The arm length stabilization system is employed in gravitational-wave detectors to reduce the velocity of the mirrors such that the arm cavities can be brought onto resonance in a controlled manner required to attain the detector operating point. For future upgrades of current gravitational wave detectors such as ${\mathrm{A}}^{\#}$, which will incorporate AlGaAs/GaAs coatings, the current frequency-doubled arm length stabilization system is unsuitable due to excessive absorption of the frequency-doubled 532 nm beam by the AlGaAs/GaAs coating. We propose a novel multiwavelength arm length stabilization scheme that uses both frequency-doubled and frequency-tripled beams. The 1596 nm auxiliary locking beam is outside the absorption bands of AlGaAs/GaAs coating. It is frequency tripled to 532 nm and phase locked with the 1064 nm science laser through its second harmonic at 532 nm. In a tabletop setup, we experimentally demonstrated the stable cavity detuning and robust cavity locking transition by controlling the 1596 nm laser and 1064 nm laser phase-locked loop. This demonstration confirmed that the proposed novel arm length stabilization scheme is compatible with future upgrades or third-generation gravitational wave detectors that use AlGaAs/GaAs-coated test masses.

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• Gravitational wave detection