def transmit2x2(fvec_in,
cmat,
fmatout=None,
tmatin=None,
tmatout=None,
fvec_out=None):
"""Transmits field vector using 2x2 method.
This functions takes a field vector that describes the input field and
computes the output transmited field using the 2x2 characteristic matrix.
"""
b = np.broadcast(fvec_in[..., 0][..., None, None], cmat)
if fmatout is None:
fmatout = f_iso(1, 0, 0)
if fvec_out is not None:
fvec_out[...] = 0
else:
fvec_out = np.zeros(b.shape[:-2] + (4, ), fvec_in.dtype)
if tmatin is not None:
evec = dotmv(tmatin, fvec_in[..., ::2], out=fvec_out[..., ::2])
else:
evec = fvec_in[..., ::2]
eout = dotmv(cmat, evec, out=fvec_out[..., ::2])
if tmatout is not None:
eout = dotmv(tmatout, eout, out=fvec_out[..., ::2])
e2h = E2H_mat(fmatout, mode=+1)
hout = dotmv(e2h, eout, out=fvec_out[..., 1::2])
return fvec_out
def transmitted_field_direct(field, beta, phi, n=1.):
ev = refind2eps([n] * 3)
ea = np.zeros_like(ev)
alpha, fmat = alphaf(beta, phi, ev, ea)
pmat = projection_mat(fmat)
field0 = np.empty_like(field)
dotmv(pmat, transpose(field), out=transpose(field0))
return field0
def field4(fmat, jones=(1, 0), amplitude=1., mode=+1, out=None):
"""Build field vector form a given polarization state, amplitude and mode.
Numpy broadcasting rules apply."""
jones = np.asarray(jones)
amplitude = np.asarray(amplitude)
c, s = jones[..., 0], jones[..., 1]
b = np.broadcast(fmat[..., 0, 0], c, amplitude)
shape = b.shape + (4, )
fmat = normalize_f(fmat)
fvec = np.zeros(shape, CDTYPE)
if mode == +1:
fvec[..., 0] = c
fvec[..., 2] = s
elif mode == -1:
fvec[..., 1] = c
fvec[..., 3] = s
else:
raise ValueError("Unknown propagation mode.")
fvec = dotmv(fmat, fvec, out=out)
a = np.asarray(amplitude)[..., None]
out = np.multiply(fvec, a, out=fvec)
return out
def _reflect2d(fvec_in, fmat_in, rmat, fmat_out, fvec_out=None):
"""Transmits/reflects field vector using 4x4 method.
This functions takes a field vector that describes the input field and
computes the output transmited field and also updates the input field
with the reflected waves.
"""
fmat_ini = inv(fmat_in)
avec = dotmv(fmat_ini, fvec_in)
a = np.zeros(avec.shape, avec.dtype)
a[..., 0::2] = avec[..., 0::2]
if fvec_out is not None:
fmat_outi = inv(fmat_out)
bvec = dotmv(fmat_outi, fvec_out)
a[..., 1::2] = bvec[..., 1::2]
else:
bvec = np.zeros_like(avec)
av = a.reshape(a.shape[:-2] + (a.shape[-2] * a.shape[-1], ))
out = dotmv(rmat, av).reshape(a.shape)
avec[..., 1::2] = out[..., 1::2]
bvec[..., ::2] = out[..., ::2]
dotmv(fmat_in, avec, out=fvec_in)
return dotmv(fmat_out, bvec, out=out)
def jonesvec(pol, phi=0., out=None):
"""Returns a normalized jones vector from an input length 2 vector., Additionaly,
you can use this function to view the jones vector in rotated coordinate frame,
defined with a rotation angle phi.
Numpy broadcasting rules apply.
Parameters
----------
pol : (...,2) array
Input jones vector. Does not need to be normalized.
phi : float or (...,1) array
If jones vector must be view in the rotated frame, this parameter
defines the rotation angle.
out : ndarray
Output array in which to put the result; if provided, it
must have a shape that the inputs broadcast to.
Returns
-------
vec : ndarray
Normalized jones vector
Example
-------
>>> jonesvec((1,1j)) #left-handed circuar polarization
array([0.70710678+0.j , 0. +0.70710678j])
In rotated frame
>>> j1,j2 = jonesvec((1,1j), (np.pi/2,np.pi/4))
>>> np.allclose(j1, (0.70710678j,-0.70710678))
True
>>> np.allclose(j2, (0.5+0.5j,-0.5+0.5j))
True
"""
pol = np.asarray(pol, CDTYPE)
phi = np.asarray(phi)
if pol.shape[-1] != 2:
raise ValueError("Invalid input shape")
norm = (pol[..., 0] * pol[..., 0].conj() +
pol[..., 1] * pol[..., 1].conj())**0.5
pol = pol / norm[..., np.newaxis]
pol = np.asarray(pol, CDTYPE)
r = rotation_matrix2(-phi)
return dotmv(r, pol, out)
def transmit(fvec_in,
cmat,
fmatin=None,
fmatout=None,
fmatini=None,
fmatouti=None,
fvec_out=None):
"""Transmits field vector using 4x4 method.
This functions takes a field vector that describes the input field and
computes the output transmited field and also updates the input field
with the reflected waves.
"""
b = np.broadcast(fvec_in[..., None], cmat, fmatin, fmatout)
if fmatini is None:
if fmatin is None:
fmatin = f_iso(1, 0, 0)
fmatini = inv(fmatin)
if fmatin is None:
fmatin = inv(fmatini)
if fmatouti is None:
if fmatout is None:
fmatout = fmatin
fmatouti = fmatini
else:
fmatouti = inv(fmatout)
if fmatout is None:
fmatout = inv(fmatouti)
smat = system_mat(cmat, fmatini=fmatini, fmatout=fmatout)
avec = dotmv(fmatini, fvec_in)
a = np.zeros(b.shape[:-1], avec.dtype)
a[..., 0::2] = avec[..., 0::2]
avec = a.copy() #so that it broadcasts
if fvec_out is not None:
bvec = dotmv(fmatouti, fvec_out)
a[..., 1::2] = bvec[..., 1::2]
else:
bvec = np.zeros_like(avec)
r = reflection_mat(smat)
out = dotmv(r, a, out=fvec_out)
avec[..., 1::2] = out[..., 1::2]
bvec[..., ::2] = out[..., ::2]
dotmv(fmatin, avec, out=fvec_in)
return dotmv(fmatout, bvec, out=out)
def apply_jonesmat(pmat, field, out=None):
"""Multiplies a (2x2) or (4x4) jones matrix with field vector
Parameters
----------
pmat : ndarray
A 4x4 jones matrix of shape (...,4,4) for field data or
2x2 jones matrix of shape (...,2,2) for E-field data or
field : array
Field vector array of shape (...,4) or (...,2).
out : array, optional
If specified, the results are written here.
Returns
-------
out : ndarray
Computed field array of shape (...,4).
"""
return dotmv(pmat, field, out=out)
def jonesvec(pol, phi=0.):
"""Returns a normalized jones vector from an input length 2 vector., Additionaly,
you can use this function to view the jones vactor in rotated coordinate frame,
defined with a rotation angle phi.
Numpy broadcasting rules apply.
Example
-------
>>> jonesvec((1,1j)) #left-handed circuar polarization
array([0.70710678+0.j , 0. +0.70710678j])
"""
pol = np.asarray(pol, CDTYPE)
assert pol.shape[-1] == 2
norm = (pol[..., 0] * pol[..., 0].conj() +
pol[..., 1] * pol[..., 1].conj())**0.5
pol = pol / norm[..., np.newaxis]
pol = np.asarray(pol, CDTYPE)
r = rotation_matrix2(-phi)
return dotmv(r, pol)