PDH_error_signal.py
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#!/usr/bin/env python
import numpy
import matplotlib.pyplot as plt
L = 14e-2
c = 299792458
R = 0.99991
fsr = c/(2*L)
print("fsr = %f GHz"%(fsr/1e9))
finesse = numpy.pi*R**0.25/(1-R**0.5)
print("finesse = %i"%finesse)
print("finesse/fsr = %f s"%(finesse/fsr))
fc = fsr*130000
df = 20e6
#print(fc)
f = 2*numpy.pi*numpy.linspace(fc-df, fc+df, 100000) # frequency array
i = complex(0,1)
fpt = ((1.-R)*numpy.exp(-2.*L*i*f/c))/(1.-R*numpy.exp(-2.*L*i*f/c))
fpr = R**0.5*(1.-numpy.exp(-2.*L*i*f/c))/(1.-R*numpy.exp(-2.*L*i*f/c))
plt.subplot(2, 1, 1)
plt.plot(f, abs(fpr))
plt.title('FP cavity')
plt.ylabel('Reflective intensity')
plt.grid()
fm = 23e6
ram = 0
fm1 = R**0.5*(1.-numpy.exp(-2.*L*i*(f+fm)/c))/(1.-R*numpy.exp(-2.*L*i*(f+fm)/c)) + ram*i
fm2 = R**0.5*(1.-numpy.exp(-2.*L*i*(f-fm)/c))/(1.-R*numpy.exp(-2.*L*i*(f-fm)/c)) + ram*i
ff = fpr*fm1.conjugate()-fpr.conjugate()*fm2
iff = ff.imag
plt.subplot(2, 1, 2)
plt.plot(f, iff)
plt.xlabel('Frequency')
plt.ylabel('PDH')
plt.grid()
plt.show()