def _layer_mat2d(k0, d, epsv, epsa, mask, betaxs, betay, indices, method):
n = len(betaxs)
kd = k0 * d
shape = epsv.shape[-2]
out = np.empty(shape=(n, n, 4, 4), dtype=CDTYPE)
beta = betaxy2beta(betaxs, betay)
phi = betaxy2phi(betaxs, betay)
for j, (beta, phi) in enumerate(zip(beta, phi)):
alpha, f, fi = alphaffi(beta, phi, epsv, epsa)
pmat = phase_mat(alpha, -kd)
if method == "4x4_1":
pmat[..., 1::2] = 0.
elif method != "4x4":
raise ValueError("Unsupported method!")
wave = eigenwave1(shape, indices[j], amplitude=1.)
#m is shape (...,4,4)
m = dotmdm(f, pmat, fi)
#wave is shape (...) make it broadcastable to (...,4,4)
mw = m * wave[..., None, None]
mf = mfft(mw, overwrite_x=True)
mf = mf[mask, ...]
out[:, j, :, :] = mf
#for i,mfj in enumerate(mf):
# out[i,j,:,:] = mfj
return out
def _layer_mat3d(k0, d, epsv, epsa, mask, betas, phis, indices, method):
n = len(betas)
kd = k0 * d #/2.
shape = epsv.shape[-3], epsv.shape[-2]
if method.startswith("2x2"):
out = np.empty(shape=(n, n, 2, 2), dtype=CDTYPE)
else:
out = np.empty(shape=(n, n, 4, 4), dtype=CDTYPE)
for j, (beta, phi) in enumerate(zip(betas, phis)):
if method.startswith("2x2"):
alpha, fmat = alphaf(beta, phi, epsv, epsa)
f = tmm.E_mat(fmat, mode=+1, copy=False)
fi = inv(f)
pmat = phase_mat(alpha[..., ::2], kd)
else:
alpha, f, fi = alphaffi(beta, phi, epsv, epsa)
pmat = phase_mat(alpha, -kd)
if method == "4x4_1":
pmat[..., 1::2] = 0.
if method != "4x4":
raise ValueError("Unsupported method.")
wave = eigenwave(shape, indices[j, 0], indices[j, 1], amplitude=1.)
m = dotmdm(f, pmat, fi)
mw = m * wave[..., None, None]
mf = mfft2(mw, overwrite_x=True)
#dd = np.linspace(0,1.,10)*d
# dmat = 0.
# for dm in dd:
# dmat = dmat + second_field_diffraction_matrix(shape, -k0, beta, phi,dm,
# epsv = (1.5,1.5,1.5),
# epsa = (0.,0.,0.), betamax = 1.4) /len(dd)
# mf = dotmm(dmat,mf)
mf = mf[mask, ...]
out[:, j, :, :] = mf
return out
def phase_matrix(alpha, kd, mode=None, mask=None, out=None):
kd = np.asarray(kd, dtype=FDTYPE)
out = phase_mat(alpha, kd[..., None, None], out=out)
if mode == "t" or mode == +1:
out[..., 1::2] = 0.
elif mode == "r" or mode == -1:
out[..., ::2] = 0.
if mask is not None:
out[mask] = 0.
return out
def Epn_correction_matrix(beta,
phi,
ks,
d=1.,
epsv=(1, 1, 1),
epsa=(0, 0, 0.),
out=None):
alpha, f = alphaf(beta, phi, epsv, epsa)
kd = -np.asarray(ks) * d
pmat = phase_mat(alpha, kd[..., None, None])
e = E_mat(f, mode=None)
ei = inv(e)
return dotmdm(e, pmat, ei, out=out)
def first_Epn_diffraction_matrix(shape,
ks,
d=1.,
epsv=(1, 1, 1),
epsa=(0, 0, 0.),
betamax=BETAMAX,
out=None):
ks = np.asarray(ks, dtype=FDTYPE)
epsv = np.asarray(epsv, dtype=CDTYPE)
epsa = np.asarray(epsa, dtype=FDTYPE)
alpha, f, fi = diffraction_alphaffi(shape,
ks,
epsv=epsv,
epsa=epsa,
betamax=betamax)
kd = ks * d
e = E_mat(f, mode=None)
pmat = phase_mat(alpha, kd[..., None, None])
return dotmdm(e, pmat, fi, out=out)
def propagate_2x2_full(field,
wavenumbers,
layer,
input_layer=None,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None):
shape = field.shape[-2:]
d, epsv, epsa = layer
if input_layer is not None:
d_in, epsv_in, epsa_in = input_layer
kd = wavenumbers * d / nsteps
if out is None:
out = np.empty_like(field)
ii, jj = np.meshgrid(range(shape[0]),
range(shape[1]),
copy=False,
indexing="ij")
for step in range(nsteps):
for i in range(len(wavenumbers)):
ffield = fft2(field[..., i, :, :, :])
ofield = np.zeros_like(out[..., i, :, :, :])
b, p = betaphi(shape, wavenumbers[i])
mask = b < betamax
amplitude = ffield[..., mask]
betas = b[mask]
phis = p[mask]
iind = ii[mask]
jind = jj[mask]
if bulk is not None:
obulk = bulk[..., i, :, :, :]
if refl is not None:
tampl = fft2(refl[..., i, :, :, :])[..., mask]
orefl = refl[..., i, :, :, :]
orefl[...] = 0.
for bp in sorted(zip(range(len(betas)), betas, phis, iind, jind),
key=lambda el: el[1],
reverse=False):
#for j,bp in enumerate(zip(betas,phis,iind,jind)):
j, beta, phi, ieig, jeig = bp
out_af = alphaf(beta, phi, epsv, epsa)
alpha, fmat_out = out_af
e = E_mat(fmat_out, mode=mode)
ei0 = inv(e)
ei = ei0
pm = phase_mat(alpha, kd[i, None, None], mode=mode)
w = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=amplitude[..., j])
if step == 0 and reflection != False:
alphain, fmat_in = alphaf(beta, phi, epsv_in, epsa_in)
if refl is not None:
ei, eri = Etri_mat(fmat_in, fmat_out, mode=mode)
ein = E_mat(fmat_in, mode=-1 * mode)
t = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=tampl[..., j])
r = dotmf(eri, w)
r = dotmf(ein, r, out=r)
np.add(orefl, r, orefl)
w = dotmf(ei, w, out=w)
t = dotmf(ei0, t, out=t)
w = np.add(t, w, out=w)
else:
ei = Eti_mat(fmat_in, fmat_out, mode=mode)
w = dotmf(ei, w, out=w)
w = dotmf(dotmd(e, pm), w, out=w)
np.add(ofield, w, ofield)
else:
w = dotmdmf(e, pm, ei, w, out=w)
np.add(ofield, w, ofield)
if bulk is not None:
e2h = E2H_mat(fmat_out, mode=mode)
obulk[..., 1::2, :, :] += dotmf(e2h, w)
obulk[..., ::2, :, :] += w
out[..., i, :, :, :] = ofield
field = out
return out, refl
def _transfer_ray_2x2_1(fft_field,
wavenumbers,
layer,
effective_layer_in,
effective_layer_out,
dmat1,
dmat2,
beta=0,
phi=0,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None,
tmpdata=None):
_out = {} if tmpdata is None else tmpdata
#fft_field = fft2(fft_field, out = out)
shape = fft_field.shape[-2:]
d_in, epsv_in, epsa_in = effective_layer_in
d_out, epsv_out, epsa_out = effective_layer_out
if reflection:
tmat, rmat = E_tr_matrix(shape,
wavenumbers,
epsv_in=epsv_in,
epsa_in=epsa_in,
epsv_out=epsv_out,
epsa_out=epsa_out,
mode=mode,
betamax=betamax)
d, epsv, epsa = layer
alpha, fmat = alphaf(beta, phi, epsv, epsa, out=_out.get("alphaf"))
e = E_mat(fmat, mode=mode, copy=False) #2x2 E-only view of fmat
ei = inv(e, out=_out.get("ei"))
#
kd = wavenumbers * d
p = phase_mat(alpha, kd[..., None, None], mode=mode, out=_out.get("p"))
if tmpdata is not None:
_out["alphaf"] = alpha, fmat
_out["ei"] = ei
_out["p"] = p
for j in range(nsteps):
if j == 0 and reflection:
#reflect only at the beginning
if refl is not None:
trans = refl.copy()
refl = dotmf(rmat, fft_field, out=refl)
fft_field = dotmf(tmat, fft_field, out=out)
fft_field = np.add(fft_field, trans, out=fft_field)
if mode == -1 and bulk is not None:
field = ifft2(fft_field)
e2h = E2H_mat(fmat, mode=mode)
bulk[..., ::2, :, :] += field
bulk[..., 1::2, :, :] += dotmf(e2h, field, out=field)
fft_field = dotmf(dmat1, fft_field, out=fft_field)
out = fft_field
else:
fft_field = dotmf(tmat, fft_field, out=out)
fft_field = dotmf(dmat1, fft_field, out=fft_field)
out = fft_field
else:
if dmat1 is not None:
fft_field = dotmf(dmat1, fft_field, out=out)
out = fft_field
field = ifft2(fft_field, out=out)
field = dotmdmf(e, p, ei, field, out=field)
fft_field = fft2(field, out=field)
if dmat2 is not None:
fft_field = dotmf(dmat2, fft_field, out=fft_field)
#return fft_field, refl
#out = ifft2(fft_field, out = out)
if mode == +1 and bulk is not None:
field = ifft2(fft_field)
e2h = E2H_mat(fmat, mode=mode)
bulk[..., 1::2, :, :] += dotmf(e2h, field)
bulk[..., ::2, :, :] += field
return fft_field, refl
def _transfer_ray_2x2_2(field,
wavenumbers,
in_layer,
out_layer,
dmat=None,
beta=0,
phi=0,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None,
tmpdata=None):
_out = {} if tmpdata is None else tmpdata
if in_layer is not None:
d, epsv, epsa = in_layer
alpha, fmat_in = alphaf(beta, phi, epsv, epsa, out=_out.get("afin"))
if tmpdata is not None:
_out["afin"] = alpha, fmat_in
d, epsv, epsa = out_layer
alpha, fmat = alphaf(beta, phi, epsv, epsa, out=_out.get("afout"))
e = E_mat(fmat, mode=mode, copy=False) #2x2 E-only view of fmat
# if refl is not None:
# ein = E_mat(fmat_in, mode = mode * (-1)) #reverse direction
#
# if reflection == 0:
# kd = wavenumbers * d
# else:
kd = wavenumbers * d / 2
p = phase_mat(alpha, kd[..., None, None], mode=mode, out=_out.get("p"))
ei0 = inv(e, out=_out.get("ei0"))
ei = ei0
if tmpdata is not None:
_out["afout"] = alpha, fmat
_out["ei0"] = ei
_out["p"] = p
for j in range(nsteps):
#reflect only at the beginning
if j == 0 and reflection != 0:
#if we need to track reflections (multipass)
if refl is not None:
#ei,eri = Etri_mat(fmat_in, fmat, mode = mode, out = _out.get("eieri"))
tmat, rmat = tr_mat(fmat_in,
fmat,
mode=mode,
out=_out.get("eieri"))
if tmpdata is not None:
#_out["eieri"] = ei,eri
_out["eieri"] = tmat, rmat
trans = refl.copy()
#refl = dotmf(eri, field, out = refl)
refl = dotmf(rmat, field, out=refl)
#field = dotmf(ei,field, out = out)
field = dotmf(tmat, field, out=out)
field = np.add(field, trans, out=field)
if mode == -1 and bulk is not None:
#tmp_field = dotmf(e,field)
tmp_field = field
e2h = E2H_mat(fmat, mode=mode)
bulk[..., ::2, :, :] += tmp_field
bulk[..., 1::2, :, :] += dotmf(e2h, tmp_field)
field = dotmf(ei, field, out=field)
if d != 0.:
field = dotmf(dotmd(e, p), field, out=field)
else:
field = dotmf(e, field, out=field)
out = field
# rmat = dotmm(ein, eri, out = eri)
# trans = refl.copy()
# refl = dotmf(rmat, field, out = refl)
# ei0 = inv(e)
# field = dotmf(ei,field, out = out)
# field = dotmf(e,field) + trans
# if d != 0.:
# field = dotmdmf(e,p,ei0,field, out = out)
ei = ei0
else:
ei = Eti_mat(fmat_in, fmat, mode=mode, out=_out.get("eti"))
field = dotmdmf(e, p, ei, field, out=out)
out = field
if tmpdata is not None:
_out["eti"] = ei
ei = ei0
else:
#no need to compute if d == 0!.. identity
if d != 0.:
field = dotmdmf(e, p, ei, field, out=out)
out = field
if dmat is not None:
field = diffract(field, dmat, out=out)
out = field
#no need to compute if d == 0!.. identity
if d != 0.:
field = dotmdmf(e, p, ei, field, out=out)
if mode == +1 and bulk is not None:
e2h = E2H_mat(fmat, mode=mode)
bulk[..., 1::2, :, :] += dotmf(e2h, field)
bulk[..., ::2, :, :] += field
return field, refl
#build field matrices
a, f, fi = tmm.alphaffi(betas, phi, eps_layer, eps_angles)
aout, fout, g = tmm.alphaffi(
betas, phi, eps_out,
eps_angles) #eps_angles does nothing because eps_out is isotropic
ain, fin, g = tmm.alphaffi(
betas, phi, eps_in,
eps_angles) #eps_angles does nothing because eps_in is isotropic
dot = dtmm.linalg.dotmm
dotd = dtmm.linalg.dotmd
dotmdm = dtmm.linalg.dotmdm
dotmv = dtmm.linalg.dotmv
intensity = tmm.intensity
intensity = tmm.poynting
p = tmm.phase_mat(a, -kd)
#p = np.exp(-1j*a*kd)
#characteristic matrix
cmat = dotmdm(f, p, fi)
#field projection matrices - used to take the forward propagating or backward propagating waves
pmat = tmm.projection_mat(fout, mode=+1)
mmat = tmm.projection_mat(fin, mode=-1)
pmatin = tmm.projection_mat(fin, mode=+1)
#: build EM field 4-vector (Ex, Hy, Ey, Hx) of a given polarization
fvec = tmm.fvec(fin, jones=pol1)
fvec = dotmv(pmatin, fvec)
#: transmit the field and update fvec with reflected waves
tfvec = tmm.transmit(fvec, cmat, fmatin=fin, fmatout=fout)
#stack = d,eps_values, eps_angles #cmat = tmm.stack_mat(stack,kd, beta = beta, phi = phi) #build field matrices a,f,fi = tmm.alphaffi(beta,phi,eps_values, eps_angles) fout = f[-1] fin = f[0] #now build layer matrices #: in 4x4 we are propagating backward--- minus sign must be taken in the phase p = tmm.phase_mat(a,-kd) # uncoment this to test that setting backward propagating waves to zero, # you have single reflections only... -same result as 2x2 with reflection. #p[...,1::2] = 0. #4x4 characteristic matrix m = dotmdm(f,p,fi) #we could have built layer matrices directly, note the there is no negative value in front of kd: #m = tmm.layer_mat(kd,eps_values, eps_angles, beta = beta, phi = phi) #e field 2x22 matrix.. skip the first layer (air) e = tmm.E_mat(f[1:], mode = +1) # the inverse, no reflections ei = linalg.inv(e) # the inverse, with reflections
