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irp
Fresnel
Commits
1fd06c6a
Commit
1fd06c6a
authored
Feb 09, 2021
by
Leon Merten Lohse
Browse files
use consistent scaling and implement CS propagator
parent
cb594a78
Changes
6
Expand all
Hide whitespace changes
Inline
Side-by-side
examples/Test2d.ipynb
View file @
1fd06c6a
%% Cell type:code id: tags:
```
python
import
sys
import
numpy
as
np
import
xraylib
as
xrl
import
matplotlib.pyplot
as
plt
from
pathlib
import
Path
# path to fresnel (adjust if necessary)
sys
.
path
.
append
(
f
'
{
Path
.
home
()
}
/fresnel/'
)
import
fresnel.solver
as
solver
```
%% Cell type:code id: tags:
```
python
from
platform
import
python_version
print
(
python_version
())
```
%%%% Output: stream
3.8.7
%% Cell type:code id: tags:
```
python
%
matplotlib
inline
```
%% Cell type:code id: tags:
```
python
import
fresnel.solver
as
solver
``
`
%%
Cell
type
:
code
id
:
tags
:
```
python
#xrl.GetCompoundDataNISTByName("Kapton Polyimide Film")
```
%% Cell type:code id: tags:
```
python
# simulation box
energy = 12. # keV
wavelength = 1.2398 / (energy
* 1e3) *
1e-3 # mm
nx = 1010
nz = 530
wg_radius = 25e-6
xtot = 10
*
wg_radius # mm
ztot = 0.4 # mm
# units
dx = xtot / nx / wavelength
dz = ztot / nz / wavelength
print(f"dx: {dx}, dz: {dz} wavelengths")
```
%%%% Output: stream
dx: 2.395787247703638, dz: 7304.89092884732 wavelengths
%% Cell type:code id: tags:
```
python
# materials and geometry
density_Ge = xrl.ElementDensity(xrl.SymbolToAtomicNumber('Ge'))
density_Polyimide = 1.42
density_Si = xrl.ElementDensity(xrl.SymbolToAtomicNumber('Si'))
n_Ge = xrl.Refractive_Index('Ge', energy, density_Ge)
n_Si = xrl.Refractive_Index('Si', energy, density_Si)
n_PI = xrl.Refractive_Index('Kapton Polyimide Film', energy, density_Polyimide)
xx = np.linspace(-xtot/2, xtot/2, nx)
core = (np.abs(xx) < wg_radius)
cladding = ~core
refractive_index = n_Ge
* cladding + 1 *
core
```
%% Cell type:code id: tags:
```
python
boundary = (0, 0,)
u0 = np.exp(-xx
**2 / (2 * (2 * wg_radius)**
2)).astype(np.complex128)
```
%% Cell type:code id: tags:
```
python
propagator = solver.Propagator2d(refractive_index, u0, dz, dx)
```
%% Cell type:code id: tags:
```
python
field = np.zeros((nz, nx), dtype=np.complex128)
field[0,...] = u0
for iz in range(1, nz):
boundary = (0,0)
field[iz, ...] = propagator.step(refractive_index, boundary)
```
%% Cell type:code id: tags:
```
python
result = field.transpose()
fig, ax = plt.subplots()
im = ax.imshow(np.abs(result[:,:])
**
2, aspect='auto', clim=(0,3), cmap='jet', extent=[0, ztot, -xtot/2
*1e6, xtot/2 *
1e6])
ax.set_ylim(-2e6
* wg_radius, 2e6 *
wg_radius )
fig.colorbar(im)
ax.set_xlabel(r'$z$ (mm)')
ax.set_ylabel(r'$x$ (nm)')
```
%%%% Output: execute_result
Text(0, 0.5, '$x$ (nm)')
%%%% Output: display_data
%% Cell type:code id: tags:
```
python
```
%% Cell type:code id: tags:
```
python
```
...
...
examples/Test3d.ipynb
View file @
1fd06c6a
%% Cell type:code id: tags:
```
python
import
sys
import
numpy
as
np
import
xraylib
as
xrl
import
matplotlib.pyplot
as
plt
from
pathlib
import
Path
# path to fresnel (adjust if necessary)
sys
.
path
.
append
(
f
'
{
Path
.
home
()
}
/fresnel/'
)
import
fresnel.solver
as
solver
```
%% Cell type:code id: tags:
```
python
%
matplotlib
inline
```
%% Cell type:code id: tags:
```
python
import
fresnel.solver
as
solver
```
%% Cell type:code id: tags:
```
python
energy
=
12.
# keV
# geometry
wavelength
=
1.2398
/
(
energy
*
1e3
)
*
1e-3
# mm
nx
=
1024
ny
=
512
nz
=
1000
ztot
=
0.4
# mm
wg_radius
=
25e-6
xtot
=
10
*
wg_radius
# mm
ytot
=
10
*
wg_radius
# units
dx
=
xtot
/
nx
/
wavelength
dy
=
ytot
/
ny
/
wavelength
dz
=
ztot
/
nz
/
wavelength
print
(
f
"dx:
{
dx
}
, dy:
{
dy
}
, dz:
{
dz
}
wavelengths"
)
```
%%%% Output: stream
dx: 2.36303234392644, dy: 4.72606468785288, dz: 3871.592192289079 wavelengths
%% Cell type:code id: tags:
```
python
density_Ge
=
xrl
.
ElementDensity
(
xrl
.
SymbolToAtomicNumber
(
'Ge'
))
density_Polyimide
=
1.42
density_Si
=
xrl
.
ElementDensity
(
xrl
.
SymbolToAtomicNumber
(
'Si'
))
n_Ge
=
xrl
.
Refractive_Index
(
'Ge'
,
energy
,
density_Ge
)
n_Si
=
xrl
.
Refractive_Index
(
'Si'
,
energy
,
density_Si
)
n_PI
=
xrl
.
Refractive_Index
(
'Kapton Polyimide Film'
,
energy
,
density_Polyimide
)
print
(
'Ge'
,
n_Ge
-
1
)
print
(
'Si'
,
n_Si
-
1
)
print
(
'PI'
,
n_PI
-
1
)
xx
=
np
.
linspace
(
-
xtot
/
2
,
xtot
/
2
,
nx
).
reshape
([
1
,
-
1
])
yy
=
np
.
linspace
(
-
ytot
/
2
,
ytot
/
2
,
ny
).
reshape
([
-
1
,
1
])
core
=
(
np
.
abs
(
xx
)
<
wg_radius
)
*
(
np
.
abs
(
yy
)
<
wg_radius
)
cladding
=
~
core
refractive_index
=
n_Ge
*
cladding
+
1
*
core
```
%%%% Output: stream
Ge (-6.426292114225518e-06+7.120128111534574e-07j)
Si (-3.3845180545943876e-06+3.810012288290064e-08j)
PI (-2.1023289580313076e-06+2.2059592416020462e-09j)
%% Cell type:code id: tags:
```
python
u0
=
np
.
exp
(
-
(
xx
**
2
+
yy
**
2
)
/
(
2
*
(
2
*
wg_radius
)
**
2
)).
astype
(
np
.
complex128
)
boundary
=
(
0
,
0
,
0
,
0
)
propagator
=
solver
.
Propagator3d
(
refractive_index
,
u0
,
dz
,
dy
,
dx
)
```
%% Cell type:code id: tags:
```
python
field
=
np
.
zeros
((
nz
,
ny
,
nx
),
dtype
=
np
.
complex128
)
field
[
0
,...]
=
u0
for
iz
in
range
(
1
,
nz
):
boundary
=
(
0
,
0
,
0
,
0
)
field
[
iz
,
...]
=
propagator
.
step
(
refractive_index
,
boundary
)
if
iz
%
100
==
0
:
print
(
iz
)
```
%%%% Output: stream
100
200
300
400
500
600
700
800
900
%% Cell type:code id: tags:
```
python
result
=
field
[:,
ny
//
2
,
:].
transpose
()
fig
,
ax
=
plt
.
subplots
()
im
=
ax
.
imshow
(
np
.
abs
(
result
)
**
2
,
aspect
=
'auto'
,
clim
=
(
0
,
4
),
cmap
=
'cubehelix'
,
extent
=
[
0
,
ztot
,
-
xtot
/
2
*
1e6
,
xtot
/
2
*
1e6
])
ax
.
set_ylim
(
-
2e6
*
wg_radius
,
2e6
*
wg_radius
)
fig
.
colorbar
(
im
)
ax
.
set_xlabel
(
r
'$z$ (mm)'
)
ax
.
set_ylabel
(
r
'$x$ (nm)'
)
result
=
field
[:,:,
nx
//
2
].
transpose
()
fig
,
ax
=
plt
.
subplots
()
im
=
ax
.
imshow
(
np
.
abs
(
result
)
**
2
,
aspect
=
'auto'
,
clim
=
(
0
,
4
),
cmap
=
'cubehelix'
,
extent
=
[
0
,
ztot
,
-
xtot
/
2
*
1e6
,
xtot
/
2
*
1e6
])
ax
.
set_ylim
(
-
2e6
*
wg_radius
,
2e6
*
wg_radius
)
fig
.
colorbar
(
im
)
ax
.
set_xlabel
(
r
'$z$ (um)'
)
ax
.
set_ylabel
(
r
'$y$ (nm)'
)
```
%%%% Output: execute_result
Text(0, 0.5, '$y$ (nm)')
%%%% Output: display_data
%%%% Output: display_data
%% Cell type:code id: tags:
```
python
``
`
%%
Cell
type
:
code
id
:
tags
:
```
python
```
...
...
examples/TestCS.ipynb
0 → 100644
View file @
1fd06c6a
This diff is collapsed.
Click to expand it.
fresnel/solver.py
View file @
1fd06c6a
...
...
@@ -7,12 +7,12 @@ _k = 2 * np.pi # all lengths are in units of the wavelength
class
Solver2d
():
"""
Solver for 2d PDEs of the form
u_z = A
* u_xx + F * u
Az(x) * u_z = -Axx(x)
* u_xx + F
(x,z)
* u
"""
dtype
=
np
.
complex128
def
__init__
(
self
,
A
0
,
F0
,
u0
,
dz
,
dx
):
def
__init__
(
self
,
A
z
,
Axx
,
F0
,
u0
,
dz
,
dx
):
self
.
_nx
=
u0
.
shape
[
-
1
]
self
.
_ones
=
np
.
ones
((
self
.
_nx
,),
dtype
=
self
.
dtype
)
...
...
@@ -23,77 +23,167 @@ class Solver2d():
self
.
dx
=
dx
self
.
dz
=
dz
self
.
_compute_coefficients
(
A0
,
F0
)
self
.
rz
=
self
.
_compute_rz
(
Az
)
self
.
rxx
=
self
.
_compute_rxx
(
Axx
)
self
.
f
=
self
.
_compute_f
(
F0
)
def
_compute_rz
(
self
,
Az
):
return
Az
*
self
.
_ones
def
_compute_rxx
(
self
,
Axx
):
return
-
Axx
*
self
.
dz
/
2.
/
self
.
dx
**
2
*
self
.
_ones
def
_compute_f
(
self
,
F
):
return
F
*
self
.
dz
/
2.
*
self
.
_ones
def
step
(
self
,
F
,
boundary
):
up
=
self
.
u
fp
=
self
.
f
def
_compute_coefficients
(
self
,
A
,
F
):
self
.
f
=
self
.
_compute_f
(
F
)
u
=
self
.
_boundary_slice
self
.
rx
=
A
*
self
.
dz
/
(
2.
*
self
.
dx
**
2
)
*
self
.
_ones
self
.
rc
=
F
*
self
.
dz
/
2.
*
self
.
_ones
# set boundary values
u
[
0
]
=
boundary
[
0
]
u
[
-
1
]
=
boundary
[
1
]
self
.
u
=
_solver
.
step1d_A0F
(
self
.
rz
,
self
.
rxx
,
fp
,
self
.
f
,
up
,
u
)
def
step
(
self
,
A
,
F
,
boundary
):
return
self
.
u
up
=
self
.
u
rxp
=
self
.
rx
rcp
=
self
.
rc
self
.
_compute_coefficients
(
A
,
F
)
class
Propagator2d
(
Solver2d
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
):
Az
=
2j
*
_k
Axx
=
1
F0
=
self
.
_compute_potential
(
n0
)
super
().
__init__
(
Az
,
Axx
,
F0
,
u0
,
dz
,
dx
)
def
_compute_potential
(
self
,
n
):
return
_k
**
2
*
(
1
-
n
*
n
)
def
step
(
self
,
n
,
boundary
):
F
=
self
.
_compute_potential
(
n
)
return
super
().
step
(
F
,
boundary
)
class
Solver2dfull
():
"""
Solver for 2d PDEs of the form
Az(x) * u_z = Axx(x) * u_xx + Ax(x) * u_x + F(x,z) * u
"""
dtype
=
np
.
complex128
def
__init__
(
self
,
Az
,
Axx
,
Ax
,
F0
,
u0
,
dz
,
dx
):
self
.
_nx
=
u0
.
shape
[
-
1
]
self
.
_ones
=
np
.
ones
((
self
.
_nx
,),
dtype
=
self
.
dtype
)
self
.
_boundary_slice
=
np
.
zeros_like
(
self
.
_ones
)
self
.
u
=
u0
*
self
.
_ones
self
.
dx
=
dx
self
.
dz
=
dz
self
.
rz
=
self
.
_compute_rz
(
Az
)
self
.
rxx
=
self
.
_compute_rxx
(
Axx
)
self
.
rx
=
self
.
_compute_rx
(
Ax
)
self
.
f
=
self
.
_compute_f
(
F0
)
def
_compute_rz
(
self
,
Az
):
return
Az
*
self
.
_ones
def
_compute_rxx
(
self
,
Axx
):
return
-
Axx
*
self
.
dz
/
2.
/
self
.
dx
**
2
*
self
.
_ones
def
_compute_rx
(
self
,
Ax
):
return
-
Ax
*
self
.
dz
/
4.
/
self
.
dx
*
self
.
_ones
def
_compute_f
(
self
,
F
):
return
F
*
self
.
dz
/
2.
*
self
.
_ones
def
step
(
self
,
F
,
boundary
):
up
=
self
.
u
fp
=
self
.
f
self
.
f
=
self
.
_compute_f
(
F
)
u
=
self
.
_boundary_slice
rx
=
self
.
rx
rc
=
self
.
rc
# set boundary values
u
[
0
]
=
boundary
[
0
]
u
[
-
1
]
=
boundary
[
1
]
self
.
u
=
_solver
.
step
_AF
(
up
,
rx
p
,
rcp
,
u
,
rx
,
rc
)
self
.
u
=
_solver
.
step
1d_AAF
(
self
.
rz
,
self
.
rx
x
,
self
.
rx
,
fp
,
self
.
f
,
up
,
u
)
return
self
.
u
class
Propagator2d
(
Solver2d
):
class
PropagatorCS
(
Solver2dfull
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
):
A
,
F
=
self
.
_compute_helmholtz_coefficients
(
n0
)
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
):
super
().
__init__
(
A
,
F
,
u0
,
dz
,
dx
)
nx
=
u0
.
shape
[
-
1
]
self
.
_x
=
np
.
linspace
(
-
nx
*
dx
/
2
,
nx
*
dx
/
2
,
nx
)
Az
=
2j
*
_k
*
self
.
_x
Axx
=
self
.
_x
Ax
=
1
F0
=
self
.
_compute_potential
(
n0
)
super
().
__init__
(
Az
,
Axx
,
Ax
,
F0
,
u0
,
dz
,
dx
)
def
_compute_helmholtz_coefficients
(
self
,
n
):
A
=
1j
/
(
2.
*
_k
)
F
=
1j
*
_k
*
(
n
*
n
-
1
)
/
2
def
_compute_potential
(
self
,
n
):
return
_k
**
2
*
(
1
-
n
*
n
)
return
A
,
F
def
step
(
self
,
n
,
boundary
):
A
,
F
=
self
.
_compute_helmholtz_coefficients
(
n
)
return
super
().
step
(
A
,
F
,
boundary
)
F
=
self
.
_compute_potential
(
n
)
*
self
.
_x
return
super
().
step
(
F
,
boundary
)
class
Solver3d
():
"""
Solver for equations of the form
u_z = A * u_xx + C * u_yy + F * u
Abbreviations:
'rx' : A * dz / dx**2
