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arXiv:2312.05701 · Optics Letters

Optical transmission of a moving Fabry–Perot interferometer

Nazar Pyvovar, Lingze Duan

Published Dec 6, 2023• 4 citations
arXivHTMLPDF

Abstract

Fabry-Perot interferometers have been widely studied and used for well over a century. However, they have always been treated as stationary devices in the past. In this Letter, we investigate the optical transmission of a longitudinally moving Fabry-Perot interferometer within the framework of relativity and establish a general relation between the transmission coefficient and the velocity for uniform motions. Several features of the transmission spectrum are analyzed, with special attentions given to the non-relativistic regime, where application prospects are evaluated. New, to the best of our knowledge, potential interferometric schemes, such as velocity-scanning interferometry and hybrid interferometers based on nested configurations, are proposed. Finally, a special case of non-uniform motion is also investigated.

DOI
10.1364/ol.505622

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Fabry-Perot interferometers have been widely studied and used for well over a century. However, they have always been treated as stationary devices in the past. In this Letter, we investigate the optical transmission of a longitudinally moving Fabry-Perot interferometer within the framework of relativity and establish a general relation between the transmission coefficient and the velocity for uniform motions. Several features of the transmission spectrum are analyzed, with special attentions given to the non-relativistic regime, where application prospects are evaluated. New, to the best of our knowledge, potential interferometric schemes, such as velocity-scanning interferometry and hybrid interferometers based on nested configurations, are proposed. Finally, a special case of non-uniform motion is also investigated.
In the first part the author reviews the classical theory of the Fabry Perot interferometer that is applicable when the interferometer is illuminated by a light beam of coherent vibrations having long duration. In the second part, he studies how a pulse of square form is transmitted through a Fabry Perot interferometer. The two parameters of duration τ and τ' that characterize the instrument were defined. τ represents the duration of light path for a forward and backward motion between the two plates and τ' characterises the duration of the exponential attenuation of the beam due to the successive multiple reflections it suffers. In the case of the pulse having duration Θ 0 > τ the emergent vibrations superpose progressively and the profile of intensity of the output pulse as a function of time is calculated. In case when Θ 0 < τ the successive separated pulses do not overlap. The Fourier analysis of the signal received by a detector has been discussed in this case. In part III, the analogy between the spectrum of the signal and the optical spectrum of the Fabry Perot has been shown. In part IV, the profile of the light reflected by the Febry Perot receiving a light pulse, in the time domain, has been established and in part V the balance of light energy stored in the Fabry Perot has been established.
Recent progress in atom optics has culminated in several demonstrations of atom interferometers. These rely on the passage of atoms through mechanical or light gratings and may be roughly characterized as Mach–Zehnder interferometers. In this communication, we propose a scheme to realize a Fabry–Perot interferometer for atoms. The mirrors are realized by the field gradient resulting from the spatial mode structure in optical or microwave cavities. When ultra- cold atoms impinge on such cavities, they experience quantum mechanical reflection and transmission that result in the appearance of longitudinal modes for the atomic wave function. We present a model of such a Fabry–Perot interferometer for two-level atoms. We discuss the intra-cavity matter–wave mode structure as well as the transmittivity and reflectivity characteristics of the interferometer. The potential generation of macroscopic quantum waves using such a device, as well as its potential as a sensitive photon detector, will be addressed.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
In the optical masers realized so far a Perot-Fabry device is used as a multimode cavity. It may be interesting to investigate the general properties of such a device when the emitting or the absorbing atoms are put inside the reflecting mirrors. Even in the case when this device works below the threshold of maser action it shows remarkable properties which are worthwhile studying experimentally. The following aspects are considered in the paper: In the case of external illumination, the distribution of light intensity inside a Perot-Fabry interferometer is calculated. It is shown that the local light intensity in the stationary waves inside can be much higher than the intensity of the incident light beam. The properties of light emitted by atoms inside the Perot-Fabry and emerging from it are investigated. Narrow fringes of very strong intensity can be obtained. If the emitting atoms are located in an atomic beam the central fringe has natural line width, the Doppler broadening being suppressed. The realization of a fluorescent medium of lamellar structure is discussed. This structure favors one special mode of emission fringes. Finally, the absorption of atoms inside the interferometer is studied. It is shown that this device is equivalent to a long absorption path in an ordinary light beam.
Specific features of the light-beam transverse structure transformation in the process of four-wave coupling in the Fabry-Perot interferometer with a resonant nonlinearity under conditions of bifurcation of the symmetry breaking and optical bistability are analyzed. The asymmetric regimes of the interaction, characterized by a difference both in the integrated transmission functions of the nonlinear interferometer for two light beams with equal intensities and in the spatial intensity distribution at the exit of the interferometer, are considered.