From bd3099d0023b0610c0faf0d4077f6fd1a9068bf3 Mon Sep 17 00:00:00 2001
From: mer0m <baptiste.marechal@femto-st.fr>
Date: Mon, 23 Jan 2017 09:40:13 +0100
Subject: [PATCH] add PDH signal

---
 tf_cavity/tf_cavity_num.py | 56 +++++++++++++++++++++++++++++++---------------
 1 file changed, 38 insertions(+), 18 deletions(-)

diff --git a/tf_cavity/tf_cavity_num.py b/tf_cavity/tf_cavity_num.py
index 85fcc77..724f6d7 100644
--- a/tf_cavity/tf_cavity_num.py
+++ b/tf_cavity/tf_cavity_num.py
@@ -55,44 +55,64 @@ mpl.rcParams.update(pgf_with_latex)
 from numpy import *
 import matplotlib.pyplot as plt
 
-r = 0.99
+r = 0.99998
 L = 140e-3
 c = 299792458
 
 tau = L/c
 fsr = 1/(2*tau)
+finesse = pi*r/(1-r**2)
+print('Finesse = %f\n FSR = %f\n FSR/Finesse = %f'%(finesse, fsr, fsr/finesse))
 
 f0 = (193e12//fsr)*fsr
 f = linspace(f0-0.1*fsr, f0+0.1*fsr, 1e5)
 
+fm = 30e6
+
 #TF of cavity in reflection
 def Fr(w):
     s = 1j*w
     return r*(exp(-2*tau*s)-1)/(1-r**2*exp(-2*tau*s))
 
 G = Fr(2*pi*f)
+Glsb = Fr(2*pi*(f-fm))
+Gusb = Fr(2*pi*(f+fm))
 
-#plot bode of F(w)
-ax1 = plt.subplot(3, 1, 1)
-ax1.set_ylabel('Magnitude')
-ax1.plot(f, abs(G))
-ax1.grid()
+#plot setup
+fig, axarr = plt.subplots(3, 2, sharex='col')
 
-ax2 = plt.subplot(3, 1, 2, sharex = ax1)
-ax2.set_ylabel('Phase (deg)')
-ax2.set_xlabel('omega (rad.s$^{-1}$)')
-ax2.plot(f, angle(G, deg = True))
-ax2.grid()
+#plot bode of F(w)
+axarr[0, 1].set_ylabel('Magnitude')
+#axarr[0, 1].set_xlabel('Frequency (Hz)')
+axarr[0, 1].plot(f, abs(G))
+axarr[0, 1].grid()
+axarr[1, 1].set_ylabel('Phase (deg)')
+#axarr[1, 1].set_xlabel('Frequency (Hz)')
+axarr[1, 1].plot(f, angle(G, deg = True))
+axarr[1, 1].grid()
+
+#PDH signal
+iG = (G*Gusb.conjugate()-G.conjugate()*Glsb).imag
+axarr[2, 1].set_ylabel('epsillon normalized')
+axarr[2, 1].set_xlabel('Frequency (Hz)')
+axarr[2, 1].xaxis.set_label_coords(0.5, -0.3)
+axarr[2, 1].plot(f, iG)
+axarr[2, 1].grid()
 
 
 #nyquist
-ax3 = plt.subplot(3, 1, 3)
-ax3.set_ylabel('$j\omega$')
-ax3.set_xlabel('$\sigma$')
-ax3.plot(real(G), imag(G))
-ax3.grid()
-ax3.axis('equal')
-
+axarr[2, 0].set_ylabel('$j\omega$')
+axarr[2, 0].set_xlabel('$\sigma$')
+axarr[2, 0].plot(real(G), imag(G))
+axarr[2, 0].grid()
+axarr[2, 0].axis('equal')
+axarr[2, 0].set_xlim([-1.1, 1.1])
+
+#layout
+axarr[0, 0].axis('off')
+axarr[1, 0].axis('off')
+fig.subplots_adjust(wspace=0.5)
+plt.tight_layout()
 #plt.savefig('fig.pgf')
 plt.show()
 
-- 
2.16.4