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- #!/usr/bin/env python
- # -*- coding: UTF-8 -*-
- #
- # Copyright (C) 2009-2015 Ovidio Peña Rodríguez <ovidio@bytesfall.com>
- #
- # This file is part of python-scattnlay
- #
- # This program is free software: you can redistribute it and/or modify
- # it under the terms of the GNU General Public License as published by
- # the Free Software Foundation, either version 3 of the License, or
- # (at your option) any later version.
- #
- # This program is distributed in the hope that it will be useful,
- # but WITHOUT ANY WARRANTY; without even the implied warranty of
- # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- # GNU General Public License for more details.
- #
- # The only additional remark is that we expect that all publications
- # describing work using this software, or all commercial products
- # using it, cite the following reference:
- # [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by
- # a multilayered sphere," Computer Physics Communications,
- # vol. 180, Nov. 2009, pp. 2348-2354.
- #
- # You should have received a copy of the GNU General Public License
- # along with this program. If not, see <http://www.gnu.org/licenses/>.
- # This test case calculates the the electric field in the
- # XY plane, for a Luneburg lens, as described in:
- # B. R. Johnson, Applied Optics 35 (1996) 3286-3296.
- # The Luneburg lens is a sphere of radius a, with a
- # radially-varying index of refraction, given by:
- # m(r) = [2 - (r/a)**1]**(1/2)
- # For the calculations, the Luneburg lens was approximated
- # as a multilayered sphere with 500 equally spaced layers.
- # The refractive index of each layer is defined to be equal to
- # m(r) at the midpoint of the layer: ml = [2 - (xm/xL)**1]**(1/2),
- # with xm = (xl-1 + xl)/2, for l = 1,2,...,L. The size
- # parameter in the lth layer is xl = l*xL/500.
- from scattnlay import fieldnlay
- import numpy as np
- nL = 500.0
- Xmax = 60.0
- x = np.ones((1, nL), dtype = np.float64)
- x[0] = np.arange(1.0, nL + 1.0)*Xmax/nL
- m = np.ones((1, nL), dtype = np.complex128)
- m[0] = np.sqrt((2.0 - ((x[0] - 0.5*Xmax/nL)/60.0)**2.0)) + 0.0j
- print "x =", x
- print "m =", m
- npts = 501
- scan = np.linspace(-10.0*x[0, -1], 10.0*x[0, -1], npts)
- coordX, coordY = np.meshgrid(scan, scan)
- coordX.resize(npts*npts)
- coordY.resize(npts*npts)
- coordZ = np.zeros(npts*npts, dtype = np.float64)
- coord = np.vstack((coordX, coordY, coordZ)).transpose()
- terms, E, H = fieldnlay(x, m, coord)
- Er = np.absolute(E)
- # |E|/|Eo|
- Eh = np.sqrt(Er[0, :, 0]**2 + Er[0, :, 1]**2 + Er[0, :, 2]**2)
- result = np.vstack((coordX, coordY, coordZ, Eh)).transpose()
- try:
- import matplotlib.pyplot as plt
- from matplotlib import cm
- from matplotlib.colors import LogNorm
- min_tick = 0.1
- max_tick = 1.0
- edata = np.resize(Eh, (npts, npts))
- fig = plt.figure()
- ax = fig.add_subplot(111)
- # Rescale to better show the axes
- scale_x = np.linspace(min(coordX), max(coordX), npts)
- scale_y = np.linspace(min(coordY), max(coordY), npts)
- # Define scale ticks
- min_tick = min(min_tick, np.amin(edata))
- max_tick = max(max_tick, np.amax(edata))
- scale_ticks = np.power(10.0, np.linspace(np.log10(min_tick), np.log10(max_tick), 6))
- # Interpolation can be 'nearest', 'bilinear' or 'bicubic'
- cax = ax.imshow(edata, interpolation = 'nearest', cmap = cm.jet,
- origin = 'lower', vmin = min_tick, vmax = max_tick,
- extent = (min(scale_x), max(scale_x), min(scale_y), max(scale_y)),
- norm = LogNorm())
- # Add colorbar
- cbar = fig.colorbar(cax, ticks = [a for a in scale_ticks])
- cbar.ax.set_yticklabels(['%3.1e' % (a) for a in scale_ticks]) # vertically oriented colorbar
- pos = list(cbar.ax.get_position().bounds)
- fig.text(pos[0] - 0.02, 0.925, '|E|/|E$_0$|', fontsize = 14)
- plt.xlabel('X')
- plt.ylabel('Y')
- # This part draws the nanoshell
- # from matplotlib import patches
- # s1 = patches.Arc((0, 0), 2.0*x[0, 0], 2.0*x[0, 0], angle=0.0, zorder=2,
- # theta1=0.0, theta2=360.0, linewidth=1, color='#00fa9a')
- # ax.add_patch(s1)
- # s2 = patches.Arc((0, 0), 2.0*x[0, 1], 2.0*x[0, 1], angle=0.0, zorder=2,
- # theta1=0.0, theta2=360.0, linewidth=1, color='#00fa9a')
- # ax.add_patch(s2)
- # End of drawing
- plt.draw()
- plt.show()
- plt.clf()
- plt.close()
- finally:
- np.savetxt("test04_field.txt", result, fmt = "%.5f")
- print result
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