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[fdfd.eme] Add basic (WIP) eignmode expansion functionality

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Jan Petykiewicz 2025-01-28 22:07:19 -08:00
commit cd5cc9eb83
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49
meanas/fdfd/bloch.py
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@ -799,3 +799,52 @@ def _rtrace_AtB(
def _symmetrize(A: NDArray[numpy.complex128]) -> NDArray[numpy.complex128]:
return (A + A.conj().T) * 0.5
def inner_product(eL, hL, eR, hR) -> complex:
# assumes x-axis propagation
assert numpy.array_equal(eR.shape, hR.shape)
assert numpy.array_equal(eL.shape, hL.shape)
assert numpy.array_equal(eR.shape, eL.shape)
# Cross product, times 2 since it's <p | n>, then divide by 4. # TODO might want to abs() this?
norm2R = (eR[1] * hR[2] - eR[2] * hR[1]).sum() / 2
norm2L = (eL[1] * hL[2] - eL[2] * hL[1]).sum() / 2
# eRxhR_x = numpy.cross(eR.reshape(3, -1), hR.reshape(3, -1), axis=0).reshape(eR.shape)[0] / normR
# logger.info(f'power {eRxhR_x.sum() / 2})
eR /= numpy.sqrt(norm2R)
hR /= numpy.sqrt(norm2R)
eL /= numpy.sqrt(norm2L)
hL /= numpy.sqrt(norm2L)
# (eR x hL)[0] and (eL x hR)[0]
eRxhL_x = eR[1] * hL[2] - eR[2] - hL[1]
eLxhR_x = eL[1] * hR[2] - eL[2] - hR[1]
#return 1j * (eRxhL_x - eLxhR_x).sum() / numpy.sqrt(norm2R * norm2L)
#return (eRxhL_x.sum() - eLxhR_x.sum()) / numpy.sqrt(norm2R * norm2L)
return eRxhL_x.sum() - eLxhR_x.sum()
def trq(eI, hI, eO, hO) -> tuple[complex, complex]:
pp = inner_product(eO, hO, eI, hI)
pn = inner_product(eO, hO, eI, -hI)
np = inner_product(eO, -hO, eI, hI)
nn = inner_product(eO, -hO, eI, -hI)
assert pp == -nn
assert pn == -np
logger.info(f'''
{pp=:4g} {pn=:4g}
{nn=:4g} {np=:4g}
{nn * pp / pn=:4g} {-np=:4g}
''')
r = -pp / pn # -<Pp|Bp>/<Pn/Bp> = -(-pp) / (-pn)
t = (np - nn * pp / pn) / 4
return t, r