[examples/fdfd] split fdfd example into two files
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103
examples/fdfd0.py
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103
examples/fdfd0.py
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import numpy
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from numpy.linalg import norm
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from matplotlib import pyplot, colors
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import logging
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import meanas
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from meanas import fdtd
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from meanas.fdmath import vec, unvec
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from meanas.fdfd import waveguide_3d, functional, scpml, operators
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from meanas.fdfd.solvers import generic as generic_solver
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import gridlock
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logging.basicConfig(level=logging.DEBUG)
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logging.getLogger('matplotlib').setLevel(logging.WARNING)
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__author__ = 'Jan Petykiewicz'
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def pcolor(ax, v) -> None:
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mappable = ax.pcolor(v, cmap='seismic', norm=colors.CenteredNorm())
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ax.axis('equal')
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ax.get_figure().colorbar(mappable)
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def test0(solver=generic_solver):
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dx = 50 # discretization (nm/cell)
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pml_thickness = 10 # (number of cells)
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wl = 1550 # Excitation wavelength
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omega = 2 * numpy.pi / wl
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# Device design parameters
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radii = (1, 0.6)
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th = 220
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center = [0, 0, 0]
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# refractive indices
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n_ring = numpy.sqrt(12.6) # ~Si
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n_air = 4.0 # air
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# Half-dimensions of the simulation grid
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xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx
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# Coordinates of the edges of the cells.
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half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max]
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edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
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# #### Create the grid, mask, and draw the device ####
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grid = gridlock.Grid(edge_coords)
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epsilon = grid.allocate(n_air**2, dtype=numpy.float32)
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grid.draw_cylinder(
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epsilon,
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h = dict(axis='z', center=center[2], span=th),
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radius = max(radii),
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center2d = center[:2],
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foreground = n_ring ** 2,
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num_points = 24,
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)
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grid.draw_cylinder(
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epsilon,
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h = dict(axis='z', center=center[2], span=th * 1.1),
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radius = min(radii),
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center2d = center[:2],
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foreground = n_air ** 2,
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num_points = 24,
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)
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dxes = [grid.dxyz, grid.autoshifted_dxyz()]
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for a in (0, 1, 2):
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for p in (-1, 1):
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dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega,
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thickness=pml_thickness)
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J = [numpy.zeros_like(epsilon[0], dtype=complex) for _ in range(3)]
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J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1
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#
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# Solve!
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#
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sim_args = dict(
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omega = omega,
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dxes = dxes,
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epsilon = vec(epsilon),
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)
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x = solver(J=vec(J), **sim_args)
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A = operators.e_full(omega, dxes, vec(epsilon)).tocsr()
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b = -1j * omega * vec(J)
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print('Norm of the residual is ', norm(A @ x - b) / norm(b))
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E = unvec(x, grid.shape)
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#
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# Plot results
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#
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grid.visualize_slice(E.real, plane=dict(z=0), which_shifts=1, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr'))
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if __name__ == '__main__':
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test0()
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@ -1,6 +1,8 @@
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import importlib
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import numpy
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from numpy.linalg import norm
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from matplotlib import pyplot, colors
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import logging
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import meanas
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from meanas import fdtd
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@ -10,9 +12,6 @@ from meanas.fdfd.solvers import generic as generic_solver
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import gridlock
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from matplotlib import pyplot
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import logging
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logging.basicConfig(level=logging.DEBUG)
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logging.getLogger('matplotlib').setLevel(logging.WARNING)
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@ -20,86 +19,6 @@ logging.getLogger('matplotlib').setLevel(logging.WARNING)
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__author__ = 'Jan Petykiewicz'
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def test0(solver=generic_solver):
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dx = 50 # discretization (nm/cell)
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pml_thickness = 10 # (number of cells)
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wl = 1550 # Excitation wavelength
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omega = 2 * numpy.pi / wl
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# Device design parameters
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radii = (1, 0.6)
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th = 220
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center = [0, 0, 0]
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# refractive indices
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n_ring = numpy.sqrt(12.6) # ~Si
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n_air = 4.0 # air
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# Half-dimensions of the simulation grid
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xyz_max = numpy.array([1.2, 1.2, 0.3]) * 1000 + pml_thickness * dx
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# Coordinates of the edges of the cells.
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half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max]
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edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
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# #### Create the grid, mask, and draw the device ####
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grid = gridlock.Grid(edge_coords)
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epsilon = grid.allocate(n_air**2, dtype=numpy.float32)
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grid.draw_cylinder(
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epsilon,
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surface_normal=2,
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center=center,
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radius=max(radii),
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thickness=th,
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foreground=n_ring**2,
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num_points=24,
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)
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grid.draw_cylinder(
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epsilon,
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surface_normal=2,
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center=center,
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radius=min(radii),
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thickness=th*1.1,
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foreground=n_air ** 2,
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num_points=24,
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)
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dxes = [grid.dxyz, grid.autoshifted_dxyz()]
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for a in (0, 1, 2):
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for p in (-1, 1):
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dxes = meanas.fdfd.scpml.stretch_with_scpml(dxes, axis=a, polarity=p, omega=omega,
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thickness=pml_thickness)
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J = [numpy.zeros_like(epsilon[0], dtype=complex) for _ in range(3)]
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J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1
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#
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# Solve!
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#
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sim_args = {
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'omega': omega,
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'dxes': dxes,
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'epsilon': vec(epsilon),
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}
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x = solver(J=vec(J), **sim_args)
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A = operators.e_full(omega, dxes, vec(epsilon)).tocsr()
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b = -1j * omega * vec(J)
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print('Norm of the residual is ', norm(A @ x - b))
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E = unvec(x, grid.shape)
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#
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# Plot results
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#
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pyplot.figure()
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pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic')
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pyplot.axis('equal')
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pyplot.show()
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def test1(solver=generic_solver):
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dx = 40 # discretization (nm/cell)
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pml_thickness = 10 # (number of cells)
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@ -126,7 +45,7 @@ def test1(solver=generic_solver):
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# #### Create the grid and draw the device ####
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grid = gridlock.Grid(edge_coords)
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epsilon = grid.allocate(n_air**2, dtype=numpy.float32)
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grid.draw_cuboid(epsilon, center=center, dimensions=[8e3, w, th], foreground=n_wg**2)
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grid.draw_cuboid(epsilon, x=dict(center=0, span=8e3), y=dict(center=0, span=w), z=dict(center=0, span=th), foreground=n_wg**2)
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dxes = [grid.dxyz, grid.autoshifted_dxyz()]
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for a in (0, 1, 2):
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@ -160,17 +79,9 @@ def test1(solver=generic_solver):
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# grid.draw_cuboid(pmcg, center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1)
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# grid.visualize_isosurface(pmcg)
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def pcolor(v) -> None:
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vmax = numpy.max(numpy.abs(v))
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pyplot.pcolor(v, cmap='seismic', vmin=-vmax, vmax=vmax)
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pyplot.axis('equal')
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pyplot.colorbar()
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ss = (1, slice(None), J.shape[2]//2+6, slice(None))
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# pyplot.figure()
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# pcolor(J3[ss].T.imag)
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# pyplot.figure()
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# pcolor((numpy.abs(J3).sum(axis=2).sum(axis=0) > 0).astype(float).T)
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grid.visualize_slice(J.imag, plane=dict(y=6*dx), which_shifts=1, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr'))
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fig, ax = pyplot.subplots()
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ax.pcolormesh((numpy.abs(J).sum(axis=2).sum(axis=0) > 0).astype(float).T, cmap='hot')
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pyplot.show(block=True)
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#
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# Plot results
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#
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center = grid.pos2ind([0, 0, 0], None).astype(int)
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pyplot.figure()
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pyplot.subplot(2, 2, 1)
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pcolor(numpy.real(E[1][center[0], :, :]).T)
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pyplot.subplot(2, 2, 2)
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pyplot.plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10))
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pyplot.grid(alpha=0.6)
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pyplot.ylabel('log10 of field')
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pyplot.subplot(2, 2, 3)
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pcolor(numpy.real(E[1][:, :, center[2]]).T)
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pyplot.subplot(2, 2, 4)
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fig, axes = pyplot.subplots(2, 2)
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grid.visualize_slice(E.real, plane=dict(x=0), which_shifts=1, ax=axes[0, 0], finalize=False, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr'))
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grid.visualize_slice(E.real, plane=dict(z=0), which_shifts=1, ax=axes[0, 1], finalize=False, pcolormesh_args=dict(norm=colors.CenteredNorm(), cmap='bwr'))
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# pcolor(axes[0, 0], numpy.real(E[1][center[0], :, :]).T)
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# pcolor(axes[0, 1], numpy.real(E[1][:, :, center[2]]).T)
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axes[1, 0].plot(numpy.log10(numpy.abs(E[1][:, center[1], center[2]]) + 1e-10))
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axes[1, 0].grid(alpha=0.6)
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axes[1, 0].set_ylabel('log10 of field')
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def poyntings(E):
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H = functional.e2h(omega, dxes)(E)
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@ -219,34 +128,35 @@ def test1(solver=generic_solver):
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return s0, s1, s2
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s0x, s1x, s2x = poyntings(E)
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pyplot.plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.')
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pyplot.plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.')
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pyplot.plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.')
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pyplot.plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x')
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pyplot.grid(alpha=0.6)
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pyplot.legend()
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pyplot.show()
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ax = axes[1, 1]
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ax.plot(s0x[0].sum(axis=2).sum(axis=1), label='s0', marker='.')
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ax.plot(s1x[0].sum(axis=2).sum(axis=1), label='s1', marker='.')
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ax.plot(s2x[0].sum(axis=2).sum(axis=1), label='s2', marker='.')
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ax.plot(E[1][:, center[1], center[2]].real.T, label='Ey', marker='x')
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ax.grid(alpha=0.6)
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ax.legend()
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p_in = (-E * J.conj()).sum() / 2 * (dx * dx * dx)
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print(f'{p_in=}')
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q = []
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for i in range(-5, 30):
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e_ovl_rolled = numpy.roll(e_overlap, i, axis=1)
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q += [numpy.abs(vec(E) @ vec(e_ovl_rolled).conj())]
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pyplot.figure()
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pyplot.plot(q, marker='.')
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pyplot.grid(alpha=0.6)
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pyplot.title('Overlap with mode')
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pyplot.show()
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q += [numpy.abs(vec(E).conj() @ vec(e_ovl_rolled))]
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fig, ax = pyplot.subplots()
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ax.plot(q, marker='.')
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ax.grid(alpha=0.6)
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ax.set_title('Overlap with mode')
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print('Average overlap with mode:', sum(q[8:32])/len(q[8:32]))
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pyplot.show(block=True)
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def module_available(name):
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return importlib.util.find_spec(name) is not None
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if __name__ == '__main__':
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#test0()
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# test1()
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if module_available('opencl_fdfd'):
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from opencl_fdfd import cg_solver as opencl_solver
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test1(opencl_solver)
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@ -257,3 +167,4 @@ if __name__ == '__main__':
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# test1(magma_solver)
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else:
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test1()
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