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221 lines
6.7 KiB
Python
221 lines
6.7 KiB
Python
"""
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Functional versions of many FDFD operators. These can be useful for performing
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FDFD calculations without needing to construct large matrices in memory.
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The functions generated here expect `fdfield_t` inputs with shape (3, X, Y, Z),
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e.g. E = [E_x, E_y, E_z] where each component has shape (X, Y, Z)
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"""
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from typing import Callable, Tuple
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import numpy # type: ignore
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from ..fdmath import dx_lists_t, fdfield_t, fdfield_updater_t
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from ..fdmath.functional import curl_forward, curl_back
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__author__ = 'Jan Petykiewicz'
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def e_full(omega: complex,
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dxes: dx_lists_t,
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epsilon: fdfield_t,
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mu: fdfield_t = None
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) -> fdfield_updater_t:
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"""
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Wave operator for use with E-field. See `operators.e_full` for details.
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Args:
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omega: Angular frequency of the simulation
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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epsilon: Dielectric constant
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mu: Magnetic permeability (default 1 everywhere)
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Return:
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Function `f` implementing the wave operator
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`f(E)` -> `-i * omega * J`
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"""
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ch = curl_back(dxes[1])
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ce = curl_forward(dxes[0])
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def op_1(e):
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curls = ch(ce(e))
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return curls - omega ** 2 * epsilon * e
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def op_mu(e):
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curls = ch(mu * ce(e))
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return curls - omega ** 2 * epsilon * e
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if numpy.any(numpy.equal(mu, None)):
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return op_1
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else:
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return op_mu
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def eh_full(omega: complex,
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dxes: dx_lists_t,
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epsilon: fdfield_t,
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mu: fdfield_t = None
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) -> Callable[[fdfield_t, fdfield_t], Tuple[fdfield_t, fdfield_t]]:
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"""
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Wave operator for full (both E and H) field representation.
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See `operators.eh_full`.
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Args:
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omega: Angular frequency of the simulation
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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epsilon: Dielectric constant
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mu: Magnetic permeability (default 1 everywhere)
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Returns:
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Function `f` implementing the wave operator
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`f(E, H)` -> `(J, -M)`
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"""
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ch = curl_back(dxes[1])
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ce = curl_forward(dxes[0])
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def op_1(e, h):
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return (ch(h) - 1j * omega * epsilon * e,
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ce(e) + 1j * omega * h)
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def op_mu(e, h):
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return (ch(h) - 1j * omega * epsilon * e,
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ce(e) + 1j * omega * mu * h)
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if numpy.any(numpy.equal(mu, None)):
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return op_1
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else:
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return op_mu
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def e2h(omega: complex,
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dxes: dx_lists_t,
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mu: fdfield_t = None,
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) -> fdfield_updater_t:
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"""
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Utility operator for converting the `E` field into the `H` field.
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For use with `e_full` -- assumes that there is no magnetic current `M`.
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Args:
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omega: Angular frequency of the simulation
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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mu: Magnetic permeability (default 1 everywhere)
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Return:
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Function `f` for converting `E` to `H`,
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`f(E)` -> `H`
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"""
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ce = curl_forward(dxes[0])
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def e2h_1_1(e):
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return ce(e) / (-1j * omega)
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def e2h_mu(e):
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return ce(e) / (-1j * omega * mu)
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if numpy.any(numpy.equal(mu, None)):
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return e2h_1_1
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else:
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return e2h_mu
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def m2j(omega: complex,
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dxes: dx_lists_t,
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mu: fdfield_t = None,
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) -> fdfield_updater_t:
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"""
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Utility operator for converting magnetic current `M` distribution
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into equivalent electric current distribution `J`.
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For use with e.g. `e_full`.
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Args:
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omega: Angular frequency of the simulation
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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mu: Magnetic permeability (default 1 everywhere)
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Returns:
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Function `f` for converting `M` to `J`,
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`f(M)` -> `J`
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"""
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ch = curl_back(dxes[1])
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def m2j_mu(m):
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J = ch(m / mu) / (-1j * omega)
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return J
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def m2j_1(m):
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J = ch(m) / (-1j * omega)
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return J
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if numpy.any(numpy.equal(mu, None)):
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return m2j_1
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else:
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return m2j_mu
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def e_tfsf_source(TF_region: fdfield_t,
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omega: complex,
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dxes: dx_lists_t,
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epsilon: fdfield_t,
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mu: fdfield_t = None,
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) -> fdfield_updater_t:
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"""
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Operator that turns an E-field distribution into a total-field/scattered-field
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(TFSF) source.
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Args:
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TF_region: mask which is set to 1 in the total-field region, and 0 elsewhere
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(i.e. in the scattered-field region).
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Should have the same shape as the simulation grid, e.g. `epsilon[0].shape`.
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omega: Angular frequency of the simulation
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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epsilon: Dielectric constant distribution
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mu: Magnetic permeability (default 1 everywhere)
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Returns:
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Function `f` which takes an E field and returns a current distribution,
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`f(E)` -> `J`
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"""
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# TODO documentation
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A = e_full(omega, dxes, epsilon, mu)
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def op(e):
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neg_iwj = A(TF_region * e) - TF_region * A(e)
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return neg_iwj / (-1j * omega)
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return op
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def poynting_e_cross_h(dxes: dx_lists_t) -> Callable[[fdfield_t, fdfield_t], fdfield_t]:
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"""
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Generates a function that takes the single-frequency `E` and `H` fields
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and calculates the cross product `E` x `H` = $E \\times H$ as required
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for the Poynting vector, $S = E \\times H$
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Note:
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This function also shifts the input `E` field by one cell as required
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for computing the Poynting cross product (see `meanas.fdfd` module docs).
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Note:
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If `E` and `H` are peak amplitudes as assumed elsewhere in this code,
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the time-average of the poynting vector is `<S> = Re(S)/2 = Re(E x H) / 2`.
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The factor of `1/2` can be omitted if root-mean-square quantities are used
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instead.
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Args:
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dxes: Grid parameters `[dx_e, dx_h]` as described in `meanas.fdmath.types`
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Returns:
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Function `f` that returns E x H as required for the poynting vector.
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"""
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def exh(e: fdfield_t, h: fdfield_t):
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s = numpy.empty_like(e)
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ex = e[0] * dxes[0][0][:, None, None]
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ey = e[1] * dxes[0][1][None, :, None]
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ez = e[2] * dxes[0][2][None, None, :]
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hx = h[0] * dxes[1][0][:, None, None]
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hy = h[1] * dxes[1][1][None, :, None]
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hz = h[2] * dxes[1][2][None, None, :]
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s[0] = numpy.roll(ey, -1, axis=0) * hz - numpy.roll(ez, -1, axis=0) * hy
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s[1] = numpy.roll(ez, -1, axis=1) * hx - numpy.roll(ex, -1, axis=1) * hz
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s[2] = numpy.roll(ex, -1, axis=2) * hy - numpy.roll(ey, -1, axis=2) * hx
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return s
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return exh
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