A quantitative performance analysis of two different interferometric alignment sensing schemes for gravitational wave detectors

TL;DR

This study quantitatively compares two alignment sensing schemes for gravitational-wave detectors: conventional WaveFront Sensing (WFS) using quadrant photodetectors with Gouy-phase separation and a novel Radio Frequency Jitter Alignment Sensing (RFJAS) employing an electro-optic beam deflector to generate HG$_{10}$ sidebands at the HOM spacing. Through a table-top bowtie-cavity experiment, the authors build diagonal sensing matrices for both methods, calibrate the PZT-driven alignment DOFs, and perform a detailed low-frequency noise budget, revealing WFS is limited by beam spot motion below $\sim 30$ Hz while RFJAS is limited by residual RF amplitude modulation. The results show high coherence between the two schemes up to $\sim 30$ Hz and suggest a blended approach—RFJAS at low frequencies and WFS at higher frequencies—could optimize alignment sensing for detectors such as Advanced LIGO. Practical considerations include beam clipping, aperture effects, and the need for site-specific validation and loop-closure experiments. Overall, the work provides actionable guidance for reducing ASC noise and informs design choices for next-generation gravitational-wave interferometers.

Abstract

Precise laser alignment in optical cavities is essential for high-precision laser interferometry. We report on a table-top optical experiment featuring two alignment sensing schemes: the conventional Wavefront Sensing (WFS) scheme which uses quadrant photodetectors (QPDs) to recover optical alignment, and the newly developed Radio Frequency Jitter Alignment Sensing (RFJAS) scheme, which uses an electro-optic beam deflector (EOBD) to apply fast angular modulation. This work evaluates the performance of RFJAS through a direct, side-by-side comparison with WFS. We present a detailed noise budget for both techniques, with particular emphasis on limitations at low frequencies, below 30\,Hz. Our results show that WFS performance is constrained by technical noise arising from beam spot motion (BSM), mainly due to beam miscentering on QPDs. In contrast, RFJAS is primarily limited by residual RF amplitude modulation. A blended scheme that combines both sensing methods may offer the most practical approach for use in gravitational wave detectors such as Advanced LIGO.

Figures (9)

• Figure 1: Alignment degrees of freedom (DOFs) of an cavity. On the top is a tilt DOF, and the bottom is the translation DOF. The black line is the cavity eigenaxis, while the red line is the misaligned input beam.
• Figure 2: The tabletop optical layout used in this experiment.
• Figure 3: Alignment sensing matrix after phase rotation as a function of modulation frequency. The solid lines are the measured data and the dashed lines are the simulation fit data. The plots are in units of V/V (data) or W/W (simulation), as it is normalized to the quadrature sum of the first sensing matrix elements. The asymmetry in the shape of the PZT2 to Q curve and PZT1 to I curve is due to the accumulated Gouy phase between the EOBD and the cavity waist. Different Gouy phases correspond to different shapes of the sweep measurement. However, the reason that PZT1 to I does not have the same value as PZT2 to Q at the zero-crossing of PZT2 to I could be due to the fact the PZTs do not drive the same misalignment DOF amplitude, as well as the presence of mode mismatch.
• Figure 4: Polar representation of the Gouy phase separation between QPD1 and QPD2. The radial component magnitude corresponds to the magnitude response of each QPD to the driving alignment DOF in volts.
• Figure 5: Left: A visualization of the wavefronts shifted to the left and right of the center of the QPD by one beam radius. Right: The difference between RF demodulated signals from the left and rights halves, normalized by the sum of the DC power on both halves, as a function of spot position offset.