Higher-order Laguerre–Gauss modes in (non-) planar four-mirror cavities for future gravitational wave detectors

One of the limiting noise sources in the current generation of gravitational wave detectors, such as the advanced laser interferometer gravitational wave observatory (aLIGO), is the thermal noise in the interferometer's test mass coatings. One proposed method to reduce the coupling of this noise source to the gravitational wave readout is using a laser beam in the higher-order spatial LG₃₃ mode within the interferometer. Here we show that the current four-mirror cavities of aLIGO are not compatible with Laguerre-Gauss modes due to astigmatism. A non-degeneracy of modes of the same order could be observed in experiment and simulation. We demonstrate that a non-planar cavity could be used instead as it compensates for the astigmatism and transmits the LG₃₃ mode undisturbed.