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