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June 10, 2014 07:22
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#!/usr/bin/env python | |
# available: https://github.com/ShigekiKarita/practice/blob/master/PH_6-2.py | |
B = [0.6961663, 0.4079426, 0.8974794] | |
wavelength = [0.0684043, 0.1162414, 9.896161] # micro-meter | |
c = 29.9792458 * 10 ** 8 * 10 ** 6 # micro-meter | |
pi = 3.141592653589793 | |
def n(x): | |
sigma = 0. | |
for j in range(0, 3): | |
sigma += B[j] * x ** 2 / (x ** 2 - wavelength[j]) | |
return (1 + sigma) ** 0.5 | |
def gradient(f, h=1. / 10 ** 6): | |
def fx(x): | |
return (f(x + h) - f(x)) / h | |
return fx | |
if __name__ == '__main__': | |
nxx = gradient(gradient(n)) # 1 / micro-meter^2 | |
x = 1.550 # micro-meter | |
D = - x / c * nxx(x) # s / micro-meter^2 | |
beta_2 = - x ** 2 / (2 * pi * c) * D # s / micro-meter | |
L_max = (0.4 * 10**-10)**2 / abs(beta_2) * 10**-9 # kilo-meter | |
print(D) | |
print(beta_2) | |
print(L_max) | |
# 3rd-party libraries to plot figures | |
import numpy as np | |
import matplotlib.pyplot as plt | |
xrange = np.linspace(0.5, 2.0, 100) | |
fig = plt.figure(1) | |
plt.subplots_adjust(hspace=0.5, wspace=0.5) | |
plt.subplot(2, 2, 1) | |
plt.plot(xrange, (lambda x: n(x) ** 2)(xrange)) | |
plt.ylabel("n^2") | |
plt.xlabel("wavelength[um]") | |
plt.subplot(2, 2, 2) | |
plt.plot(xrange, n(xrange)) | |
plt.ylabel("n") | |
plt.xlabel("wavelength[um]") | |
plt.subplot(2, 2, 3) | |
plt.plot(xrange, gradient(n)(xrange)) | |
plt.ylabel("n'[um^-1]") | |
plt.xlabel("wavelength[um]") | |
plt.subplot(2, 2, 4) | |
plt.plot(xrange, nxx(xrange)) | |
plt.ylabel("n''[um^-2]") | |
plt.xlabel("wavelength[um]") | |
fig.savefig("ph.pdf") |
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SiO2's dispersion-limited transmission distance