masque/examples/tutorial/pcgen.py

313 lines
11 KiB
Python

"""
Routines for creating normalized 2D lattices and common photonic crystal
cavity designs.
"""
from typing import Sequence, Tuple
import numpy
from numpy.typing import ArrayLike, NDArray
def triangular_lattice(
dims: Sequence[int],
asymmetric: bool = False,
origin: str = 'center',
) -> NDArray[numpy.float64]:
"""
Return an ndarray of `[[x0, y0], [x1, y1], ...]` denoting lattice sites for
a triangular lattice in 2D.
Args:
dims: Number of lattice sites in the [x, y] directions.
asymmetric: If true, each row will contain the same number of
x-coord lattice sites. If false, every other row will be
one site shorter (to make the structure symmetric).
origin: If 'corner', the least-(x,y) lattice site is placed at (0, 0)
If 'center', the center of the lattice (not necessarily a
lattice site) is placed at (0, 0).
Returns:
`[[x0, y0], [x1, 1], ...]` denoting lattice sites.
"""
sx, sy = numpy.meshgrid(numpy.arange(dims[0], dtype=float),
numpy.arange(dims[1], dtype=float), indexing='ij')
sx[sy % 2 == 1] += 0.5
sy *= numpy.sqrt(3) / 2
if not asymmetric:
which = sx != sx.max()
sx = sx[which]
sy = sy[which]
xy = numpy.column_stack((sx.flat, sy.flat))
if origin == 'center':
xy -= (xy.max(axis=0) - xy.min(axis=0)) / 2
elif origin == 'corner':
pass
else:
raise Exception(f'Invalid value for `origin`: {origin}')
return xy[xy[:, 0].argsort(), :]
def square_lattice(dims: Sequence[int]) -> NDArray[numpy.float64]:
"""
Return an ndarray of `[[x0, y0], [x1, y1], ...]` denoting lattice sites for
a square lattice in 2D. The lattice will be centered around (0, 0).
Args:
dims: Number of lattice sites in the [x, y] directions.
Returns:
`[[x0, y0], [x1, 1], ...]` denoting lattice sites.
"""
xs, ys = numpy.meshgrid(range(dims[0]), range(dims[1]), 'xy')
xs -= dims[0]/2
ys -= dims[1]/2
xy = numpy.vstack((xs.flatten(), ys.flatten())).T
return xy[xy[:, 0].argsort(), ]
# ### Photonic crystal functions ###
def nanobeam_holes(
a_defect: float,
num_defect_holes: int,
num_mirror_holes: int
) -> NDArray[numpy.float64]:
"""
Returns a list of `[[x0, r0], [x1, r1], ...]` of nanobeam hole positions and radii.
Creates a region in which the lattice constant and radius are progressively
(linearly) altered over num_defect_holes holes until they reach the value
specified by a_defect, then symmetrically returned to a lattice constant and
radius of 1, which is repeated num_mirror_holes times on each side.
Args:
a_defect: Minimum lattice constant for the defect, as a fraction of the
mirror lattice constant (ie., for no defect, a_defect = 1).
num_defect_holes: How many holes form the defect (per-side)
num_mirror_holes: How many holes form the mirror (per-side)
Returns:
Ndarray `[[x0, r0], [x1, r1], ...]` of nanobeam hole positions and radii.
"""
a_values = numpy.linspace(a_defect, 1, num_defect_holes, endpoint=False)
xs = a_values.cumsum() - (a_values[0] / 2) # Later mirroring makes center distance 2x as long
mirror_xs = numpy.arange(1, num_mirror_holes + 1, dtype=float) + xs[-1]
mirror_rs = numpy.ones_like(mirror_xs)
return numpy.vstack((numpy.hstack((-mirror_xs[::-1], -xs[::-1], xs, mirror_xs)),
numpy.hstack((mirror_rs[::-1], a_values[::-1], a_values, mirror_rs)))).T
def waveguide(length: int, num_mirror: int) -> NDArray[numpy.float64]:
"""
Line defect waveguide in a triangular lattice.
Args:
length: waveguide length (number of holes in x direction)
num_mirror: Mirror length (number of holes per side; total size is
`2 * n + 1` holes.
Returns:
`[[x0, y0], [x1, y1], ...]` for all the holes
"""
p = triangular_lattice([length + 2, 2 * num_mirror + 1])
p = p[p[:, 1] != 0, :]
p = p[numpy.abs(p[:, 0]) <= length / 2]
return p
def wgbend(num_mirror: int) -> NDArray[numpy.float64]:
"""
Line defect waveguide bend in a triangular lattice.
Args:
num_mirror: Mirror length (number of holes per side; total size is
approximately `2 * n + 1`
Returns:
`[[x0, y0], [x1, y1], ...]` for all the holes
"""
p = triangular_lattice([4 * num_mirror + 1, 4 * num_mirror + 1])
left_horiz = (p[:, 1] == 0) & (p[:, 0] <= 0)
p = p[~left_horiz, :]
right_diag = numpy.isclose(p[:, 1], p[:, 0] * numpy.sqrt(3)) & (p[:, 0] >= 0)
p = p[~right_diag, :]
edge_left = p[:, 0] < -num_mirror
edge_bot = p[:, 1] < -num_mirror
p = p[~edge_left & ~edge_bot, :]
edge_diag_up = p[:, 0] * numpy.sqrt(3) > p[:, 1] + 2 * num_mirror + 0.1
edge_diag_dn = p[:, 0] / numpy.sqrt(3) > -p[:, 1] + num_mirror + 1.1
p = p[~edge_diag_up & ~edge_diag_dn, :]
return p
def y_splitter(num_mirror: int) -> NDArray[numpy.float64]:
"""
Line defect waveguide y-splitter in a triangular lattice.
Args:
num_mirror: Mirror length (number of holes per side; total size is
approximately `2 * n + 1` holes.
Returns:
`[[x0, y0], [x1, y1], ...]` for all the holes
"""
p = triangular_lattice([4 * num_mirror + 1, 4 * num_mirror + 1])
left_horiz = (p[:, 1] == 0) & (p[:, 0] <= 0)
p = p[~left_horiz, :]
# y = +-sqrt(3) * x
right_diag_up = numpy.isclose(p[:, 1], p[:, 0] * numpy.sqrt(3)) & (p[:, 0] >= 0)
right_diag_dn = numpy.isclose(p[:, 1], -p[:, 0] * numpy.sqrt(3)) & (p[:, 0] >= 0)
p = p[~right_diag_up & ~right_diag_dn, :]
edge_left = p[:, 0] < -num_mirror
p = p[~edge_left, :]
edge_diag_up = p[:, 0] / numpy.sqrt(3) > p[:, 1] + num_mirror + 1.1
edge_diag_dn = p[:, 0] / numpy.sqrt(3) > -p[:, 1] + num_mirror + 1.1
p = p[~edge_diag_up & ~edge_diag_dn, :]
return p
def ln_defect(
mirror_dims: Sequence[int],
defect_length: int,
) -> NDArray[numpy.float64]:
"""
N-hole defect in a triangular lattice.
Args:
mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
is 2 * n + 1 in each direction.
defect_length: Length of defect. Should be an odd number.
Returns:
`[[x0, y0], [x1, y1], ...]` for all the holes
"""
if defect_length % 2 != 1:
raise Exception('defect_length must be odd!')
p = triangular_lattice([2 * d + 1 for d in mirror_dims])
half_length = numpy.floor(defect_length / 2)
hole_nums = numpy.arange(-half_length, half_length + 1)
holes_to_keep = numpy.in1d(p[:, 0], hole_nums, invert=True)
return p[numpy.logical_or(holes_to_keep, p[:, 1] != 0), ]
def ln_shift_defect(
mirror_dims: Sequence[int],
defect_length: int,
shifts_a: ArrayLike = (0.15, 0, 0.075),
shifts_r: ArrayLike = (1, 1, 1),
) -> NDArray[numpy.float64]:
"""
N-hole defect with shifted holes (intended to give the mode a gaussian profile
in real- and k-space so as to improve both Q and confinement). Holes along the
defect line are shifted and altered according to the shifts_* parameters.
Args:
mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
is `2 * n + 1` in each direction.
defect_length: Length of defect. Should be an odd number.
shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line
shifts_r: Factor to multiply the radius by. Should match length of shifts_a
Returns:
`[[x0, y0, r0], [x1, y1, r1], ...]` for all the holes
"""
xy = ln_defect(mirror_dims, defect_length)
# Add column for radius
xyr = numpy.hstack((xy, numpy.ones((xy.shape[0], 1))))
# Shift holes
# Expand shifts as necessary
tmp_a = numpy.array(shifts_a)
tmp_r = numpy.array(shifts_r)
n_shifted = max(tmp_a.size, tmp_r.size)
shifts_a = numpy.ones(n_shifted)
shifts_r = numpy.ones(n_shifted)
shifts_a[:len(tmp_a)] = tmp_a
shifts_r[:len(tmp_r)] = tmp_r
x_removed = numpy.floor(defect_length / 2)
for ind in range(n_shifted):
for sign in (-1, 1):
x_val = sign * (x_removed + ind + 1)
which = numpy.logical_and(xyr[:, 0] == x_val, xyr[:, 1] == 0)
xyr[which, ] = (x_val + numpy.sign(x_val) * shifts_a[ind], 0, shifts_r[ind])
return xyr
def r6_defect(mirror_dims: Sequence[int]) -> NDArray[numpy.float64]:
"""
R6 defect in a triangular lattice.
Args:
mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
is 2 * n + 1 in each direction.
Returns:
`[[x0, y0], [x1, y1], ...]` specifying hole centers.
"""
xy = triangular_lattice([2 * d + 1 for d in mirror_dims])
rem_holes_plus = numpy.array([[1, 0],
[0.5, +numpy.sqrt(3)/2],
[0.5, -numpy.sqrt(3)/2]])
rem_holes = numpy.vstack((rem_holes_plus, -rem_holes_plus))
for rem_xy in rem_holes:
xy = xy[(xy != rem_xy).any(axis=1), ]
return xy
def l3_shift_perturbed_defect(
mirror_dims: Sequence[int],
perturbed_radius: float = 1.1,
shifts_a: Sequence[float] = (),
shifts_r: Sequence[float] = ()
) -> NDArray[numpy.float64]:
"""
3-hole defect with perturbed hole sizes intended to form an upwards-directed
beam. Can also include shifted holes along the defect line, intended
to give the mode a more gaussian profile to improve Q.
Args:
mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes
is 2 * n + 1 in each direction.
perturbed_radius: Amount to perturb the radius of the holes used for beam-forming
shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line
shifts_r: Factor to multiply the radius by. Should match length of shifts_a
Returns:
`[[x0, y0, r0], [x1, y1, r1], ...]` for all the holes
"""
xyr = ln_shift_defect(mirror_dims, 3, shifts_a, shifts_r)
abs_x, abs_y = (numpy.fabs(xyr[:, i]) for i in (0, 1))
# Sorted unique xs and ys
# Ignore row y=0 because it might have shifted holes
xs = numpy.unique(abs_x[abs_x != 0])
ys = numpy.unique(abs_y)
# which holes should be perturbed? (xs[[3, 7]], ys[1]) and (xs[[2, 6]], ys[2])
perturbed_holes = ((xs[a], ys[b]) for a, b in ((3, 1), (7, 1), (2, 2), (6, 2)))
for row in xyr:
if numpy.fabs(row) in perturbed_holes:
row[2] = perturbed_radius
return xyr