Generalized method for seeking q-preserving configurations of multi-pass cells

Area of Science:

• Optics and Photonics
• Optical Engineering
• Laser Physics

Background:

• Multi-pass cells (MPCs) are crucial for extending light path lengths in optical systems.
• Traditional methods using 2x2 matrices are limited by astigmatism.
• Maintaining Gaussian beam quality (q-parameter preservation) is essential for many applications.

Purpose of the Study:

• To develop a robust method for finding q-preserving MPC configurations.
• To extend the analysis of MPCs to systems with astigmatism using 4x4 matrices.
• To identify optimal MPC designs with minimal deviation from ideal q-preserving properties.

Main Methods:

• Utilizing 4x4 transfer matrices to model MPCs, accounting for astigmatism.
• Employing the Frobenius norm (F-norm) to quantify the deviation of the transfer matrix from the identity matrix.
• Analyzing q-preserving configurations in four-objective multi-pass matrix systems (FO-MMS) and double-row circular MPCs (DR-CMPC).

Main Results:

• The method successfully identified optimal q-preserving structures for FO-MMS and DR-CMPC.
• Achieved minimal matrix deviations of 0.0047 for FO-MMS and 0.0051 for DR-CMPC.
• The optimal DR-CMPC design offers a significantly smaller deviation (three orders of magnitude) compared to traditional MPCs with similar spherical reflectors.

Conclusions:

• The 4x4 transfer matrix method provides an effective approach for designing astigmatism-tolerant q-preserving MPCs.
• Optimal configurations were found for specific MPC types, balancing optical path length and beam quality preservation.
• This method advances the design of high-performance optical resonators and beam delivery systems.