Adding function for filter cavity optimisation.

pykat/tools/filter_cavity.py

+import numpy as np
+
+
+def filter_cavity_parameters(P, lambda0, m, Titm, Tsrm, L, loss=0):
+    """
+    Compute the optimal filter cavity detuning phase and input mirror
+    transmissivity for frequency-dependent squeezing in a tuned, dual-recycled
+    interferometer.
+
+    P - Arm cavity circulating power [W]
+    lambda0 - main laser wavelength [m]
+    m - mass of test masses (mirrors) [kg]
+    Titm - Power transmissivity of input test mass
+    Tsrm - Power transmissivity of signal recycling mirror
+    L - Filter cavity length [m]
+    loss - Filter cavity round-trip power loss
+
+    See Kwee et al. `Decoherence and degradation of squeezed states in
+    quantum filter cavities` Physical Review D, 2014, 90, 062006
+    """
+    c = 299792458.0
+    w0 = 2 * np.pi * c / lambda0
+    FSR = c / (2.0 * L)
+
+    # Approximate frequency at which IFO reaches SQL
+    # (i.e. radiation pressure noise = shot noise)
+    w_sql_0 = 8 / c * np.sqrt(P * w0 / (m * Titm))
+    w_sql = np.sqrt(Tsrm) / (1 + np.sqrt(1 - Tsrm)) * w_sql_0
+
+    if loss > 0:
+        epsilon = 4 / (
+            2 + np.sqrt(2 + 2 * np.sqrt(1 + (2 * w_sql / (FSR * loss)) ** 4))
+        )
+    else:
+        epsilon = 0
+
+    # Filter cavity bandwidth
+    gamma_f = (
+        np.sqrt(2 / ((2 - epsilon) * np.sqrt(1 - epsilon)))
+        * w_sql
+        / (2 * np.pi * np.sqrt(2))
+    )
+
+    # Detuning
+    delta = np.sqrt(1 - epsilon) * gamma_f
+
+    phi = -delta / FSR * 180.0
+    T = 2.0 * gamma_f / FSR * 2 * np.pi
+    return phi, T