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