add bloch example

examples/bloch.py

@@ -0,0 +1,68 @@
+import numpy, scipy, gridlock, fdfd_tools
+from fdfd_tools import bloch
+from numpy.linalg import norm
+import logging
+
+logging.basicConfig(level=logging.DEBUG)
+logger = logging.getLogger(__name__)
+
+
+dx = 40
+x_period = 400
+y_period = z_period = 2000
+g = gridlock.Grid([numpy.arange(-x_period/2, x_period/2, dx),
+                   numpy.arange(-1000, 1000, dx),
+                   numpy.arange(-1000, 1000, dx)],
+                  shifts=numpy.array([[0,0,0]]),
+                  initial=1.445**2,
+                  periodic=True)
+
+g.draw_cuboid([0,0,0], [200e8, 220, 220], eps=3.47**2)
+
+#x_period = y_period = z_period = 13000
+#g = gridlock.Grid([numpy.arange(3), ]*3,
+#                  shifts=numpy.array([[0, 0, 0]]),
+#                  initial=2.0**2,
+#                  periodic=True)
+
+g2 = g.copy()
+g2.shifts = numpy.zeros((6,3))
+g2.grids = [numpy.zeros(g.shape) for _ in range(6)]
+
+epsilon = [g.grids[0],] * 3
+reciprocal_lattice = numpy.diag(1e6/numpy.array([x_period, y_period, z_period])) #cols are vectors
+
+#print('Finding k at 1550nm')
+#k, f = bloch.find_k(frequency=1/1550,
+#                    tolerance=(1/1550 - 1/1551),
+#                    direction=[1, 0, 0],
+#                    G_matrix=reciprocal_lattice,
+#                    epsilon=epsilon,
+#                    band=0)
+#
+#print("k={}, f={}, 1/f={}, k/f={}".format(k, f, 1/f, norm(reciprocal_lattice @ k) / f ))
+
+print('Finding f at [0.25, 0, 0]')
+for k0x in [.25]:
+    k0 = numpy.array([k0x, 0, 0])
+
+    kmag = norm(reciprocal_lattice @ k0)
+    tolerance = (1e6/1550) * 1e-4/1.5  # df = f * dn_eff / n
+    logger.info('tolerance {}'.format(tolerance))
+
+    n, v = bloch.eigsolve(4, k0, G_matrix=reciprocal_lattice, epsilon=epsilon, tolerance=tolerance)
+    v2e = bloch.hmn_2_exyz(k0, G_matrix=reciprocal_lattice, epsilon=epsilon)
+    v2h = bloch.hmn_2_hxyz(k0, G_matrix=reciprocal_lattice, epsilon=epsilon)
+    ki = bloch.generate_kmn(k0, reciprocal_lattice, g.shape)
+
+    z = 0
+    e = v2e(v[0])
+    for i in range(3):
+        g2.grids[i] += numpy.real(e[i])
+        g2.grids[i+3] += numpy.imag(e[i])
+
+    f = numpy.sqrt(numpy.real(numpy.abs(n))) # TODO
+    print('k0x = {:3g}\n eigval = {}\n f = {}\n'.format(k0x, n, f))
+    n_eff = norm(reciprocal_lattice @ k0) / f
+    print('kmag/f = n_eff =  {} \n wl = {}\n'.format(n_eff, 1/f ))
+