dims[1][0] = dims[0][0] ind_dims = (grid.pos2ind(dims[0], which_shifts=None).astype(int), grid.pos2ind(dims[1], which_shifts=None).astype(int)) src_axis = 0 wg_args = { 'slices': [slice(i, f+1) for i, f in zip(*ind_dims)], 'dxes': dxes, 'axis': src_axis, 'polarity': +1, } wg_results = waveguide_3d.solve_mode(mode_number=0, omega=omega, epsilon=grid.grids, **wg_args) J = waveguide_3d.compute_source(E=wg_results['E'], wavenumber=wg_results['wavenumber'], omega=omega, epsilon=grid.grids, **wg_args) e_overlap = waveguide_3d.compute_overlap_e(E=wg_results['E'], wavenumber=wg_results['wavenumber'], **wg_args) pecg = gridlock.Grid(edge_coords, initial=0.0, num_grids=3) # pecg.draw_cuboid(center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1) # pecg.visualize_isosurface() pmcg = gridlock.Grid(edge_coords, initial=0.0, num_grids=3) # pmcg.draw_cuboid(center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1) # pmcg.visualize_isosurface() def pcolor(v): vmax = numpy.max(numpy.abs(v)) pyplot.pcolor(v, cmap='seismic', vmin=-vmax, vmax=vmax) pyplot.axis('equal') pyplot.colorbar() ss = (1, slice(None), J.shape[2]//2+6, slice(None)) # pyplot.figure() # pcolor(J3[ss].T.imag) # pyplot.figure() # pcolor((numpy.abs(J3).sum(axis=2).sum(axis=0) > 0).astype(float).T) pyplot.show(block=True) ''' Solve! ''' sim_args = { 'omega': omega, 'dxes': dxes, 'epsilon': vec(grid.grids), 'pec': vec(pecg.grids), 'pmc': vec(pmcg.grids), } x = solver(J=vec(J), **sim_args) b = -1j * omega * vec(J) A = operators.e_full(**sim_args).tocsr() print('Norm of the residual is ', norm(A @ x - b)) E = unvec(x, grid.shape) ''' Plot results ''' center = grid.pos2ind([0, 0, 0], None).astype(int) pyplot.figure() pyplot.subplot(2, 2, 1) pcolor(numpy.real(E[1][center[0], :, :]).T) pyplot.subplot(2, 2, 2) pyplot.plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10)) pyplot.grid(alpha=0.6) pyplot.ylabel('log10 of field') pyplot.subplot(2, 2, 3) pcolor(numpy.real(E[1][:, :, center[2]]).T) pyplot.subplot(2, 2, 4) def poyntings(E): H = functional.e2h(omega, dxes)(E) poynting = fdtd.poynting(e=E, h=H.conj(), dxes=dxes) cross1 = operators.poynting_e_cross(vec(E), dxes) @ vec(H).conj() cross2 = operators.poynting_h_cross(vec(H), dxes) @ vec(E).conj() * -1 s1 = 0.5 * unvec(numpy.real(cross1), grid.shape) s2 = 0.5 * unvec(numpy.real(cross2), grid.shape) s0 = 0.5 * poynting.real # s2 = poynting.imag return s0, s1, s2 s0x, s1x, s2x = poyntings(E) pyplot.plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.') pyplot.plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.') pyplot.plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.') pyplot.plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x') pyplot.grid(alpha=0.6) pyplot.legend() pyplot.show() q = [] for i in range(-5, 30): e_ovl_rolled = numpy.roll(e_overlap, i, axis=1) q += [numpy.abs(vec(E) @ vec(e_ovl_rolled).conj())] pyplot.figure() pyplot.plot(q, marker='.') pyplot.grid(alpha=0.6) pyplot.title('Overlap with mode') pyplot.show() print('Average overlap with mode:', sum(q)/len(q)) def module_available(name): return importlib.util.find_spec(name) is not None if __name__ == '__main__': #test0() # test1() if module_available('opencl_fdfd'): from opencl_fdfd import cg_solver as opencl_solver test1(opencl_solver) # from opencl_fdfd.csr import fdfd_cg_solver as opencl_csr_solver # test1(opencl_csr_solver) # elif module_available('magma_fdfd'): # from magma_fdfd import solver as magma_solver # test1(magma_solver) else: test1()