gistfile1.txt

import numpy
import EMpy
import pylab




def epsfunc(x_, y_):
    """Return a matrix describing a 2d material.

    :param x_: x values
    :param y_: y values
    :return: 2d-matrix
    """
    xx, yy = numpy.meshgrid(x_, y_)

    
    E = numpy.where((numpy.abs(xx.T - 1.24e-6) <= .24e-6) *
                       (numpy.abs(yy.T - 1.11e-6) <= .11e-6),
                       3.4757**2,
                       1.446**2)

    return E


wl = 1.55e-6
x = numpy.linspace(0, 2.48e-6, 125)
y = numpy.linspace(0, 2.22e-6, 112)

#For the plotting
x_1 = numpy.linspace(0, 2.48e-6, 124)
y_1 = numpy.linspace(0, 2.22e-6, 111)


X,Y = numpy.meshgrid(x_1,y_1) #for the plot of the E field
X_2,Y_2= numpy.meshgrid(x,y)  #for the plot of the H field


neigs = 2
tol = 1e-8
boundary = '0000'

solver = EMpy.modesolvers.FD.VFDModeSolver(wl, x, y, epsfunc, boundary).solve(
    neigs, tol)




#####################################################################################
#calculate the H field from the E field
##################################################################


######
#Define Variables needed for the calculation of the H filed from the E field
######

Ex = solver.modes[1].Ex
Ey = solver.modes[1].Ey
Ez = solver.modes[1].Ez


dx = 2.48e-6/124
dy = 2.22e-6/111

c = 299792458.              # speed of light in vacuum
mu_0 = 4 * numpy.pi * 1e-7         # permeability
k = 2*numpy.pi / wl           #wave number
angularFrequency = k * c


#Define the H grating
Hx = numpy.zeros(numpy.shape(Ex),complex)
Hy = numpy.zeros(numpy.shape(Ey),complex)
Hz = numpy.zeros(numpy.shape(Ez),complex)


def difference(E,index_x,index_y,axis):
  #Calculates dE at a certain point in direction of the axis

  #in x direction
  if axis == 'x':
    #to make it work at the end of the array
      if index_x+1 == numpy.shape(E)[0]:
          diff = E[index_x,index_y]-E[index_x-1,index_y]
      else:
          diff = E[index_x+1,index_y]-E[index_x,index_y]
     

  #in y direction
  if axis == 'y':
      #to make it work at the end of the array
      if index_y+1 == numpy.shape(E)[1]:
          diff = E[index_x,index_y]-E[index_x,index_y-1]
      else:
          diff = E[index_x,index_y+1]-E[index_x,index_y]

  return diff



#Calculates the Magnetic field from the Electric field

for i in range(len(x)-1):
  for j in range(len(y)-1):
    #dEx/dy-dEy/dx
    Hz[i,j] = -1/(1j* angularFrequency*mu_0 )\
        *(difference(Ey,i,j,'x')/dx\
       -difference(Ex,i,j,'y')/dy )

     #dEz/dy
    Hx[i,j] = -1/(1j* angularFrequency*mu_0 )\
        *difference(Ez,i,j,'y')/dy
    #-dEz/dx
    Hy[i,j] = -1/(1j* angularFrequency*mu_0 )\
        *-difference(Ez,i,j,'x')/dx


#######################################################
#plot
#######################################################


#linear
fig = pylab.figure()
fig.add_subplot(3, 3, 1)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ex),50)
pylab.title('Ex')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 2)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ey),50)
pylab.title('Ey')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 3)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ez),50)
pylab.title('Ez')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 4)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hx),50)
pylab.title('Hx')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 5)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hy),50)
pylab.title('Hy')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 6)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hz),50)
pylab.title('Hz')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 7)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hx),50)
pylab.title('Hx from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 8)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hy),50)
pylab.title('Hy from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 9)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hz),50)
pylab.title('Hz from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()

pylab.tight_layout()
pylab.show()






#log
fig = pylab.figure()
fig.add_subplot(3, 3, 1)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ex),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Ex')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 2)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ey),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Ey')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 3)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(solver.modes[1].Ez),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Ez')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 4)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hx),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Hx')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 5)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hy),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Hy')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 6)
pylab.contourf(X_2.T*1e6,Y_2.T*1e6,abs(solver.modes[1].Hz),levels=numpy.logspace(2,7,10), locator=pylab.LogLocator())
pylab.title('Hz')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 7)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hx),levels=numpy.logspace(0,5,10), locator=pylab.LogLocator())
pylab.title('Hx from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 8)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hy),levels=numpy.logspace(0,5,10), locator=pylab.LogLocator())
pylab.title('Hy from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()
fig.add_subplot(3, 3, 9)
pylab.contourf(X.T*1e6,Y.T*1e6,abs(Hz),levels=numpy.logspace(0,5,10), locator=pylab.LogLocator())
pylab.title('Hz from E')
pylab.xlabel('x [um]')
pylab.ylabel('y [um]')
pylab.colorbar()

pylab.tight_layout()
pylab.show()