Eigenmodes of misaligned unstable optical resonators with circular mirrors.

Area of Science:

• Optical physics
• Resonator optics
• Computational physics

Background:

• Unstable optical resonators are crucial for high-power lasers.
• Tilted mirrors introduce misalignment, complicating mode analysis.
• Accurate computation of transverse eigenmodes is essential for resonator design.

Purpose of the Study:

• To develop a numerical method for computing diffractive transverse eigenmodes in unstable optical cavities with tilted mirrors.
• To validate the convergence and accuracy of the proposed expansion method.
• To investigate the effects of mirror tilt on resonator modes.

Main Methods:

• Expansion of misaligned cavity eigenmodes in terms of aligned cavity eigenmodes.
• Utilizing the biorthogonality property of aligned eigenmodes to determine expansion coefficients.
• Numerical simulations for circular mirror resonators with hard-edge and graded reflectivity mirrors.

Main Results:

• The series expansion method converges for misaligned modes.
• Computed eigenvalues closely match results from the Prony method.
• Insights into the impact of mirror tilt on resonator modes were gained.

Conclusions:

• The modal expansion method provides an accurate and efficient way to compute eigenmodes in tilted unstable resonators.
• This approach offers a valuable tool for analyzing and designing optical resonators with misaligned components.
• The study highlights the importance of considering mirror tilt in resonator mode analysis.