285 lines
9.6 KiB
Python
285 lines
9.6 KiB
Python
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from simphony.elements import Model
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from simphony.netlist import Subcircuit
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from simphony.simulation import SweepSimulation
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from matplotlib import pyplot as plt
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class PeriodicLayer(Model):
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def __init__(self, left_modes, right_modes, s_params):
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self.left_modes = left_modes
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self.right_modes = right_modes
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self.left_ports = len(self.left_modes)
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self.right_ports = len(self.right_modes)
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self.normalize_fields()
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self.s_params = s_params
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def normalize_fields(self):
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for mode in range(len(self.left_modes)):
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self.left_modes[mode].normalize()
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for mode in range(len(self.right_modes)):
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self.right_modes[mode].normalize()
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class PeriodicEME:
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def __init__(self, layers=[], num_periods=1):
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self.layers = layers
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self.num_periods = num_periods
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self.wavelength = wavelength
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def propagate(self):
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wl = self.wavelength
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if not len(self.layers):
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raise Exception("Must place layers before propagating")
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num_modes = max([l.num_modes for l in self.layers])
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iface = InterfaceSingleMode if num_modes == 1 else InterfaceMultiMode
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eme = EME(layers=self.layers)
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left, right = eme.propagate()
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self.single_period = eme.s_matrix
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period_layer = PeriodicLayer(left.modes, right.modes, self.single_period)
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current_layer = PeriodicLayer(left.modes, right.modes, self.single_period)
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interface = iface(right, left)
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for _ in range(self.num_periods - 1):
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current_layer.s_params = cascade(current_layer, interface, wl)
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current_layer.s_params = cascade(current_layer, period_layer, wl)
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self.s_params = current_layer.s_params
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class EME:
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def __init__(self, layers=[]):
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self.layers = layers
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self.wavelength = None
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def propagate(self):
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layers = self.layers
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wl = layers[0].wavelength if self.wavelength is None else self.wavelength
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if not len(layers):
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raise Exception("Must place layers before propagating")
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num_modes = max([l.num_modes for l in layers])
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iface = InterfaceSingleMode if num_modes == 1 else InterfaceMultiMode
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first_layer = layers[0]
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current = Current(wl, first_layer)
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interface = iface(first_layer, layers[1])
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current.s = cascade(current, interface, wl)
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current.right_pins = interface.right_pins
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for index in range(1, len(layers) - 1):
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layer1 = layers[index]
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layer2 = layers[index + 1]
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interface = iface(layer1, layer2)
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current.s = cascade(current, layer1, wl)
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current.right_pins = layer1.right_pins
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current.s = cascade(current, interface, wl)
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current.right_pins = interface.right_pins
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last_layer = layers[-1]
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current.s = cascade(current, last_layer, wl)
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current.right_pins = last_layer.right_pins
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self.s_matrix = current.s
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return first_layer, last_layer
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def stack(sa, sb):
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qab = numpy.eye() - sa.r11 @ sb.r11
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qba = numpy.eye() - sa.r11 @ sb.r11
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#s.t12 = sa.t12 @ numpy.pinv(qab) @ sb.t12
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#s.r21 = sa.t12 @ numpy.pinv(qab) @ sb.r22 @ sa.t21 + sa.r22
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#s.r12 = sb.t21 @ numpy.pinv(qba) @ sa.r11 @ sb.t12 + sb.r11
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#s.t21 = sb.t21 @ numpy.pinv(qba) @ sa.t21
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s.t12 = sa.t12 @ numpy.linalg.solve(qab, sb.t12)
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s.r21 = sa.t12 @ numpy.linalg.solve(qab, sb.r22 @ sa.t21) + sa.r22
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s.r12 = sb.t21 @ numpy.linalg.solve(qba, sa.r11 @ sb.t12) + sb.r11
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s.t21 = sb.t21 @ numpy.linalg.solve(qba, sa.t21)
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return s
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def cascade(first, second, wavelength):
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circuit = Subcircuit("Device")
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circuit.add([(first, "first"), (second, "second")])
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for port in range(first.right_ports):
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circuit.connect("first", "right" + str(port), "second", "left" + str(port))
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simulation = SweepSimulation(circuit, wavelength, wavelength, num=1)
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result = simulation.simulate()
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return result.s
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class InterfaceSingleMode(Model):
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def __init__(self, layer1, layer2, num_modes=1):
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self.num_modes = num_modes
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self.num_ports = 2 * num_modes
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self.s = self.solve(layer1, layer2, num_modes)
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def solve(self, layer1, layer2, num_modes):
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nm = num_modes
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s = numpy.zeros((2 * nm, 2 * nm), dtype=complex)
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for ii, left_mode in enumerate(layer1.modes):
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for oo, right_mode in enumerate(layer2.modes):
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r, t = get_rt(left_mode, right_mode)
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s[ oo, ii] = r
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s[nm + oo, ii] = t
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for ii, right_mode in enumerate(layer2.modes):
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for oo, left_mode in enumerate(layer1.modes):
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r, t = get_rt(right_mode, left_mode)
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s[ oo, nm + ii] = t
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s[nm + oo, nm + ii] = r
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return s
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class InterfaceMultiMode(Model):
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def __init__(self, layer1, layer2):
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self.s = self.solve(layer1, layer2)
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def solve(self, layer1, layer2):
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n1p = layer1.num_modes
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n2p = layer2.num_modes
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num_ports = n1p + n2p
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s = numpy.zeros((num_ports, num_ports), dtype=complex)
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for l1p in range(n1p):
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ts = get_t(l1p, layer1, layer2)
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rs = get_r(l1p, layer1, layer2, ts)
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s[n1p:, l1p] = ts
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s[:n1p, l1p] = rs
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for l2p in range(n2p):
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ts = get_t(l2p, layer2, layer1)
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rs = get_r(l2p, layer2, layer1, ts)
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s[:n1p, n1p + l2p] = ts
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s[n1p:, n1p + l2p] = rs
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return s
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def get_t(p, left, right):
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A = numpy.empty(left.shape[0], right.shape[0], dtype=complex)
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for ll in range(left.shape[0]):
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for rr in range(right.shape[0]):
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# TODO optimize loop?
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A[i, k] = inner_product(right[rr], left[ll]) + inner_product(left[ll], right[rr])
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b = numpy.zeros(left.shape[0i])
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b[p] = 2 * inner_product(left[p], left[p])
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x = numpy.linalg.solve(A, b)
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# NOTE: `A` does not depend on `p`, so it might make sense to partially precompute
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# the solution (pinv(A), or LU decomposition?)
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# Actually solve() can take multiple vectors, so just pass it something with the full diagonal?
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xx = numpy.matmul(numpy.linalg.pinv(A), b) #TODO verify
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assert(numpy.allclose(xx, x))
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return x
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def get_r(p, left, right, t):
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r = numpy.empty(left.num_modes, dtype=complex)
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for ii in range(left.num_modes):
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r[ii] = sum((inner_product(right[kk], left[ii]) - inner_product(left[ii], right[kk])) * t[kk]
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for kk in range(right.num_modes)
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) / (2 * inner_product(left[ii], left[ii]))
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return r
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def get_rt(left, right):
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s = 0.5 * (inner_product(left, right) + inner_product(right, left))
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d = 0.5 * (inner_product(left, right) - inner_product(right, left))
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t = (s * s - d * d) / s
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r = 1 - t / (s + d)
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return -r, t
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def inner_product(left_E, right_H, dxes):
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cross_z = left_E[0] * right_H.conj()[1] - left_E[1] * right_H[0].conj()
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# cross_z = numpy.cross(left_E, numpy.conj(right_H), axisa=0, axisb=0, axisc=0)[2]
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return numpy.trapz(numpy.trapz(cross_z, dxes[0][0]), dxes[0][1]) / 2 # TODO might need cumsum on dxes
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def propagation_matrix(self, modes, wavelength, distance):
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eigenv = numpy.array([mode.neff for mode in modes]) * 2 * numpy.pi / wavelength
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prop_diag = numpy.diag(numpy.exp(distance * 1j * numpy.hstack((eigenv, eigenv))))
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prop_matrix = numpy.roll(prop_diag, len(eigenv), axis=0)
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return prop_matrix
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def connect_s(A: numpy.ndarray, k: int, B: numpy.ndarray, l: int):
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"""
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TODO
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connect two n-port networks' s-matrices together.
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specifically, connect port `k` on network `A` to port `l` on network
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`B`. The resultant network has nports = (A.rank + B.rank-2).
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Args:
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A: S-parameter matrix of `A`, shape is fxnxn
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k: port index on `A` (port indices start from 0)
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B: S-parameter matrix of `B`, shape is fxnxn
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l: port index on `B`
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Returns:
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C: new S-parameter matrix
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"""
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if k > A.shape[-1] - 1 or l > B.shape[-1] - 1:
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raise (ValueError("port indices are out of range"))
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C = scipy.sparse.block_diag((A, B), dtype=complex)
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return innerconnect_s(C, k, A.shape[0] + l)
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def innerconnect_s(A, k, l):
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"""
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TODO
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n x n x freq
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connect two ports of a single n-port network's s-matrix.
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Specifically, connect port `k` to port `l` on `A`. This results in
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a (n-2)-port network.
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Args:
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A: S-parameter matrix of `A`, shape is fxnxn
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k: port index on `A` (port indices start from 0)
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l: port index on `A`
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Returns:
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C: new S-parameter matrix
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Notes:
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Relevant papers:
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- Compton, R.C.; , "Perspectives in microwave circuit analysis," Circuits and Systems, 1989., Proceedings of the 32nd Midwest Symposium on , vol., no., pp.716-718 vol.2, 14-16 Aug 1989. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=101955&isnumber=3167
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- Filipsson, Gunnar; , "A New General Computer Algorithm for S-Matrix Calculation of Interconnected Multiports," Microwave Conference, 1981. 11th European , vol., no., pp.700-704, 7-11 Sept. 1981. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4131699&isnumber=4131585
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"""
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if k > A.shape[-1] - 1 or l > A.shape[-1] - 1:
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raise (ValueError("port indices are out of range"))
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l = [l]
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k = [k]
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mkl = 1 - A[k, l]
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mlk = 1 - A[l, k]
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C = A + (A[k, :] * A[:, l] * mlk
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+ A[l, :] * A[:, k] * mkk
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+ A[k, :] * A[l, l] * A[:, k]
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+ A[l, :] * A[k, k] * A[:, l]
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) / (
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mlk * mkl - A[k, k] * A[l, l]
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)
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# remove connected ports
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C = npy.delete(C, (k, l), 1)
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C = npy.delete(C, (k, l), 2)
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return C
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