#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 26 17:19:41 2019

@author: simon_evered
"""
import numpy as np
import cmath
import matplotlib.pyplot as plt


# Input beam polarization angle
theta = 15 * 2*np.pi/360
E0 = 1

# Cavity parameters
r1 = .98
t1 = 1 - r1
r = .9999**3 * .9

def HC_error(phi = 0):
    E_par = E0 * np.cos(theta)
    E_perp = E0 * np.sin(theta)

    E_par_ref = E_par * (np.sqrt(r1) - t1*r*complex(np.cos(phi)-r, np.sin(phi))
        /(np.sqrt(r1)*(1-r)**2+4*r*np.sin(phi/2)**2))
    E_perp_ref = E_perp * np.sqrt(r1)

    Ia = abs(.5 * complex(E_par_ref,E_perp_ref))
    Ib = abs(.5 * complex(E_par_ref, -E_perp_ref))
    return Ia - Ib


## Plotting error as a function of phi ##
phi = np.arange(-4*np.pi, 4*np.pi, 0.01)
result = [HC_error(p) for p in phi]

fig = plt.figure(figsize=(15,10))
ax = fig.add_subplot(111)
ax.set_xlabel('Phase offset', fontsize = '20')
ax.set_ylabel('Error signal', fontsize = '20')
lines = [ax.axvline(0, color='black'),ax.axvline(2*np.pi, color='black'),ax.axvline(-2*np.pi, color='black')]
for l in lines: l.set_linestyle('dotted')
plt.plot(phi, result)
plt.show()