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| Keywords: SPP silver-air interface 370nm.gif en E-field of a surface plasmon polariton at the silver-air interface The animation shows how the E-field varies over an optical cycle Free-space wavelength is 370nm so the permittivity of silver is -2 62 + 0 626i The picture is 0 3 370 nanometers across horizontally 2013-12-02 16 58 33 own Sbyrnes321 cc-zero Source code Created with Matplotlib <source lang python > C Steven Byrnes 2013 This code is released under the MIT license http //opensource org/licenses/MIT This code runs in Python 2 7 or 3 3 It requires imagemagick to be installed; that's how it assembles images into animated GIFs Creates an animation of the electric field vectors of a surface-plasmon-polariton wave The metal-dielectric interface is at z 0 with metal at z<0 and dielectric such as air at z>0 Use Python 3 style division and print a/b is real division a//b is integer division from __future__ import division print_function import numpy as np from cmath import exp pi import matplotlib pyplot as plt from matplotlib path import Path import matplotlib patches as patches import subprocess os directory_now os path dirname os path realpath __file__ --- PART 1 OF 2 PHYSICS --- def Efield x_times_kvac z_times_kvac t_times_omega eps_m eps_d print_wave_properties False Inputs x_times_kvac and z_times_kvac are the coordinates x z multiplied by the vacuum angular wavenumber kvac omega / c t_times_nu is the time t multiplied by frequency nu eps_m and eps_d are the complex permittivities of the metal and dielectric Output The electric field vector E_x E_z It is scaled so that E_z 0 0 tw e1 e2 cos tw on the dielectric side of the interface Calculate components of the angular wavevector in the dielectric and metal as a multiple of kvac omega / c eps_m complex eps_m cast to complex so square roots won't raise errors kx_over_kvac eps_m eps_d / eps_m + eps_d 1/2 kzd_over_kvac eps_d - kx_over_kvac 2 1/2 kzm_over_kvac eps_m - kx_over_kvac 2 1/2 Pick the correct square-roots so that e i k z decays away from interface if kzd_over_kvac imag < 0 kzd_over_kvac -1 if kzm_over_kvac imag > 0 kzm_over_kvac -1 double-check the boundary condition almost_equal lambda a b tolerance abs a-b / abs a + abs b < tolerance if not almost_equal kzd_over_kvac eps_m kzm_over_kvac eps_d 1e-10 raise ValueError 'Something is wrong Boundary condition fails ' if print_wave_properties print 'kx / kvac ' kx_over_kvac print 'kzd / kvac ' kzd_over_kvac print 'kzm / kvac ' kzm_over_kvac print 'Wavelength / Vacuum wavelength ' 1/ kx_over_kvac real if kx_over_kvac imag 0 print ' Decay length / Vacuum wavelength ' 1/ kx_over_kvac imag else print 'Wave does not decay it propagates forever ' print ' Decay length into dielectric / Vacuum wavelength ' 1/ kzd_over_kvac imag print ' Decay length into metal / Vacuum wavelength ' -1/ kzm_over_kvac imag if z_times_kvac > 0 dielectric Ez exp 1j kx_over_kvac x_times_kvac + 1j kzd_over_kvac z_times_kvac - 1j t_times_omega Ex -Ez kzd_over_kvac / kx_over_kvac else metal Ez kzd_over_kvac / kzm_over_kvac exp 1j kx_over_kvac x_times_kvac + 1j kzm_over_kvac z_times_kvac - 1j t_times_omega Ex -Ez kzm_over_kvac / kx_over_kvac return Ex real Ez real --- PART 2 OF 2 DRAWING --- def draw_box x1 x2 y1 y2 color Code to draw a rectangular box in matplotlib used to color the metal area See http //matplotlib org/users/path_tutorial html vertices x1 y1 x1 y2 x2 y2 x2 y1 x1 y1 codes Path MOVETO Path LINETO Path LINETO Path LINETO Path CLOSEPOLY path Path vertices codes lw 0 means no outline; zorder -1 means it shouldn't block the arrows return patches PathPatch path facecolor color lw 0 zorder -1 def draw_frame t_times_omega eps_m eps_d aspect_ratio 1 5 frac_metal 0 5 fig_width_px 480 x_range_times_kvac 2 img_filename None Draw one frame of the animation Inputs t_times_omega is time multiplied by angular frequency it goes 0 --> 2pi each cycle eps_m and eps_d are the dielectric constants of the metal and dielectric aspect_ratio is width over height frac_metal is how much of the image is taken up by the metal fig_width_px is figure width in pixels x_range_times_kvac is the width of the image as a multiple of kvac img_filename is what to save the frame as or None to not save it Figure geometry fig_height_px fig_width_px // aspect_ratio dpi 80 This number doesn't affect the final animation fig_width_inches fig_width_px / dpi fig_height_inches fig_height_px / dpi Coordinate limits in figure All are implicitly multiplied by kvac z_range_times_kvac x_range_times_kvac / aspect_ratio xmin 0 xmax x_range_times_kvac zmin -z_range_times_kvac frac_metal zmax z_range_times_kvac 1-frac_metal How many arrows to draw num_arrows_x 15 num_arrows_z num_arrows_x // aspect_ratio Pick arrow coordinates arrow_x_list spacing np linspace xmin xmax num num_arrows_x endpoint False retstep True arrow_x_list + spacing / 2 arrow_z_list spacing np linspace zmin zmax num num_arrows_z endpoint False retstep True arrow_z_list + spacing / 2 X Z np meshgrid arrow_x_list arrow_z_list Arrow length scale Larger number smaller arrows arrow_len_scale 15 Calculate the length of each arrow Ex_func np vectorize lambda x z Efield x z t_times_omega eps_m eps_d 0 Ex_array Ex_func X Z Ez_func np vectorize lambda x z Efield x z t_times_omega eps_m eps_d 1 Ez_array Ez_func X Z Open a new figure with correct aspect ratio and pixel count and white background fig plt figure figsize fig_width_inches fig_height_inches dpi dpi facecolor 'w' Draw a new set of axes that fill the entire figure area ax fig add_axes 0 0 1 1 axisbg 'w' ax set_axis_off Color the metal part metal_color ' dddddd' light gray ax add_patch draw_box xmin xmax zmin 0 metal_color Draw the arrows ax quiver X Z Ex_array Ez_array scale arrow_len_scale scale_units 'width' pivot 'middle' ax set_xlim xmin xmax ax set_ylim zmin zmax if img_filename is not None fig savefig os path join directory_now img_filename dpi dpi def draw_anim eps_m eps_d anim_filename 'anim gif' frames_in_anim 30 total_anim_time_in_sec 2 keep_frame_images False kwargs Create an animated GIF kwargs are all the keyword arguments to draw_frame keep_frame_images True to save the individual frame image files that make up the animation; otherwise they are created and immediately deleted filename_list 'temp' + str n + ' png' for n in range frames_in_anim for n in range frames_in_anim draw_frame 2 pi n/frames_in_anim eps_m eps_d img_filename filename_listn kwargs seconds_per_frame total_anim_time_in_sec / frames_in_anim frame_delay str seconds_per_frame 100 command_list 'convert' '-delay' frame_delay '-loop' '0' + filename_list + anim_filename Use the convert command part of ImageMagick to build the animation subprocess call command_list cwd directory_now if keep_frame_images is False for filename in filename_list os remove os path join directory_now filename if True Silver-air interface at 370nm using data from Palik eps_m -2 62 + 0 626j eps_d 1 Print diagnostics Efield 0 0 0 eps_m eps_d print_wave_properties True Create animation draw_anim eps_m eps_d anim_filename 'Silver_370nm_Palik gif' </source> Uploaded with UploadWizard Electromagnetic field Images with Python source code Animations of vibrations and waves Plasma oscillations | ||||
