Practical solution of a compact system with a higher-order mode for PDH laser frequency stabilization

We propose and analyze the use of higher-order modes for Pound-Drever-Hall (PDH) frequency stabilization in compact ultrastable laser cavities. A spatial light modulation scheme is introduced to generate the HG₃₃ mode with a theoretical efficiency of 56%, providing a practical method for exciting higher-order modes. Finite element analysis and numerical simulations are then employed to evaluate the thermal noise limits, intensity noise, and resonant stabilities of Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes in a 5 cm space-borne prototype cavity. Our results show that symmetric HG and LG modes outperform the fundamental mode in suppressing both thermal noise and optical intensity noise, with the HG₃₃ mode reducing the thermal noise limit by 33.0% (from 10.0 to 6.7Hz/Hz at 1 mHz). Finally, we analyze the impact of alignment errors between the cavity and external optics on the PDH error signal and establish quantitative alignment tolerance requirements to preserve mode purity. These findings demonstrate that HG₃₃ offers a practical balance between noise reduction, stability, and implementation feasibility for compact, space-deployable ultrastable laser systems.