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 ```""" ``` ```Routines for creating normalized 2D lattices and common photonic crystal ``` ``` cavity designs. ``` ```""" ``` ``` ``` ```from typing import List ``` ``` ``` ```import numpy ``` ``` ``` ``` ``` ```def triangular_lattice(dims: List[int], ``` ``` asymmetrical: bool=False ``` ``` ) -> numpy.ndarray: ``` ``` """ ``` ``` Return an ndarray of [[x0, y0], [x1, y1], ...] denoting lattice sites for ``` ``` a triangular lattice in 2D. The lattice will be centered around (0, 0), ``` ``` unless asymmetrical=True in which case there will be extra holes in the +x ``` ``` direction. ``` ``` ``` ``` :param dims: Number of lattice sites in the [x, y] directions. ``` ``` :param asymmetrical: If true, each row in x will contain the same number of ``` ``` lattice sites. If false, the structure is symmetrical around (0, 0). ``` ``` :return: [[x0, y0], [x1, 1], ...] denoting lattice sites. ``` ``` """ ``` ``` dims = numpy.array(dims, dtype=int) ``` ``` ``` ``` if asymmetrical: ``` ``` k = 0 ``` ``` else: ``` ``` k = 1 ``` ``` ``` ``` positions = [] ``` ``` ymax = (dims - 1)/2 ``` ``` for j in numpy.linspace(-ymax, ymax, dims): ``` ``` j_odd = numpy.floor(j) % 2 ``` ``` ``` ``` x_offset = j_odd * 0.5 ``` ``` y_offset = j * numpy.sqrt(3)/2 ``` ``` ``` ``` num_x = dims - k * j_odd ``` ``` xmax = (dims - 1)/2 ``` ``` xs = numpy.linspace(-xmax, xmax - k * j_odd, num_x) + x_offset ``` ``` ys = numpy.full_like(xs, y_offset) ``` ``` ``` ``` positions += [numpy.vstack((xs, ys)).T] ``` ``` ``` ``` xy = numpy.vstack(tuple(positions)) ``` ``` return xy[xy[:, 0].argsort(), ] ``` ``` ``` ``` ``` ```def square_lattice(dims: List[int]) -> numpy.ndarray: ``` ``` """ ``` ``` 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). ``` ``` ``` ``` :param dims: Number of lattice sites in the [x, y] directions. ``` ``` :return: [[x0, y0], [x1, 1], ...] denoting lattice sites. ``` ``` """ ``` ``` xs, ys = numpy.meshgrid(range(dims), range(dims), 'xy') ``` ``` xs -= dims/2 ``` ``` ys -= dims/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 ``` ``` ) -> numpy.ndarray: ``` ``` """ ``` ``` 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. ``` ``` ``` ``` :param a_defect: Minimum lattice constant for the defect, as a fraction of the ``` ``` mirror lattice constant (ie., for no defect, a_defect = 1). ``` ``` :param num_defect_holes: How many holes form the defect (per-side) ``` ``` :param num_mirror_holes: How many holes form the mirror (per-side) ``` ``` :return: 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 / 2) # Later mirroring makes center distance 2x as long ``` ``` mirror_xs = numpy.arange(1, num_mirror_holes + 1) + 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 ln_defect(mirror_dims: List[int], defect_length: int) -> numpy.ndarray: ``` ``` """ ``` ``` N-hole defect in a triangular lattice. ``` ``` ``` ``` :param mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes ``` ``` is 2 * n + 1 in each direction. ``` ``` :param defect_length: Length of defect. Should be an odd number. ``` ``` :return: [[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: List[int], ``` ``` defect_length: int, ``` ``` shifts_a: List[float]=(0.15, 0, 0.075), ``` ``` shifts_r: List[float]=(1, 1, 1) ``` ``` ) -> numpy.ndarray: ``` ``` """ ``` ``` 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. ``` ``` ``` ``` :param mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes ``` ``` is 2 * n + 1 in each direction. ``` ``` :param defect_length: Length of defect. Should be an odd number. ``` ``` :param shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line ``` ``` :param shifts_r: Factor to multiply the radius by. Should match length of shifts_a ``` ``` :return: [[x0, y0, r0], [x1, y1, r1], ...] for all the holes ``` ``` """ ``` ``` if not hasattr(shifts_a, "__len__") and shifts_a is not None: ``` ``` shifts_a = [shifts_a] ``` ``` if not hasattr(shifts_r, "__len__") and shifts_r is not None: ``` ``` shifts_r = [shifts_r] ``` ``` ``` ``` xy = ln_defect(mirror_dims, defect_length) ``` ``` ``` ``` # Add column for radius ``` ``` xyr = numpy.hstack((xy, numpy.ones((xy.shape, 1)))) ``` ``` ``` ``` # Shift holes ``` ``` # Expand shifts as necessary ``` ``` n_shifted = max(len(shifts_a), len(shifts_r)) ``` ``` ``` ``` tmp_a = numpy.array(shifts_a) ``` ``` shifts_a = numpy.ones((n_shifted, )) ``` ``` shifts_a[:len(tmp_a)] = tmp_a ``` ``` ``` ``` tmp_r = numpy.array(shifts_r) ``` ``` shifts_r = numpy.ones((n_shifted, )) ``` ``` 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: List[int]) -> numpy.ndarray: ``` ``` """ ``` ``` R6 defect in a triangular lattice. ``` ``` ``` ``` :param mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes ``` ``` is 2 * n + 1 in each direction. ``` ``` :return: [[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: List[int], ``` ``` perturbed_radius: float=1.1, ``` ``` shifts_a: List[float]=(), ``` ``` shifts_r: List[float]=() ``` ``` ) -> numpy.ndarray: ``` ``` """ ``` ``` 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. ``` ``` ``` ``` :param mirror_dims: [x, y] mirror lengths (number of holes). Total number of holes ``` ``` is 2 * n + 1 in each direction. ``` ``` :param perturbed_radius: Amount to perturb the radius of the holes used for beam-forming ``` ``` :param shifts_a: Percentage of a to shift (1st, 2nd, 3rd,...) holes along the defect line ``` ``` :param shifts_r: Factor to multiply the radius by. Should match length of shifts_a ``` ``` :return: [[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) and (xs[[2, 6]], ys) ``` ``` 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 = perturbed_radius ``` ``` return xyr ```