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

Year: 2026

Authors: Lorenzi F., Pelizzo M.G., Salasnich L.

Autors Affiliation: Univ Padua, Dipartimento Ingn Informaz, Via Gradenigo 6A, I-35131 Padua, Italy; Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, Ctr Ateneo Studi & Attiv Spaziali, Viale Venezia1, I-35131 Padua, Italy; Sez Padova, Ist Nazl Fis Nucl INFN, Via Marzolo 8, I-35131 Padua, Italy; CNR, Ist Foton & Nanotecnol, Via Trasea 7, I-35131 Padua, Italy; Univ Padua, Padua QTech Ctr, Via Gradenigo 6A, I-35131 Padua, Italy; Consiglio Nazl Ric CNR, Ist Nazl Ott INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

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.

Journal/Review: JOURNAL OF PHYSICS-PHOTONICS

Volume: 8 (1)      Pages from: 15023-1  to: 15023-15

More Information: M G P acknowledges Progetto Space-it Up!, Bando (Prot. CI-2022-DSR-042) per le ’Attivita spaziali’ (tematica 15), MUR n. 341 del 15/03/2022.
KeyWords: optomechanics; special relativity; optical cavity; laser propulsion
DOI: 10.1088/2515-7647/ae271c