"""
Routines for creating normalized 2D lattices and common photonic crystal
cavity designs.
"""
from collection.abc import Sequence
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.asarray(shifts_a)
tmp_r = numpy.asarray(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