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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

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Optical axis perturbation in folded planar ring resonators.

Jie Yuan¹, Xingwu Long, Bin Zhang

¹Department of Optoelectronic Engineering, College of Optoelectronic Science and Engineering, National University of Defence Technology, Changsha 410073, China. jieyuan@nudt.edu.cn

|September 7, 2007

Summary

A mathematical model analyzes planar ring resonators for laser gyroscopes. Longer mirror radii increase decentration sensitivity but decrease tilt sensitivity, offering insights for cavity design and alignment.

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Area of Science:

Optics and Photonics
Optical Engineering
Laser Technology

Background:

Planar ring resonators are crucial components in ring laser gyroscopes.
Understanding optical axis perturbation is vital for resonator performance and stability.
Existing models may not fully capture the nuances of different resonator geometries.

Purpose of the Study:

To establish a comprehensive mathematical model for four-sided folded planar ring resonators.
To analyze optical axis perturbation (decentration and tilt) in various resonator configurations.
To investigate the impact of design parameters like incident angle and side ratio on resonator sensitivity.

Main Methods:

Development of an extended matrix formulation for resonator analysis.
Modification of the model to represent triangular, square, and four-sided folded ring resonators.
Detailed analysis of optical axis decentration and tilt based on geometric parameters.

Main Results:

Longer mirror radii correlate with larger mode volumes, higher optical axis decentration sensitivity, and lower optical axis tilt sensitivity.
A conventional ratio of 1:[cos(Ai)]^2 describes mirror misalignment effects at symmetrical points.
Optical axis tilt sensitivity exhibits singular behavior at the edge of the second stable region, particularly for small incident angles (e.g., 15 degrees).

Conclusions:

The established model provides a versatile framework for analyzing diverse planar ring resonator designs.
Findings offer critical insights into the relationship between resonator geometry, mirror characteristics, and optical axis stability.
The study highlights the importance of considering singular behaviors in optical axis tilt sensitivity for optimal cavity design and alignment in ring laser gyroscopes.