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Chinese Physics Letters

Time Delay Properties of a Fabry-Pérot Interferometer

Yuan Shi, Man Wei-Ning, Yu Jin, Jin-Yue Gao

Published Feb 8, 2001• 5 citations
Publisher

Abstract

The time delay properties of a Fabry-Pérot interferometer are investigated. We found that the group velocity of light through a Fabry-Pérot interferometer can be reduced to 10 -4 of the light speed in vacuum and the time delay is 210 ns, when the reflectivity is 0.999 and the distance between two mirrors is 1 cm. The system is analogous to the recently proposed one-dimensional photonic band-gap structures with a defect [Zhu et al. Opt. Commun. 174(2000)139].

DOI
10.1088/0256-307x/18/3/318

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The time delay properties of a Fabry-Pérot interferometer are investigated. We found that the group velocity of light through a Fabry-Pérot interferometer can be reduced to 10 -4 of the light speed in vacuum and the time delay is 210 ns, when the reflectivity is 0.999 and the distance between two mirrors is 1 cm. The system is analogous to the recently proposed one-dimensional photonic band-gap structures with a defect [Zhu et al. Opt. Commun. 174(2000)139].
We have theoretically investigated the time delay of a chirped light pulse,defined as the temporal difference of peaks of the output and input light pulses after transmitting a Fabry-Perot interferometer.The results show that for an interferometer of known parameters,the chirp of the light pulse makes the time delaly become intensively smaller.The mismatch between the central frequency of the light pulse and the resonance frequency of the interferometer also has an influence on the time delay.Under some circumstances,this mismatch will induce a time delay smaller than t0 that is defined as the one-way traverse time of the light inside the interferometer.
We have theoretically investigated the time delay of a chirped light pulse, defined as the temporal difference of peaks of the output and input light pulses after transmitting a Fabry-Perot interferometer. The results show that for an interferometer of known parameters, the chirp of the light pulse makes the time delay become intensively smaller. The mismatch between the central frequency of the light pulse and the resonance frequency of the interferometer also has an influence on the time delay. Under some circumstances, this mismatch will induce a time delay smaller than t0 that is defined as the one-way traverse time of the light inside the interferometer.
Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.
Extraordinary group delays shorter than the transit time of light propagating at ccc through an equal distance have been experimentally demonstrated in single-Fabry-P\'erot (FP) waveguide systems and cascaded-FP structures under off-resonant conditions. These ``superluminal'' phenomena are well explained by the multiple-reflection destructive interference that reduces the intracavity stored energy when operating off resonances. Excellent agreement between theory and experiment is obtained when the dispersive effects of reflective boundaries are considered. These results provide further insight into the nature of apparent superluminality in regions of allowed propagation.
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.