Abstract
Motivated by the potential factor of 2.65 improvement in coating Brownian noise power spectral density using the \(LG_{33}\) mode, as shown in section 2.7, a numerical investigation into the interferometric performance of the \(LG_{33}\) mode was pursued.
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Notes
- 1.
This is a somewhat arbitrary number, but it is commonly used throughout the gravitational wave community, and is related to the acceptable round trip cavity losses.
- 2.
The opposite sign of the error signal in the case of the \(\mathrm{LG}_{33}\) mode is of no consequence; one could simply alter the demodulation phase or invert the signal after demodulation to recover the same sign.
- 3.
Cavity tuning, expressed in degrees, is a convenient definition of either cavity length change as a fraction of wavelength, or frequency change as a function of cavity FSR.
- 4.
In the misalignment regime we are concerned with (100s of picoradians), the fringe spacing is of the order of km; far greater than the overlapping region of the beams.
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Fulda, P. (2014). Simulation Study into \(\mathrm{LG}_{33}\) Mode Interferometry and Production. In: Precision Interferometry in a New Shape. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01375-6_3
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