Mirror-orientation noise in a Fabry-Perot interferometer gravitational wave detector

Area of Science:

• Optics and Gravitational Wave Astronomy

Background:

• Fabry-Perot resonators are crucial for high-precision measurements.
• Angular mirror-orientation errors can affect resonator length and stability.
• Accurate measurement of gravitational radiation requires minimizing such errors.

Purpose of the Study:

• To geometrically analyze the influence of angular mirror-orientation errors on Fabry-Perot resonator length.
• To develop a model for predicting cavity length fluctuations due to mirror-orientation noise.
• To inform the design of mirror control systems for gravitational wave observatories.

Main Methods:

• Geometric analysis of mirror-orientation errors in a Fabry-Perot resonator.
• Modeling short-term cavity length fluctuations caused by mirror-orientation noise.
• Experimental verification using the Laser Interferometer Gravitational-Wave Observatory (LIGO) 40-m interferometer test-bed.

Main Results:

• A simple geometric model accurately predicts cavity length fluctuations from static or slowly varying mirror-orientation errors.
• The model provides insights into the spectrum of short-term cavity length fluctuations.
• Experimental validation confirmed the model's predictions on the LIGO test-bed.

Conclusions:

• Geometric analysis offers a practical method for understanding and predicting mirror-orientation error effects in Fabry-Perot resonators.
• The developed model is directly applicable to enhancing mirror control systems for gravitational wave detection.
• This research contributes to the precision required for astrophysical gravitational radiation measurements by observatories like LIGO.