Optical cavities with both optimized resonant conditions and high quality factors are important metrological tools. In particular, they are used for laser gravitational wave (GW) detectors. It is necessary to suppress the parametric instability by damping the resonant conditions of harmful higher order optical modes (HOOM) in order to have high cavity powers in GW detectors. This can be achieved effectively by using non spherical mirrors in symmetric Fabry-Perot (FP) cavities by increasing roundtrip losses of HOOMs. Fabry-Perot cavities in most of the GW detectors have non-identical mirrors to optimize clipping losses and reduce thermal noise by reducing the beam size on one side of the cavity facing to the beam splitter and recycling cavities. We here present a general method to design non spherical non-identical mirrors in non-symmetric FP cavities to damp HOOMs. The proposed design allows to the suppress the loss of the arm power caused by point absorbers on test masses.
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 dual-pass differential Fabry-Perot interferometer (DPDFPI) is one candidate of the interferometer configurations utilized in future Fabry-Perot type space gravitational wave antennas, such as Deci-hertz Interferometer Gravitational Wave Observatory. In this paper, the working principle of the DPDFPI has been investigated and necessity to adjust the absolute length of the cavity for the operation of the DPDFPI has been found. In addition, using the 55-cm-long prototype, the operation of the DPDFPI has been demonstrated for the first time and it has been confirmed that the adjustment of the ab…
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…
The Doppler effect in Fabry-Perot cavities with suspended mirrors is analyzed. Intrinsically small, the Doppler shift accumulates in the cavity and becomes comparable to or greater than the line-width of the cavity if its finesse is high or its length is large. As a result, damped oscillations of the cavity field occur when one of the mirrors passes a resonance position. A formula for this transient is derived. It is shown that the frequency of the oscillations is equal to the accumulated Doppler shift and the relaxation time of the oscillations is equal to the storage time of the cavity. Comp…
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 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.
Optical resonators are one of the most promising optical devices for manufacturing high-performance pressure sensors for photoacoustic imaging. Among these, Fabry-Pérot (FP) based pressure sensors have been successfully used for a multitude of applications. However, critical performance aspects of FP based pressure sensors have not been extensively studied, including the effects system parameters such as beam diameter and cavity misalignment have on transfer function shape. Here, we discuss the possible origins of the transfer function asymmetry, the impact it has on measurement sensitivity as…
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 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.
The achievable instrument sensitivity is a critical parameter for the continued development of THz applications. Techniques such as Cavity-Enhanced Techniques and Cavity Ring Down Spectroscopy have not yet been employed at THz frequency due to the difficulties to construct a high finesse Fabry-Pérot cavity. Here, we describe such a THz resonator based on a low-loss oversized corrugated waveguide with highly reflective photonic mirrors obtaining a finesse above 3000 around 620 GHz. These components enable a Fabry-Perot THz Absorption Spectrometer with an equivalent interaction length of one kil…
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.
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.
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…
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.
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.
We demonstrate the elements of a coupled-resonator optical waveguide in a side-coupled Fabry-Pérot configuration, and show that the coupling rate between adjacent waveguides can be widely tuned through the thermo-optic effect. The device is linearly scalable and can be combined with other integrated devices, with applications as an optical delay line or as a key element in a cavity-QED based quantum simulator.
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.
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…
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.
Challenging optical resonant gain achieved via the use of two geometrically modematched Fabry-Perot cavities is anticipated in Any Light Particle Search II (ALPS II) to extend the search sensitivity of light-weight sub-eV dark matter candidates to uncharted parameter space of scientific interest. We report on the precision optomechanics developed for geometrical modematching of optical cavities. The general concept, the mechanical mounting scheme, and the use of an autocollimator to streamline the metrology procedure are rigorously examined using optical interferometry, all of which meet the r…
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 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.
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…
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.
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.
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…
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 …
We demonstrate a compact 29.3 GHz visible astro-comb covering the spectrum from 560nm to 700nm. A 837 MHz Yb:fiber laser frequency comb phase locked to a Rb clock served as the seed comb to ensure the frequency stability and high side mode suppression ratio. After the visible super-continuum generation, a cavity-length-fixed Fabry-Perot cavity made by ultra-low expansion glass was utilized to filter the comb teeth for eliminating the rapid active dithering. The mirrors were home-made complementary chirped mirrors pair with zero dispersion and high reflection to guarantee no mode skipping. Thes…
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.
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 here present an investigation of the ringing effect observed on the VIRGO mode-cleaner prototype MC30. The results of a numerical calculation show how a simple empirical formula can determine the cavity expansion rate from the oscillatory behavior. We also show how the simulation output can be adjusted to estimate the finesse value of the suspended cavity.
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…
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.
In recent years quantum phenomena have been experimentally demonstrated on variety of optomechanical systems ranging from micro-oscillators to photonic crystals. Since single photon couplings are quite small, most experimental approaches rely on the realization of high finesse Fabry-Perot cavities in order to enhance the effective coupling. Here we show that by exploiting a, long path, low finesse fiber Fabry-Perot interferometer ground state cooling can be achieved. We model a 100 m long cavity with a finesse of 10 and analyze the impact of additional noise sources arising from the fiber. As …
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.
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…
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 …
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 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 …
Optical nanofiber cavity research has mainly focused on the fundamental mode. Here, a Fabry-Pérot fiber cavity with an optical nanofiber supporting the higher-order modes, TE01, TM01, HE21o, and HE21e, is demonstrated. Using cavity spectroscopy, with mode imaging and analysis, we observe cavity resonances that exhibit complex, inhomogeneous states of polarization with topological features containing Stokes singularities such as C-points, Poincaré vortices, and L-lines. In situ tuning of the intracavity birefringence enables the desired profile and polarization of the cavity mode to be obtained…
We introduce the use of Fabry-Perot (FP) lasers as potential neuromorphic computing machines with parallel processing capabilities. With the use of optical injection between a master FP laser and a slave FP laser under feedback we demonstrate the potential for scaling up the processing power at longitudinal mode granularity and perform real-time processing for signal equalization in 25 Gbaud intensity modulation direct detection optical communication systems. We demonstrate the improvement of classification performance as the number of nodes increases and the capability of simultaneous process…
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…
