Bow tie cavity

Below, we model the output mode cleaner (OMC) of LIGO, which is a type of ring optical cavity made of four mirrors (denoted \(\text{OMC}_1\) to \(\text{OMC}_4\)) arranged so that the optical path crosses itself, forming a shape similar to a bow tie.

In optics, any laser beam can be described as a sum of transverse Gaussian modes (see Higher-order spatial modes), which form a complete basis of functions for the transverse field profile. The ideal beam in an interferometer is the fundamental TEM00 mode, and imperfections in the interferometer optics, as mirror surface defects or small mirror tilts, couple part of the light into higher-order modes of this basis.

The input mode cleaner (see Triangular cavity) is placed before the main interferometer to ensure that a clean TEM00 beam enters the instrument. But even if the input beam is perfectly clean, additional higher-order modes can be generated inside the interferometer by optical imperfections and misalignments. That’s why an output mode cleaner is placed at the detection port. The OMC transmits the fundamental mode that carries the gravitational-wave signal and suppresses higher-order modes produced by the interferometer itself.

import finesse
from finesse.analysis.actions import Xaxis
finesse.init_plotting()

# parameters from https://finesse.docs.ligo.org/finesse-ligo/parameter_files/llo.html 

OMC_model = finesse.Model()
OMC_model.parse(
    """
    l l1 P=125                  # laser with P=125W
    s s1 l1.p1 OMC_1.p1 L=1     # space of 1m length connectint laser to OMC

    # Output Mode Cleaner (OMC) mirrors
    # Light transmitted through OMC_1 (from p1 to p3) enters OMC_2 (in p1 and is
    # reflected in p2). It continues into OMC_3 (enters in p1, reflected in p2).
    # Then it continues into OMC_4 (enters in p1, reflected in p2).
    # Finally it returns from OMC_4.p2 into OMC_1.p4, which reflects back into OMC_1.p3,
    # closing the bow tie cavity.
    bs OMC_1    T=0.0076    L=0     alpha=2.7609
    bs OMC_2    T=0.0075    L=0     alpha=2.7609
    bs OMC_3    T=36.0u     L=0     alpha=4.004     Rc=2.57321
    bs OMC_4    T=35.9u     L=0     alpha=4.004     Rc=2.57369

    # Connect spaces to form a bow tie
    s sOMC_1    OMC_1.p3    OMC_2.p1    L=0.2815 
    s sOMC_2    OMC_2.p2    OMC_3.p1    L=0.2842
    s sOMC_3    OMC_3.p2    OMC_4.p1    L=0.2815 
    s sOMC_4    OMC_4.p2    OMC_1.p4    L=0.2842

    # Photodiodes measuring the reflected, circulating, and transmitted light
    pd power_reflected      OMC_1.p2.o
    pd power_circulating    OMC_1.p3.o
    pd power_transmitted    OMC_2.p3.o
    """
)

# Change the tuning of mirror OMC_2 from 0 to 360 degrees
out = OMC_model.run(Xaxis('OMC_2.phi', 'lin', 0, 360, 1000))
out.plot(logy=True);