add fdtd and test

examples/test_fdtd.py

@@ -0,0 +1,175 @@
+"""
+Example code for running an OpenCL FDTD simulation
+
+See main() for simulation setup.
+"""
+
+import sys
+import time
+
+import numpy
+import h5py
+
+from fdfd_tools import fdtd
+from masque import Pattern, shapes
+import gridlock
+import pcgen
+
+
+def perturbed_l3(a: float, radius: float, **kwargs) -> Pattern:
+    """
+    Generate a masque.Pattern object containing a perturbed L3 cavity.
+
+    :param a: Lattice constant.
+    :param radius: Hole radius, in units of a (lattice constant).
+    :param kwargs: Keyword arguments:
+        hole_dose, trench_dose, hole_layer, trench_layer: Shape properties for Pattern.
+                Defaults *_dose=1, hole_layer=0, trench_layer=1.
+        shifts_a, shifts_r: passed to pcgen.l3_shift; specifies lattice constant (1 -
+                multiplicative factor) and radius (multiplicative factor) for shifting
+                holes adjacent to the defect (same row). Defaults are 0.15 shift for
+                first hole, 0.075 shift for third hole, and no radius change.
+        xy_size: [x, y] number of mirror periods in each direction; total size is
+                2 * n + 1 holes in each direction. Default [10, 10].
+        perturbed_radius: radius of holes perturbed to form an upwards-driected beam
+                (multiplicative factor). Default 1.1.
+        trench width: Width of the undercut trenches. Default 1.2e3.
+    :return: masque.Pattern object containing the L3 design
+    """
+
+    default_args = {'hole_dose':    1,
+                    'trench_dose':  1,
+                    'hole_layer':   0,
+                    'trench_layer': 1,
+                    'shifts_a':     (0.15, 0, 0.075),
+                    'shifts_r':     (1.0, 1.0, 1.0),
+                    'xy_size':      (10, 10),
+                    'perturbed_radius': 1.1,
+                    'trench_width': 1.2e3,
+                    }
+    kwargs = {**default_args, **kwargs}
+
+    xyr = pcgen.l3_shift_perturbed_defect(mirror_dims=kwargs['xy_size'],
+                                          perturbed_radius=kwargs['perturbed_radius'],
+                                          shifts_a=kwargs['shifts_a'],
+                                          shifts_r=kwargs['shifts_r'])
+    xyr *= a
+    xyr[:, 2] *= radius
+
+    pat = Pattern()
+    pat.name = 'L3p-a{:g}r{:g}rp{:g}'.format(a, radius, kwargs['perturbed_radius'])
+    pat.shapes += [shapes.Circle(radius=r, offset=(x, y),
+                                 dose=kwargs['hole_dose'],
+                                 layer=kwargs['hole_layer'])
+                   for x, y, r in xyr]
+
+    maxes = numpy.max(numpy.fabs(xyr), axis=0)
+    pat.shapes += [shapes.Polygon.rectangle(
+        lx=(2 * maxes[0]), ly=kwargs['trench_width'],
+        offset=(0, s * (maxes[1] + a + kwargs['trench_width'] / 2)),
+        dose=kwargs['trench_dose'], layer=kwargs['trench_layer'])
+                   for s in (-1, 1)]
+    return pat
+
+
+def main():
+    dtype = numpy.float32
+    max_t = 8000            # number of timesteps
+
+    dx = 40                 # discretization (nm/cell)
+    pml_thickness = 8       # (number of cells)
+
+    wl = 1550               # Excitation wavelength and fwhm
+    dwl = 200
+
+    # Device design parameters
+    xy_size = numpy.array([10, 10])
+    a = 430
+    r = 0.285
+    th = 170
+
+    # refractive indices
+    n_slab = 3.408  # InGaAsP(80, 50) @ 1550nm
+    n_air = 1.0   # air
+
+    # Half-dimensions of the simulation grid
+    xy_max = (xy_size + 1) * a * [1, numpy.sqrt(3)/2]
+    z_max = 1.6 * a
+    xyz_max = numpy.hstack((xy_max, z_max)) + pml_thickness * dx
+
+    # Coordinates of the edges of the cells. The fdtd package can only do square grids at the moment.
+    half_edge_coords = [numpy.arange(dx/2, m + dx, step=dx) for m in xyz_max]
+    edge_coords = [numpy.hstack((-h[::-1], h)) for h in half_edge_coords]
+
+    # #### Create the grid, mask, and draw the device ####
+    grid = gridlock.Grid(edge_coords, initial=n_air**2, num_grids=3)
+    grid.draw_slab(surface_normal=gridlock.Direction.z,
+                   center=[0, 0, 0],
+                   thickness=th,
+                   eps=n_slab**2)
+    mask = perturbed_l3(a, r)
+
+    grid.draw_polygons(surface_normal=gridlock.Direction.z,
+                       center=[0, 0, 0],
+                       thickness=2 * th,
+                       eps=n_air**2,
+                       polygons=mask.as_polygons())
+
+    print(grid.shape)
+    # #### Create the simulation grid ####
+    epsilon = [eps.astype(dtype) for eps in grid.grids]
+
+    dt = .99/numpy.sqrt(3)
+    e = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)]
+    h = [numpy.zeros_like(epsilon[0], dtype=dtype) for _ in range(3)]
+
+    update_e = fdtd.maxwell_e(dt)
+    update_h = fdtd.maxwell_h(dt)
+
+    # PMLs in every direction
+    pml_e_funcs = []
+    pml_h_funcs = []
+    pml_fields = {}
+    for d in (0, 1, 2):
+        for p in (-1, 1):
+            ef, hf, psis = fdtd.cpml(direction=d, polarity=p, dt=dt, epsilon=epsilon, epsilon_eff=n_slab**2, dtype=dtype)
+            pml_e_funcs.append(ef)
+            pml_h_funcs.append(hf)
+            pml_fields.update(psis)
+
+    # Source parameters and function
+    w = 2 * numpy.pi * dx / wl
+    fwhm = dwl * w * w / (2 * numpy.pi * dx)
+    alpha = (fwhm ** 2) / 8 * numpy.log(2)
+    delay = 7/numpy.sqrt(2 * alpha)
+
+    def field_source(i):
+        t0 = i * dt - delay
+        return numpy.sin(w * t0) * numpy.exp(-alpha * t0**2)
+
+    # #### Run a bunch of iterations ####
+    output_file = h5py.File('simulation_output.h5', 'w')
+    start = time.perf_counter()
+    for t in range(max_t):
+        [f(e, h, epsilon) for f in pml_e_funcs]
+        update_e(e, h, epsilon)
+
+        e[1][tuple(grid.shape//2)] += field_source(t)
+        [f(e, h) for f in pml_h_funcs]
+        update_h(e, h)
+
+        print('iteration {}: average {} iterations per sec'.format(t, (t+1)/(time.perf_counter()-start)))
+        sys.stdout.flush()
+
+        if t % 20 == 0:
+            r = sum([(f * f * e).sum() for f, e in zip(e, epsilon)])
+            print('E sum', r)
+
+        # Save field slices
+        if (t % 20 == 0 and (max_t - t <= 1000 or t <= 2000)) or t == max_t-1:
+            print('saving E-field')
+            for j, f in enumerate(e):
+                output_file['/E{}_t{}'.format('xyz'[j], t)] = f[:, :, round(f.shape[2]/2)]
+
+if __name__ == '__main__':
+    main()

fdfd_tools/fdtd.py

@@ -0,0 +1,239 @@
+from typing import List, Callable, Tuple, Dict
+import numpy
+
+from . import dx_lists_t, field_t
+
+__author__ = 'Jan Petykiewicz'
+
+
+functional_matrix = Callable[[field_t], field_t]
+
+
+def curl_h(dxes: dx_lists_t = None) -> functional_matrix:
+    """
+    Curl operator for use with the H field.
+
+    :param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
+    :return: Function for taking the discretized curl of the H-field, F(H) -> curlH
+    """
+    if dxes:
+        dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
+
+        def dh(f, ax):
+            return (f - numpy.roll(f, 1, axis=ax)) / dxyz_b[ax]
+    else:
+        def dh(f, ax):
+            return f - numpy.roll(f, 1, axis=ax)
+
+    def ch_fun(h: field_t) -> field_t:
+        e = [dh(h[2], 1) - dh(h[1], 2),
+             dh(h[0], 2) - dh(h[2], 0),
+             dh(h[1], 0) - dh(h[0], 1)]
+        return e
+
+    return ch_fun
+
+
+def curl_e(dxes: dx_lists_t = None) -> functional_matrix:
+    """
+    Curl operator for use with the E field.
+
+    :param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
+    :return: Function for taking the discretized curl of the E-field, F(E) -> curlE
+    """
+    if dxes is not None:
+        dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
+
+        def de(f, ax):
+            return (numpy.roll(f, -1, axis=ax) - f) / dxyz_a[ax]
+    else:
+        def de(f, ax):
+            return numpy.roll(f, -1, axis=ax) - f
+
+    def ce_fun(e: field_t) -> field_t:
+        h = [de(e[2], 1) - de(e[1], 2),
+             de(e[0], 2) - de(e[2], 0),
+             de(e[1], 0) - de(e[0], 1)]
+        return h
+
+    return ce_fun
+
+
+def maxwell_e(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
+    curl_h_fun = curl_h(dxes)
+
+    def me_fun(e: field_t, h: field_t, epsilon: field_t):
+        ch = curl_h_fun(h)
+        for ei, ci, epsi in zip(e, ch, epsilon):
+            ei += dt * ci / epsi
+        return e
+
+    return me_fun
+
+
+def maxwell_h(dt: float, dxes: dx_lists_t = None) -> functional_matrix:
+    curl_e_fun = curl_e(dxes)
+
+    def mh_fun(e: field_t, h: field_t):
+        ce = curl_e_fun(e)
+        for hi, ci in zip(h, ce):
+            hi -= dt * ci
+        return h
+
+    return mh_fun
+
+
+def conducting_boundary(direction: int,
+                        polarity: int
+                        ) -> Tuple[functional_matrix, functional_matrix]:
+    dirs = [0, 1, 2]
+    if direction not in dirs:
+        raise Exception('Invalid direction: {}'.format(direction))
+    dirs.remove(direction)
+    u, v = dirs
+
+    if polarity < 0:
+        boundary_slice = [slice(None)] * 3
+        shifted1_slice = [slice(None)] * 3
+        boundary_slice[direction] = 0
+        shifted1_slice[direction] = 1
+
+        def en(e: field_t):
+            e[direction][boundary_slice] = 0
+            e[u][boundary_slice] = e[u][shifted1_slice]
+            e[v][boundary_slice] = e[v][shifted1_slice]
+            return e
+
+        def hn(h: field_t):
+            h[direction][boundary_slice] = h[direction][shifted1_slice]
+            h[u][boundary_slice] = 0
+            h[v][boundary_slice] = 0
+            return h
+
+        return en, hn
+
+    elif polarity > 0:
+        boundary_slice = [slice(None)] * 3
+        shifted1_slice = [slice(None)] * 3
+        shifted2_slice = [slice(None)] * 3
+        boundary_slice[direction] = -1
+        shifted1_slice[direction] = -2
+        shifted2_slice[direction] = -3
+
+        def ep(e: field_t):
+            e[direction][boundary_slice] = -e[direction][shifted2_slice]
+            e[direction][shifted1_slice] = 0
+            e[u][boundary_slice] = e[u][shifted1_slice]
+            e[v][boundary_slice] = e[v][shifted1_slice]
+            return e
+
+        def hp(h: field_t):
+            h[direction][boundary_slice] = h[direction][shifted1_slice]
+            h[u][boundary_slice] = -h[u][shifted2_slice]
+            h[u][shifted1_slice] = 0
+            h[v][boundary_slice] = -h[v][shifted2_slice]
+            h[v][shifted1_slice] = 0
+            return h
+
+        return ep, hp
+
+    else:
+        raise Exception('Bad polarity: {}'.format(polarity))
+
+
+def cpml(direction:int,
+         polarity: int,
+         dt: float,
+         epsilon: field_t,
+         thickness: int = 8,
+         epsilon_eff: float = 1,
+         dtype: numpy.dtype = numpy.float32,
+         ) -> Tuple[Callable, Callable, Dict[str, field_t]]:
+
+    if direction not in range(3):
+        raise Exception('Invalid direction: {}'.format(direction))
+
+    if polarity not in (-1, 1):
+        raise Exception('Invalid polarity: {}'.format(polarity))
+
+    if thickness <= 2:
+        raise Exception('It would be wise to have a pml with 4+ cells of thickness')
+
+    if epsilon_eff <= 0:
+        raise Exception('epsilon_eff must be positive')
+
+    m = (3.5, 1)
+    sigma_max = 0.8 * (m[0] + 1) / numpy.sqrt(epsilon_eff)
+    alpha_max = 0  # TODO: Decide what to do about non-zero alpha
+    transverse = numpy.delete(range(3), direction)
+    u, v = transverse
+
+    xe = numpy.arange(1, thickness+1, dtype=float)
+    xh = numpy.arange(1, thickness+1, dtype=float)
+    if polarity > 0:
+        xe -= 0.5
+    elif polarity < 0:
+        xh -= 0.5
+        xe = xe[::-1]
+        xh = xh[::-1]
+    else:
+        raise Exception('Bad polarity!')
+
+    expand_slice = [None] * 3
+    expand_slice[direction] = slice(None)
+
+    def par(x):
+        sigma = ((x / thickness) ** m[0]) * sigma_max
+        alpha = ((1 - x / thickness) ** m[1]) * alpha_max
+        p0 = numpy.exp(-(sigma + alpha) * dt)
+        p1 = sigma / (sigma + alpha) * (p0 - 1)
+        return p0[expand_slice], p1[expand_slice]
+
+    p0e, p1e = par(xe)
+    p0h, p1h = par(xh)
+
+    region = [slice(None)] * 3
+    if polarity < 0:
+        region[direction] = slice(None, thickness)
+    elif polarity > 0:
+        region[direction] = slice(-thickness, None)
+    else:
+        raise Exception('Bad polarity!')
+
+    if direction == 1:
+        se = 1
+    else:
+        se = -1
+
+    # TODO check if epsilon is uniform?
+    shape = list(epsilon[0].shape)
+    shape[direction] = thickness
+    psi_e = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
+    psi_h = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
+
+    fields = {
+        'psi_e_u': psi_e[0],
+        'psi_e_v': psi_e[1],
+        'psi_h_u': psi_h[0],
+        'psi_h_v': psi_h[1],
+    }
+
+    def pml_e(e: field_t, h: field_t, epsilon: field_t) -> Tuple[field_t, field_t]:
+        psi_e[0] *= p0e
+        psi_e[0] += p1e * (h[v][region] - numpy.roll(h[v], 1, axis=direction)[region])
+        psi_e[1] *= p0e
+        psi_e[1] += p1e * (h[u][region] - numpy.roll(h[u], 1, axis=direction)[region])
+        e[u][region] += se * dt * psi_e[0] / epsilon[u][region]
+        e[v][region] -= se * dt * psi_e[1] / epsilon[v][region]
+        return e, h
+
+    def pml_h(e: field_t, h: field_t) -> Tuple[field_t, field_t]:
+        psi_h[0] *= p0h
+        psi_h[0] += p1h * (numpy.roll(e[v], -1, axis=direction)[region] - e[v][region])
+        psi_h[1] *= p0h
+        psi_h[1] += p1h * (numpy.roll(e[u], -1, axis=direction)[region] - e[u][region])
+        h[u][region] -= se * dt * psi_h[0]
+        h[v][region] += se * dt * psi_h[1]
+        return e, h
+
+    return pml_e, pml_h, fields