The complex reflected and transmitted amplitudes from a Fabry-Perot interferometer are analyzed using a phase-space approach, in which the real and imaginary parts of those amplitudes are taken as basic variables. As functions of the optical path length of the cavity, the reflected amplitude describes a circle, whereas the transmitted is given by a hippopede. The system performance can be directly related to the geometrical parameters of these curves.
We discuss the parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are deduced. The results are compared with the results for gravita- tional wave interferometers LIGO and LIGO Voyager.
In this paper we revisited the theory of selective reflection from a dilute vapor cell. A self-consistent theory was developed for reflection spectrum for Fabry-Perot interferometer. Formulas for single and multiple reflections were obtained. We also obtained the effective refractive index for a single selective reflection. The results of the paper are in a good agreement with existing experimental results.
The use of negative index materials is highly efficient for tayloring the spectral dispersion properties of a quarter-wavelength Bragg mirror and for obtaining a resonant behavior of a multilayer Fabry-Perot cavity over a very large spectral range. An optimization method is proposed and validated on some first promising devices.
We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anticaustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit.
An anisotropic photonic crystal containing two anisotropic defect layers is considered. It is demonstrated that the system under can support a Fabry-Perot bound state in the continuum (FP-BIC). A fully analytic solution of the scattering problem as well as a condition for FP-BIC have been derived in the framework of the temporal coupled-mode theory.
A Mach-Zehnder interferometer with absorbing Fabry-Pérot cavities is used to measure the optical phase differences upon rotation around a vertical axis. The details of the expected experimental results are described based on the idea that a conducting medium can introduce phase differences due to changes in material conductivity that are expected to occur when a medium moves with respect to a reference frame. Experimental details and results are discussed.
A class of multiwavelength Fabry-Perot lasers is introduced where the spectrum is tailored through a non-periodic patterning of the cavity effective index. The cavity geometry is obtained using an inverse scattering approach and can be designed such that the spacing of discrete Fabry-Perot lasing modes is limited only by the bandwidth of the inverted gain medium. A specific two-color semiconductor laser with a mode spacing in the THz regime is designed, and measurements are presented demonstrating the simultaneous oscillation of the two wavelengths. The extension of the Fabry-Perot laser conce…
We report the first observation of a nonlinear mode in a cylindrical nonlinear Fabry-Perot cavity. The field enhancement from cavity buildup, as well as the large chi3 optical nonlinearity due to resonantly-excited Rb-85 vapor, allows the nonlinear mode to form at low incident optical powers of less than a milliwatt. The mode is observed to occur for both the self-focusing and self-defocusing nonlinearity.
The method of images, when applied to an opto-mechanical Fabry-Perot resonator with a heavy, charged mirror, and a light, charged mirror that can be driven into motion, reveals that the highest order images can move relativistically when the Q of the superconducting resonator is on the order of 10^10. The implications of such relativistic motions of the charge and mass of these images to the emission of electromagnetic and gravitational radiation within the resonator is explored.
In this paper we present a theoretical and experimental study of the dynamical behaviour of birefringent cavities. Our experimental data show that usual hypothesis which provides that a Fabry-Perot cavity is a first-order low pass filter cannot explain the behaviour of a birefringent cavity. We explain this phenomenon, and give the theoretical expression of the equivalent cavity filter which corresponds to a second-order low pass filter.
We demonstrate passive harmonic mode-locking of a quantum well laser diode designed to support a discrete comb of Fabry-Perot modes. Spectral filtering of the mode spectrum was achieved using a non-periodic patterning of the cavity effective index. By selecting six modes spaced at twice the fundamental mode spacing, near-transform limited pulsed output with 2 ps pulse duration was obtained at a repetition rate of 100 GHz.
The dynamics of light in Fabry-Perot cavities with varying length and input laser frequency are analyzed and the exact condition for resonance is derived. This dynamic resonance depends on the light transit time in the cavity and the Doppler effect due to the mirror motions. The response of the cavity to length variations is very different from its response to laser frequency variations. If the frequency of these variations is equal to multiples of the cavity free spectral range, the response to length is maximized while the response to the laser frequency is zero. Implications of these result…
We analyze an optical 3-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3 orders of diffraction are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input output relations of a 3-port grating coupled cavity and find distinct properties not present in 2-port coupled cavities. The cavity relations further reveal that the 3-port coupler can be designed such that the additional cavity port interferes destructively. In this case the all-reflective, low-loss…
Various four-mirror optical resonators are studied in the perspective of realizing passive stacking cavities. A comparative study of the mechanical stability is provided. The polarization properties of the cavity eigenmodes are described and it is shown that the effect of mirror misalignments (or motions) induces polarization and stacking power instabilities. These instabilities increase with the finesse of the Fabry-Perot cavity. A tetrahedral configuration of the four mirrors is found to minimize the consequences of the mirrors's motion and misalignment by reducing the instability parameter …
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the complete first-order corrections in the short-wavelength limit to eigenmodes and eigenfrequencies in a Fabry-Perot resonator with perfectly conducting mirrors. Experimentally relevant effects are predicted. Modes which are degenerate according to the paraxial approximation are split according to their total angular momentum. This includes a splitting due to co…
We propose to take advantage of the properties of long Josephson junctions to realize a frequency variable Fabry-Perot Filter that operates in the range 100-500 GHz with a bandwidth below 1 GHz. In fact, we show that it is possible to exploit the tunability of the effective impedance of the Josephson component, that is controlled by a dc bias, to tune, up to $10\%$ of the central frequency, the resonance of the system. An analysis of the linearized system indicates the range of operation and the main characteristic parameters Numerical simulations of the full nonlinear Josephson element confir…
A key issue in developing pendular Fabry-Perot interferometers as very accurate displacement measurement devices, is the noise level. The Fabry-Perot pendulums are the most promising device to detect gravitational waves, and therefore the background and the internal noise should be accurately measured and reduced. In fact terminal masses generates additional internal noise mainly due to thermal fluctuations and vibrations. We propose to exploit the reflectivity change, that occurs in some special points, to monitor the pendulums free oscillations and possibly estimate the noise level. We find …
A temporal boundary refers to a specific time at which the properties of an optical medium are abruptly changed. When light interacts with the temporal boundary, its spectral content can be redistributed due to the breaking of continuous time-translational symmetry of the medium where light resides. In this work, we use this principle to demonstrate, at terahertz (THz) frequencies, the resonance-enhanced spectral funneling of light coupled to a Fabry-Perot resonator with a temporal boundary mirror. To produce a temporal boundary effect, we abruptly increase the reflectance of a mirror constitu…
Symmetry-Broken Cavity Solitons and Collective Polarization Conformity in Fabry-Perot Kerr Resonators
Université Bourgogne Europe（勃艮第欧洲大学）；CNRS（法国国家科学研究中心）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich Alexander University Erlangen-Nuremberg（埃尔兰根-纽伦堡弗里德里希·阿历山大大学）；Alexandria University（亚历山大大学）；Huazhong University of Science and Technology（华中科技大学）；University of Strathclyde（思克莱德大学）；The University of Auckland（奥克兰大学）
The factors limiting the resolution of displacement sensor based on extrinsic Fabry-Perot interferometer were studied. An analytical model giving the dependency of EFPI resolution on the parameters of an optical setup and a sensor interrogator was developed. The proposed model enables one to either estimate the limit of possible resolution achievable with a given setup, or to derive the requirements for optical elements and/or a sensor interrogator necessary for attaining the desired sensor resolution. An experiment supporting the analytical derivations was performed, demonstrating a large dyn…
Factors that contribute to the temperature dependence of a resonant frequency in a low-expansion optical cavity are discussed, including deformation at the cavity ends due to different coefficients of thermal expansion (CTE) of the spacer, optically-contacted mirror substrate and coating. A model of the temperature dependence is presented that incorporates finite-element-analysis of the cavity ends. A measurement of frequency versus temperature of a cavity mode is used along with the model to deduce a spacers CTE versus temperature profile. The measured profile correlates very well with a sepa…
In this letter, we demonstrate for the first time that by combining the effects of the Wood-Rayleigh Anomaly (WRA) and the Fabry-Perot (FP) resonance, transmission efficiencies of $1$D metallo-dielectric gratings on substrates can be significantly improved compared to when these two phenomena work separately. Results of combining the WRA and the FP resonance can be utilized to eliminate the necessity of using the index matching technique and the core-shell structure for enhancing the performance of extraordinary optical transmission devices. Further, the outcomes of combining the WRA and the F…
We measured the far-field emission patterns in three dimensions of flat organic dye microlasers using a solid angle scanner. Polymer-based microcavities of ribbon shape (i.e., Fabry-Perot type) were investigated. Out of plane emission from the cavities was observed, with significant differences for the two cases of resonators either fully supported by the substrate or sustained by a pedestal. In both cases, the emission diagrams are accounted for by a model combining diffraction at the cavity edges and reflections from the substrate.
Free-running Fabry-Perot lasers normally operate in a single-mode regime until the pumping current is increased beyond the single-mode instability threshold, above which they evolve into a multimode state. As a result of this instability, the single-mode operation of these lasers is typically constrained to few percents of their output power range, this being an undesired limitation in spectroscopy applications. In order to expand the span of single-mode operation, we use an optical injection seed generated by an external-cavity single-mode laser source to force the Fabry-Perot quantum cascade…
We present a method to engineer the frequency splitting of polarization eigenmodes in fiber Fabry-Perot (FFP) cavities. Using specific pattern of multiple CO$_2$ laser pulses, we machine paraboloidal micromirrors with controlled elliptical shape in a large range of radius of curvature. This method is versatile and can be used to produce cavities with maximized or near-zero polarization mode splitting. In addition, we realize dual-wavelength FFP cavities with finesse exceeding $40\,000$ at 780$\,$nm and at 1559$\,$nm in the telecom range. We provide direct evidence that the birefringent frequen…
We perform a theoretical study of finesse limitations of a Fabry-Perot (FP) cavity occurring due to finite size, asymmetry, as well as imperfections of the cavity mirrors. A method of numerical simulations of the eigenvalue problem applicable for both the fundamental and high order cavity modes is suggested. Using this technique we find spatial profile of the modes and their round-trip diffraction loss. The results of the numerical simulations and analytical calculations are nearly identical when we consider a conventional FP cavity. The proposed numerical technique has much broader applicabil…
High finesse Fabry-Perot(FP) cavity is a very important frequency reference for laser stabiliza- tion, and is widely used for applications such as precision measurement, laser cooling of ions or molecules. But the non-linear response of the piezoelectric ceramic transducer (PZT) in the FP cav- ity limits the performance of the laser stabilization. Measuring and controlling such non-linearity are important. Here we report an in-situ, optical method to characterize this non-linearity by measuring the resonance signals of a dual-frequency laser. The differential measurement makes it insensitive t…
We address the response, both in amplitude and intensity, of a Fabry-Perot from a variety of viewpoints. These complementary pictures conspire to achieve a comprehensive and consistent theory of the operation of this system.
A spherical Fabry-Perot interferometer with adjustable mirror spacing is used to produce interference fringes with frequency separation (c/2L)/N, N=2-15. The conditions for observation of these fringes are derived from the consideration of the eigenmodes of the cavity with high transverse indices.
One way of optically monitoring molecule concentrations is to utilise the high sensitivity of the transmission and reflection rates of Fabry-Perot cavities to changes of their optical properties. Up to now, intrinsic and extrinsic Fabry-Perot cavity sensors have been considered with analytes either being placed inside the resonator or coupled to evanescent fields on the outside. Here we show that Fabry-Perot cavities can also be used to monitor molecule concentrations non-invasively and remotely, since the reflection of light from the target molecules back into the Fabry-Perot cavity adds upwa…
We present a general and useful method to predict the existence, frequency, and spatial properties of gap states in photonic (and other) structures with a gapped spectrum. This method is established using the scattering approach. It offers a viewpoint based on a geometrical Fabry-Perot model. We demonstrate the capabilities of this model by predicting the behaviour of topological edge states in quasi-periodic structures. A proposition to use this model in Casimir physics is presented.
In this paper we describe a Fabry-Perot interferometer in the language of quantum optics. We go on to model the Fabry-Perot interferometer as a beam splitter having frequency dependent transmissivity and reflectivity coefficients. The antibunching, a totally non-classical effect, is to be expected if one excites this interferometer with carefully frequency-selected single photons arriving simultaneously from opposite directions. Contrary to a normal beam splitter, even slightly different frequency single photons should be able to show this effect, as long as the photon counters are not frequen…
This document records the results of a comparison of the interferometer simulation Finesse against an analytic (MATLAB based) calculation of the alignment sensing signals of a Fabry Perot cavity. This task was started during the commissioning workshop at the LIGO Livingston site between the 28.1. and 1.02 2013 with the aim of creating a reference example for validating numerical simulation tools. The FFT based simulation OSCAR joined the battle later.
Optical Fabry-Perot cavities always show a non-degeneracy of two orthogonal polarisation states. This is due to the unavoidable birefringence of dielectric mirrors whose effects are extremely important in Fabry-Perot based high-accuracy polarimeters. We have developed and present here a theory of the polarisation state dynamics in a birefringent Fabry-Perot resonator, and we validate it through measurements performed with the polarimeter of the PVLAS experiment. The measurements are performed while a laser is frequency-locked to the cavity, and provide values for the finesse of the cavity and …
We propose a novel photonic structure composed of metal nanolayer, Bragg mirror and metal nanolayer. The structure supports resonances that are transitional between Fabry-Perot and Tamm modes. When the dielectric contrast of the DBR is removed these modes are a pair of conventional Fabry-Perot resonances. They spectrally merge into a Tamm mode at high contrast. Such behavior differs from the results for structures supporting Tamm modes reported earlier. The optical properties of the structure in the frequency range of the DBR stop band, including highly beneficial 50% transmittivity through th…
We present a method for remote interrogation of passive fiber Bragg grating Fabry-Perot resonators, employing current modulation of the diode laser source. With the presence of both RF amplitude and frequency modulation, it is a variant of the ultra-sensitive Pound-Drever-Hall laser frequency locking technique. We demonstrate that current modulation and interferometric demodulation removes the need for a phase modulator in the sensing architecture.
We present the first demonstration of real-time closed-loop control and deterministic tuning of an independently suspended Fabry-Perot optical cavity using digitally-enhanced heterodyne interferometry, realising a peak sensitivity of $\sim$10 pm$/\sqrt{\mathrm{Hz}}$ over the 10-1000 Hz frequency band. The methods presented are readily extensible to multiple coupled cavities. As such, we anticipate that refinements of this technique may find application in future interferometric gravitational-wave detectors.
The dynamical response of an optical Fabry-Perot cavity is investigated experimentally. We observe oscillations in the transmitted and reflected light intensity if the frequency of the incoupled light field is rapidly changed. In addition, the decay of a cavity-stored light field is accelerated if the phase and intensity of the incoupled light are switched in an appropriate way. The theoretical model by M. J. Lawrence em et al, JOSA B 16, 523 (1999) agrees with our observations.
Fabry-Perot interferometers have stimulated numerous scientific and technical applications ranging from high resolution spectroscopy over metrology, optical filters to interfaces of light and matter at the quantum limit and more. End facet machining of optical fibers has enabled the miniaturization of optical Fabry-Perot cavities. Integration with fiber wave guide technology allows for small yet open devices with favorable scaling properties including mechanical stability and compact mode geometry. These Fiber Fabry-Perot Cavities (FFPCs) are stimulating extended applications in many fields in…
The scattering of weak dispersive waves (DW) on several equally spaced temporal solitons is studied. It is shown by systematic numerical simulations that the reflection of the DWs from the soliton trains strongly depends on the distance between the solitons. The dependence of the reflection and transmission coefficients on the inter-soliton distance and the frequency of the incident waves is studied in detail, revealing fascinating quasi-periodic behavior. The analogy between the observed nonlinear phenomena in temporal domain and usual Fabry-Perot and Bragg resonators is discussed.
We study a dispersion-compensated high-finesse optical Fabry-Perot microcavity under high-intensity cw pumping. The Kerr non-linearity in the optical coatings causes a spontaneous four-wave mixing process, which leads to the emission of time-correlated photon pairs. The photon frequencies are shifted by $\pm 1$ free spectral range relative to the pump frequency. This setup allows for constructing a photon-pair source with precisely adjustable frequency difference between the emitted photons, which may have applications in quantum communication.
Absorbing metamaterials have attracted a widespread interest but suffer from the metallic ohmic losses that limits their Q-factor to values around 10. In this paper, we report the engineering and experimental characterization of a high Q dark-mode in a metasurface resulting from the coupling of several individual nano-Fabry-Perot structures supporting low-contrast resonances. The resulting resonance has a Q-factor above 20 and a nearly total absorption. Moreover, we also demonstrate that several dark-mode resonances can be excited simultaneously, by exploiting the coupling of various pairs of …
In this study, we theoretically and numerically investigate the resonant modes and reflectance of an optical grating consisting of a wavy dielectric slab by applying the spectral element method. The presence of the wavy shape transforms the waveguide modes into leaky resonant modes. A few resonant modes with specific longitudinal wave number have infinitely large Q factor, while the other resonant modes have finite Q factor. For the leaky resonant mode with zero longitudinal wave number, the Q factor is inversely proportional to the amplitude of the wavy shape. An array of multiple low-Q wavy …
We show that an escape from the potential minimum of Fabry-Perot interferometers can be detected measuring the associated sudden change of reflectivity. We demonstrate that the loss of information that occurs retaining only the sequence of escapes, rather than the full trajectory, can be very mild and can lead to an effective method to reveal the noise intensity or the presence of a coherent signal.
A moving pellicle superconducting mirror, which is driven by radiation pressure on its one side, and by the Coulomb force on its other side, can become a parametric oscillator that can generate microwaves when placed within a high-Q superconducting Fabry-Perot resonator system. A paraxial-wave analysis shows that the fundamental resonator eigenmode needed for parametric oscillation is the TM011 mode. A double Fabry-Perot structure is introduced to resonate the pump and the idler modes, but to reject the parasitic anti-Stokes mode. The threshold for oscillation is estimated based on the radiati…
Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A non-paraxial vector theory predicts that the frequency degeneracy within these clusters is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper, we calculate this fine structure for microcavities and show how it originates from various non-paraxial effects and is co-determined by mirror aberrations. The presented theory, which appl…
We experimentally realize a Fabry-Perot-type optical microresonator near the cesium D2 line wavelength based on a tapered optical fiber, equipped with two fiber Bragg gratings which enclose a sub-wavelength diameter waist. Owing to the very low taper losses, the finesse of the resonator reaches F = 86 while the on-resonance transmission is T = 11 %. The characteristics of our resonator fulfill the requirements of non-linear optics and cavity quantum electrodynamics in the strong coupling regime. In combination with its demonstrated ease of use and its advantageous mode geometry, it thus opens …
