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@ -137,7 +137,9 @@ def test1(solver=generic_solver):
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wg_results = waveguide_mode.solve_waveguide_mode(mode_number=0, **wg_args)
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J = waveguide_mode.compute_source(**wg_args, E=wg_results['E'], wavenumber=wg_results['wavenumber'])
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H_overlap = waveguide_mode.compute_overlap_e(**wg_args, **wg_results)
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H_overlap, slices = waveguide_mode.compute_overlap_ce(E=wg_results['E'], wavenumber=wg_results['wavenumber'],
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dxes=dxes, axis=src_axis, polarity=wg_args['polarity'],
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slices=wg_args['slices'])
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pecg = gridlock.Grid(edge_coords, initial=0.0, num_grids=3)
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# pecg.draw_cuboid(center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1)
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@ -153,6 +155,13 @@ def test1(solver=generic_solver):
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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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pyplot.show(block=True)
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'''
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Solve!
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'''
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@ -186,12 +195,14 @@ def test1(solver=generic_solver):
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pyplot.subplot(2, 2, 4)
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def poyntings(E):
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e = vec(E)
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h = operators.e2h(omega, dxes) @ e
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cross1 = operators.poynting_e_cross(e, dxes) @ h.conj()
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cross2 = operators.poynting_h_cross(h.conj(), dxes) @ e
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H = functional.e2h(omega, dxes)(E)
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poynting = 0.5 * fdtd.poynting(e=E, h=H.conj()) * dx * dx
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cross1 = operators.poynting_e_cross(vec(E), dxes) @ vec(H).conj()
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# cross2 = operators.poynting_h_cross(h.conj(), dxes) @ e
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s1 = unvec(0.5 * numpy.real(cross1), grid.shape)
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s2 = unvec(0.5 * numpy.real(-cross2), grid.shape)
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# s2 = unvec(0.5 * numpy.real(-cross2), grid.shape)
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s2 = poynting.real
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# s2 = poynting.imag
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return s1, s2
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s1x, s2x = poyntings(E)
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@ -202,7 +213,7 @@ def test1(solver=generic_solver):
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q = []
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for i in range(-5, 30):
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H_rolled = [numpy.roll(h, i, axis=0) for h in H_overlap]
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q += [numpy.abs(vec(E) @ vec(H_rolled))]
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q += [numpy.abs(vec(E) @ vec(H_rolled).conj())]
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pyplot.figure()
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pyplot.plot(q)
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pyplot.title('Overlap with mode')
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@ -453,8 +453,7 @@ def poynting_e_cross(e: vfield_t, dxes: dx_lists_t) -> sparse.spmatrix:
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"""
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shape = [len(dx) for dx in dxes[0]]
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fx, fy, fz = [avgf(i, shape) for i in range(3)]
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bx, by, bz = [avgb(i, shape) for i in range(3)]
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bx, by, bz = [rotation(i, shape, -1) for i in range(3)]
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dxag = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[0], indexing='ij')]
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dbgx, dbgy, dbgz = [sparse.diags(dx.ravel(order='C'))
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@ -463,12 +462,11 @@ def poynting_e_cross(e: vfield_t, dxes: dx_lists_t) -> sparse.spmatrix:
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Ex, Ey, Ez = [sparse.diags(ei * da) for ei, da in zip(numpy.split(e, 3), dxag)]
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n = numpy.prod(shape)
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zero = sparse.csr_matrix((n, n))
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P = sparse.bmat(
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[[ zero, -fx @ Ez @ bz @ dbgy, fx @ Ey @ by @ dbgz],
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[ fy @ Ez @ bz @ dbgx, zero, -fy @ Ex @ bx @ dbgz],
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[-fz @ Ey @ by @ dbgx, fz @ Ex @ bx @ dbgy, zero]])
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[[ None, -bx @ Ez @ dbgy, bx @ Ey @ dbgz],
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[ by @ Ez @ dbgx, None, -by @ Ex @ dbgz],
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[-bz @ Ey @ dbgx, bz @ Ex @ dbgy, None]])
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return P
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@ -482,7 +480,7 @@ def poynting_h_cross(h: vfield_t, dxes: dx_lists_t) -> sparse.spmatrix:
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"""
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shape = [len(dx) for dx in dxes[0]]
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fx, fy, fz = [avgf(i, shape) for i in range(3)]
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fx, fy, fz = [avgf(i, shape) for i in range(3)] #TODO
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bx, by, bz = [avgb(i, shape) for i in range(3)]
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dxbg = [dx.ravel(order='C') for dx in numpy.meshgrid(*dxes[1], indexing='ij')]
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@ -545,4 +543,12 @@ def e_boundary_source(mask: vfield_t,
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r3 = sparse.block_diag((r, r, r))
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jmask = numpy.logical_or(jmask, numpy.abs(r3 @ mask))
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# jmask = ((numpy.roll(mask, -1, axis=0) != mask) |
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# (numpy.roll(mask, +1, axis=0) != mask) |
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# (numpy.roll(mask, -1, axis=1) != mask) |
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# (numpy.roll(mask, +1, axis=1) != mask) |
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# (numpy.roll(mask, -1, axis=2) != mask) |
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# (numpy.roll(mask, +1, axis=2) != mask))
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return sparse.diags(jmask.astype(int)) @ full
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@ -186,7 +186,7 @@ def _normalized_fields(e: numpy.ndarray,
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norm_amplitude = 1 / numpy.sqrt(P)
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norm_angle = -numpy.angle(e[energy.argmax()]) # Will randomly add a negative sign when mode is symmetric
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# Try to break symmetry to assign a consistent sign [experimental]
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# Try to break symmetry to assign a consistent sign [experimental TODO]
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E_weighted = unvec(e * energy * numpy.exp(1j * norm_angle), shape)
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sign = numpy.sign(E_weighted[:, :max(shape[0]//2, 1), :max(shape[1]//2, 1)].real.sum())
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@ -112,6 +112,8 @@ def solve_waveguide_mode(mode_number: int,
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Apply corrections and expand to 3D
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'''
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# Correct wavenumber to account for numerical dispersion.
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print(fields_2d['wavenumber'] / (2/dx_prop * numpy.arcsin(fields_2d['wavenumber'] * dx_prop/2)))
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print(fields_2d['wavenumber'].real / (2/dx_prop * numpy.arcsin(fields_2d['wavenumber'].real * dx_prop/2)))
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fields_2d['wavenumber'] = 2/dx_prop * numpy.arcsin(fields_2d['wavenumber'] * dx_prop/2)
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# Adjust for propagation direction
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@ -179,20 +181,16 @@ def compute_source(E: field_t,
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def compute_overlap_e(E: field_t,
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H: field_t,
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wavenumber: complex,
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omega: complex,
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dxes: dx_lists_t,
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axis: int,
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polarity: int,
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slices: List[slice],
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epsilon: field_t, # TODO unused??
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mu: field_t = None,
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) -> field_t:
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) -> field_t: # TODO DOCS
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"""
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Given an eigenmode obtained by solve_waveguide_mode, calculates overlap_e for the
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mode orthogonality relation Integrate(((E x H_mode) + (E_mode x H)) dot dn)
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[assumes reflection symmetry].
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[assumes reflection symmetry].i
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overlap_e makes use of the e2h operator to collapse the above expression into
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(vec(E) @ vec(overlap_e)), allowing for simple calculation of the mode overlap.
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@ -211,45 +209,20 @@ def compute_overlap_e(E: field_t,
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"""
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slices = tuple(slices)
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cross_plane = [slice(None)] * 4
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cross_plane[axis + 1] = slices[axis]
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cross_plane = tuple(cross_plane)
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Ee = expand_wgmode_e(E=E, wavenumber=wavenumber, dxes=dxes,
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axis=axis, polarity=polarity, slices=slices)
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# Determine phase factors for parallel slices
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a_shape = numpy.roll([-1, 1, 1], axis)
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a_E = numpy.real(dxes[0][axis]).cumsum()
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a_H = numpy.real(dxes[1][axis]).cumsum()
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iphi = -polarity * 1j * wavenumber
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phase_E = numpy.exp(iphi * (a_E - a_E[slices[axis]])).reshape(a_shape)
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phase_H = numpy.exp(iphi * (a_H - a_H[slices[axis]])).reshape(a_shape)
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start, stop = sorted((slices[axis].start, slices[axis].start - 2 * polarity))
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# Expand our slice to the entire grid using the calculated phase factors
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Ee = phase_E * E[cross_plane]
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He = phase_H * H[cross_plane]
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slices2 = list(slices)
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slices2[axis] = slice(start, stop)
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slices2 = (slice(None), *slices2)
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Etgt = numpy.zeros_like(Ee)
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Etgt[slices2] = Ee[slices2]
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# Write out the operator product for the mode orthogonality integral
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domain = numpy.zeros_like(E[0], dtype=int)
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domain[slices] = 1
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npts = E[0].size
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dn = numpy.zeros(npts * 3, dtype=int)
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dn[0:npts] = 1
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dn = numpy.roll(dn, npts * axis)
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e2h = operators.e2h(omega, dxes, mu)
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ds = sparse.diags(vec([domain]*3))
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h_cross_ = operators.poynting_h_cross(vec(He), dxes)
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e_cross_ = operators.poynting_e_cross(vec(Ee), dxes)
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overlap_e = dn @ ds @ (-h_cross_ + e_cross_ @ e2h)
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# Normalize
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dx_forward = dxes[0][axis][slices[axis]]
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norm_factor = numpy.abs(overlap_e @ vec(Ee))
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overlap_e /= norm_factor * dx_forward
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return unvec(overlap_e, E[0].shape)
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Etgt /= (Etgt.conj() * Etgt).sum()
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return Etgt.conj()
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def solve_waveguide_mode_cylindrical(mode_number: int,
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@ -307,31 +280,6 @@ def solve_waveguide_mode_cylindrical(mode_number: int,
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return fields
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def compute_overlap_ce(E: field_t,
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wavenumber: complex,
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dxes: dx_lists_t,
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axis: int,
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polarity: int,
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slices: List[slice],
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) -> field_t:
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slices = tuple(slices)
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Ee = expand_wgmode_e(E=E, wavenumber=wavenumber, dxes=dxes,
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axis=axis, polarity=polarity, slices=slices)
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start, stop = sorted((slices[axis].start, slices[axis].start - 2 * polarity))
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slices2 = list(slices)
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slices2[axis] = slice(start, stop)
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slices2 = (slice(None), *slices2)
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Etgt = numpy.zeros_like(Ee)
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Etgt[slices2] = Ee[slices2]
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Etgt /= (Etgt.conj() * Etgt).sum()
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return Etgt, slices2
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def expand_wgmode_e(E: field_t,
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wavenumber: complex,
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dxes: dx_lists_t,
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