Inverse solving the Schrödinger equation for precision alignment of a microcavity
- URL: http://arxiv.org/abs/2404.07760v1
- Date: Thu, 11 Apr 2024 14:03:01 GMT
- Title: Inverse solving the Schrödinger equation for precision alignment of a microcavity
- Authors: Charlie Mattschas, Marius Puplauskis, Chris Toebes, Violetta Sharoglazova, Jan Klaers,
- Abstract summary: We apply solution strategies for inverse problems to determine and control the relative orientation of two mirrors forming an optical microcavity.
Our approach employs the inversion of the Schr"odinger equation to reconstruct the effective potential landscape.
Our method consistently achieves an angle resolution of order 100 nanoradians per measurement.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: In paraxial approximation, the electromagnetic eigenmodes inside an optical microresonator can be derived from a Schr\"odinger-type eigenvalue problem. In this framework, tilting the cavity mirrors effectively introduces a linear potential to the system. In our work, we apply solution strategies for inverse problems to precisely determine and control the relative orientation of two mirrors forming an optical microcavity. Our approach employs the inversion of the Schr\"odinger equation to reconstruct the effective potential landscape, and thus mirror tilts, from observed mode patterns. We investigate regularization techniques to address the ill-posed nature of inverse problems and to improve the stability of solutions. Our method consistently achieves an angle resolution of order 100 nanoradians per measurement.
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