In [165]:
import matplotlib.pyplot as plt
from numpy import pi, sin, cos, linspace, exp, real, imag, angle, abs, conj, meshgrid
from numpy.fft import fft, fftshift
from mpl_toolkits.mplot3d import axes3d
In [3]:
%matplotlib inline
In [ ]:
w=
In [116]:
Z_1=1
In [117]:
def Z_2(x):
return 2*x
def Z_3(y):
return 2*y
In [118]:
def Z_4(x,y):
return (6**.5)*2*x*y
In [119]:
def Z_5(x,y):
return (3**.5)*(2*x**2+2*y**2-1)
def Z_6(x,y):
return (6**.5)*(x**2 - y**2)
In [120]:
def Z_7(x,y):
return (8**.5)*(3*x**2*y-y**3)
def Z_8(x,y):
return (8**.5)*(3*x**2*y-y+3*y**3-2*y)
In [121]:
def Z_9(x,y):
return (8**.5)*(3*x**3+3*x*y**2-2*x)
def Z_10(x,y):
return (8**.5)*(x**3-3*x*y**2)
In [143]:
def Psi(x,y,w,Cn=[1,0,0,0.5,0,0,0,0,0,0]):
Zsum = Cn[0]*Z_1 + Cn[1]*Z_2(x) + Cn[2]*Z_3(y) + Cn[3]*Z_4(x,y) + Cn[4]*Z_5(x,y)
Zsum += Cn[5]*Z_6(x,y) + Cn[6]*Z_7(x,y) + Cn[7]*Z_8(x,y) + Cn[8]*Z_9(x,y) + Cn[9]*Z_10(x,y)
return exp(-(x**2 + y**2)/ w**2)* exp(1j*2*pi*Zsum)
In [182]:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x=linspace(-.006,.006,600)
y=linspace(-.006,.006,600)
X, Y = meshgrid(x,y)
Z=Psi(X,Y,w=.003,Cn=[.158,-.025,.025,-.007,-.143,-.008,-.006,.007,.01,-.011])
ax.plot_wireframe(X, Y, abs(Z), rstride=10, cstride=10)
Out[182]:
<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x7f536a3713c8>
In [183]:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X, Y, angle(Z), rstride=10, cstride=10)
Out[183]:
<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x7f536a2701d0>
In [160]:
plt.imshow(imag(Z))
Out[160]:
<matplotlib.image.AxesImage at 0x7f536a8534e0>
In [161]:
plt.imshow(real(Z))
Out[161]:
<matplotlib.image.AxesImage at 0x7f536a89b470>
In [162]:
plt.imshow(Z_2(Y))
Out[162]:
<matplotlib.image.AxesImage at 0x7f536af7f0f0>
In [180]:
LObeam = Z[:,300]
plt.plot(abs(LObeam))
plt.plot(angle(LObeam))
Out[180]:
[<matplotlib.lines.Line2D at 0x7f536d577208>]
In [179]:
LObeam
Out[179]:
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In [ ]:
Content source: DawesLab/LabNotebooks
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