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arXiv · 2601.01635

Variational treatment of the electromagnetic field in an optical cavity with a moving mirror

Francesco Lorenzi·Maria Guglielmina Pelizzo·Luca Salasnich
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Abstract

Optical cavities with moving mirrors provide a versatile platform for exploring radiation-matter interactions and optically mediated mechanical effects, whose control has wide technological implications. However, capturing the coupled dynamics of the electromagnetic field and of the mirror within a consistent theoretical framework remains challenging. We analyze the problem of the coupling between classical electromagnetic fields in a cavity and a movable mirror, considering both nonrelativistic and relativistic regimes of motion. Starting from the equations of motion for a mirror subject to a generic external potential, we provide a variational formulation of the mirror-radiation interaction. Within this framework, a single-mode variational approximation is introduced, which captures the essential dynamical features of the coupled system. In the special case of a mirror undergoing free motion, the variational method yields an exact solution. This unified treatment highlights the connection between different dynamical regimes and provides a basis for analyzing applications ranging from precision interferometry to relativistic radiation-pressure effects.

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Francesco Lorenzi, Maria Guglielmina Pelizzo, Luca Salasnich. 2026-01-04. Variational treatment of the electromagnetic field in an optical cavity with a moving mirror. https://doi.org/10.1088/2515-7647%2Fae271c

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