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.
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 demonstrate that a proton irradiation with fluences of $3.6\times10^{10}$/cm$^{2}$ at low energy ($<$ 36 MeV) and $1.46 \times 10^{10}$/cm$^{2}$ at high energy (40 MeV and 90 MeV combined) on the dielectric mirrors of Fabry-Pérot cavities with a finesse of about 700 000 causes less than 5% change in the finesse. Furthermore, no influence on the coupling efficiency to the cavities was observed, the efficiency being approximately 70%. The irradiation was carried out with a spectrum approximating the proton energy spectrum of a highly elliptic Earth orbit with duration of 5 years, proposed for…
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…
We have realized a fiber-based Fabry-Perot cavity with CO2 laser-machined mirrors. It combines very small size, high finesse F>=130000, small waist and mode volume, and good mode matching between the fiber and cavity modes. This combination of features is a major advance for cavity quantum electrodynamics (CQED), as shown in recent CQED experiments with Bose-Einstein condensates enabled by this cavity [Y. Colombe et al., Nature 450, 272 (2007)]. It should also be suitable for a wide range of other applications, including coupling to solid-state emitters, gas detection at the single-particle le…
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…
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry-Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound-Drever-Hall locking technique is compared to a novel rigid cavity design that makes use of the hig…
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 demonstrate the fabrication of ultra-low-loss, all-fiber Fabry-Pérot cavities containing a nanofiber section, optimized for cavity quantum electrodynamics. By continuously monitoring the finesse and fiber radius during fabrication of a nanofiber between two fiber Bragg gratings, we are able to precisely evaluate taper transmission as a function of radius. The resulting cavities have an internal round-trip loss of only 0.31% at a nanofiber waist radius of 207 nm, with a total finesse of 1380, and a maximum expected internal cooperativity of $\sim$ 1050 for a cesium atom on the nanofiber surf…
The Fabry-Pérot resonator is one of the most widely used optical devices, enabling scientific and technological breakthroughs in diverse fields including cavity QED, optical clocks, precision length metrology and spectroscopy. Though resonator designs vary widely, all high-end applications benefit from mirrors with the lowest loss and highest finesse possible. Fabrication of the highest finesse mirrors relies on centuries-old mechanical polishing techniques, which offer losses at the part-per-million (ppm) level. However, no existing fabrication techniques are able to produce high finesse reso…
We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can be operated at cavity lengths as large as 1.5mm without significant deterioration of the finesse. This is achieved by using a laser dot machining technique to shape spherical mirrors with ultralow roughness and employing single-mode fibers with large mode area for good mode matching to the cavity. Additionally, in contrast to previous FFPs, these cavities can be used over an octave-spanning frequency range with adequate coatings. We also show directly that shape deviations caused by the fiber's index profile lead to …
Light scattering by a two-dimensional photonic crystal slab (PCS) can result in dramatic interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors or filters for various applications such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors, or non-linear optical components. Suspended PCSs also find natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high finesse …
A stable optical resonator has been built using a 30 micrometer-wide, metal-coated microcantilever as one mirror. The second mirror was a 12.7 mm-diameter concave dielectric mirror. By positioning the two mirrors 75 mm apart in a near-hemispherical configuration, a Fabry-Perot cavity with a finesse equal to 55 was achieved. The finesse was limited by the optical loss in the cantilever's metal coating; diffraction losses from the small mirror were negligible. The cavity achieved passive laser cooling of the cantilever's Brownian motion.
High-finesse, open-geometry microcavities have recently emerged as a versatile tool for enhancing interactions between photons and material systems, with a range of applications in quantum optics and quantum information science. However, mechanical vibrations pose a considerable challenge to their operation within a closed-cycle cryostat, particularly when spatial tunability and free-space optical access are required. Here, we present the design and characterization of a system that can achieve $\sim$16 pm-rms passive mechanical stability between two high-finesse mirrors while permitting both …
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 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.
The use of low-dimensional objects in the field of cavity optomechanics is limited by their low scattering cross section compared to the size of the optical cavity mode. Fiber-based Fabry-Pérot microcavities can feature tiny mode cross sections and still maintain a high finesse, boosting the light-matter interaction and thus enabling the sensitive detection of the displacement of minute objects. Here we present such an ultrasensitive microcavity setup with the highest finesse reported so far in loaded fiber cavities, $\mathcal{F} = 195\,000$. We are able to position-tune the static optomechani…
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…
We describe the design, construction, and characterization of a medium-finesse Fabry-Pérot cavity for simultaneous frequency stabilization of two lasers operating at 960 and 780 nm wavelengths, respectively. The lasers are applied in experiments with ultracold rubidium Rydberg atoms, for which a combined laser linewidth similar to the natural Rydberg linewidth (approximately 10 kHz) is desired. The cavity, with a finesse of approximately 1500, is used to reduce the linewidth of the lasers to below this level. By using a spacer made of ultra low expansion (ULE) glass with active temperature sta…
We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy of Laguerre-Gauss modes with distinct orbital angular momentum (OAM) and polarization, but identical transverse order N, will become observably lifted at sufficiently small size and high finesse. The resulting paraxial eigenmodes possess two distinct OAM components, the fractional composition subtly depending on mirror structure.
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 …
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 demonstrate a fiber-integrated Fabry-Pérot cavity formed by attaching a pair of dielectric metasurfaces to the ends of a hollow-core photonic-crystal fiber segment. The metasurfaces consist of perforated membranes designed as photonic-crystal slabs that act as planar mirrors but can potentially allow injection of gases through their holes into the hollow core of the fiber. We have so far observed cavities with finesse of ~11 and Q factors of ~$4.5 \times 10^5$, but much higher values should be achievable with improved fabrication procedures. We expect this device to enable development of ne…
Although experimental efforts have been active for about 30 years now, a direct laboratory observation of vacuum magnetic birefringence, an effect due to vacuum fluctuations, still needs confirmation. Indeed, the predicted birefringence of vacuum is $Δn = 4.0\times 10^{-24}$ @ 1~T. One of the key ingredients when designing a polarimeter capable of detecting such a small birefringence is a long optical path length within the magnetic field and a time dependent effect. To lengthen the optical path within the magnetic field a Fabry-Perot optical cavity is generally used with a finesse ranging fro…
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…
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…
Nearly concentric optical cavities can be used to prepare optical fields with a very small mode volume. We implement an anaclastic design of a such a cavity that significantly simplifies mode matching to the fundamental cavity mode. The cavity is shown to have diffraction-limited performance for a mode volume of $\approx10^4λ^3$. This is in sharp contrast with the behavior of cavities with plano-concave mirrors, where aberrations significantly increase the losses in the fundamental mode. We estimate the related cavity QED parameters and show that the proposed cavity design allows for strong co…
We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound-Drever-Hall feedback lock incorporating …
Lasers stabilized to vacuum-gap Fabry-Pérot optical reference cavities display extraordinarily low noise and high stability, with linewidths much less than 1 Hz. These lasers can expand into new applications and ubiquitous use with the development of compact, portable cavities that are manufacturable at scale. Here we demonstrate an 8 mL volume Fabry-Pérot cavity constructed with mirrors that are fabricated lithographically with finesse near 1 million. A laser locked to the cavity exhibits phase noise limited by the cavity thermal noise for offset frequencies ranging from 1 Hz to $\approx$ 1 k…
We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We first derive the general multimode Hamiltonian describing the radiation pressure interaction between the cavity modes and the vibrational modes of the membrane. We then restrict the analysis to the standard case of a single cavity mode interacting with a single mechanical resonator and we determine to what extent optical absorption by the membrane hinder reaching a quantum regime for the cavity-membrane system. We show that membrane absorption does n…
We demonstrate laser-written concave hemispherical structures produced on the endfacets of optical fibers that serve as mirror substrates for tunable open-access microcavities. We achieve finesse values of up to 250, and a mostly constant performance across the entire stability range. This enables cavity operation also close to the stability limit, where a peak quality factor of $1.5\times 10^4$ is reached. Together with a small mode waist of $2.3\; \mathrm{μm}$, the cavity achieves a Purcell factor of $C \sim 2.5$, which is useful for experiments that require good lateral optical access or ot…
Confining a laser field between two high reflectivity mirrors of a high-finesse cavity can increase the probability of a given cavity photon to be scattered by an atom traversing the confined photon mode. This enhanced coupling between light and atoms is successfully employed in cavity quantum electrodynamics experiments and led to a very prolific research in quantum optics. The idea of extending such experiments to sub-wavelength sized nanomechanical systems has been recently proposed in the context of optical cavity cooling. Here we present an experiment involving a single nanorod consisting…
We report on the thermomechanical and thermal tuning properties of curved-mirror Fabry-Perot resonators, fabricated by the guided assembly of circular delamination buckles within a multilayer a-Si/SiO2 stack. Analytical models for temperature dependence, effective spring constants, and mechanical mode frequencies are described and shown to be in good agreement with experimental results. The cavities exhibit mode volumes as small as $\sim10λ^3$, reflectance-limited finesse $\sim3\times10^3$, and mechanical resonance frequencies in the MHz range. Monolithic cavity arrays of this type might be of…
Vacuum magnetic birefringence was predicted long time ago and is still lacking a direct experimental confirmation. Several experimental efforts are striving to reach this goal, and the sequence of results promises a success in the next few years. This measurement generally is accompanied by the search for hypothetical light particles that couple to two photons. The PVLAS experiment employs a sensitive polarimeter based on a high finesse Fabry-Perot cavity. In this paper we report on the latest experimental results of this experiment. The data are analysed taking into account the intrinsic bire…
We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO2 laser-machined, high-finesse optical Fabry-Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections t…
We present three high finesse tunable monolithic fiber Fabry-Perot cavities (FFPCs) with high passive mechanical stability. The fiber mirrors are fixed inside slotted glass ferrules, which guarantee an inherent alignment of the resonators. An attached piezoelectric element enables fast tuning of the FFPC resonance frequency over the entire free-spectral range for two of the designs. Stable locking of the cavity resonance is achieved for feedback bandwidths as low as $20\,$mHz, demonstrating the high passive stability. At the other limit, locking bandwidths up to $27\,$kHz, close to the first m…
Open Fabry-Perot microcavities represent a promising route for achieving a quantum electrodynamics (cavity-QED) platform with diamond-based emitters. In particular, they offer the opportunity to introduce high purity, minimally fabricated material into a tunable, high quality factor optical resonator. Here, we demonstrate a fiber-based microcavity incorporating a thick (> 10 μm) diamond membrane with a finesse of 17,000, corresponding to a quality factor Q ~ $10^6$. Such minimally fabricated, thick samples can contain optically stable emitters similar to those found in bulk diamond. We observe…
Experiments were performed with Fabry-Perot optical resonators in vacuum at low temperatures. Mirrors were applied on substrates of various optical materials. The infrared laser with a wavelength of 1.064 microns was used. The pump power at the maximum could reach 450 mW. The evolution of the optical properties of the FP cavity was traced in the temperature range (300 - 10)K. The main parameters measured were the integral characteristics of the FP resonances: sharpness (finesse) and contrast of interference. Three types of substrates were tested: a sitall -- the optical glass with ultra low th…
We report on the first demonstration of a fully suspended 10m Fabry-Perot cavity incorporating a waveguide grating as the coupling mirror. The cavity was kept on resonance by reading out the length fluctuations via the Pound-Drever-Hall method and employing feedback to the laser frequency. From the achieved finesse of 790 the grating reflectivity was determined to exceed 99.2% at the laser wavelength of 1064\,nm, which is in good agreement with rigorous simulations. Our waveguide grating design was based on tantala and fused silica and included a ~20nm thin etch stop layer made of Al2O3 that a…
The coupling of mechanical oscillators with light has seen a recent surge of interest, as recent reviews report.[1, 2] This coupling is enhanced when confining light in an optical cavity where the mechanical oscillator is integrated as back- mirror or movable wall. At the nano-scale, the optomechanical coupling increases further thanks to a smaller optomechanical interaction volume and reduced mass of the mechanical oscillator. In view of realizing such cavity nano- optomechanics experiments, a scheme was proposed where a sub-wavelength sized nanomechanical oscillator is coupled to a high fine…
Earth-based gravitational-wave detectors will be limited by quantum noise in a large part of their spectrum. The most promising technique to achieve a broadband reduction of such noise is the injection of a frequency dependent squeezed vacuum state from the output port of the detector, whit the squeeze angle rotated by the reflection off a Fabry-Perot filter cavity. One of the most important parameters limiting the squeezing performance is represented by the optical losses of the filter cavity. We report here the operation of a 300 m filter cavity prototype installed at the National Astronomic…
We present a monolithic semiconductor microcavity design for enhanced light-matter interaction and photon extraction efficiency of an embedded quantum emitter such as a quantum dot or color center. The microcavity is a hemispherical Fabry-Perot design consisting of a planar back mirror and a top curved mirror. Higher order modes are suppressed in the structure by reducing the height of the curved mirror, leading to efficient photon extraction into a fundamental mode with a Gaussian far-field radiation pattern. The cavity finesse can be varied easily by changing the reflectivity of the mirrors …
When illuminated by a white light source, the discrete resonances of a Fabry-Perot interferometer (FP) provide a broad bandwidth, comb-like spectrum useful for frequency calibration. We report on the design, construction and laboratory characterization of two planar, passively stabilized, low finesse (~40) FPs spanning 380 nm to 930 nm and 780 nm to 1300 nm, with nominal free spectral ranges of 20 GHz and 30 GHz respectively. These instruments are intended to calibrate astronomical spectrographs in radial velocity searches for extrasolar planets. By tracking the frequency drift of three widely…
The third-generation gravitational wave detectors are under development by operating the detector in cryogenic temperature to reduce the thermal noise. Silicon and sapphire are promising candidate materials for the test masses and suspension elements due to their remarkable mechanical and thermal properties at cryogenic temperature. Here we present the performances of the cryogenic thermal cycling and strength testing on hydroxide catalysis bonding between sapphire and silicon. Our results suggest that although these two materials have very different coefficients of thermal expansion, but if t…
Positronium is an ideal system for the research of the bound state QED. The hyperfine splitting of positronium (Ps-HFS: about 203 GHz) is sensitive to new physics beyond the Standard Model via a vacuum oscillation between an ortho-Ps and a virtual photon. Previous experimental results of the Ps-HFS show 3.9 sigma(15 ppm) discrepancy from the QED calculation. All previous experiments used an indirect method with static magnetic field to cause Zeeman splitting (a few GHz) between triplet states of ortho-Ps, from which the HFS value was derived. One possible systematic error source of the indirec…
It is prohibitively expensive to deposit customized dielectric coatings on individual optics. One solution is to batch-coat many optics with extra dielectric layers, then remove layers from individual optics as needed. Here we present a low-cost, single-step, monitored wet etch technique for reliably removing (or partially removing) individual SiO$_2$ and Ta$_2$O$_5$ dielectric layers, in this case from a high-reflectivity fiber mirror. By immersing in acid and monitoring off-band reflected light, we show it is straightforward to iteratively (or continuously) remove six bilayers. At each stage…
We report on the optical characterization of an ultra-high diffraction efficiency grating in 1st order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high reflection mirror. Measurement of the cavity finesse provided precise information about the grating's diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635$\pm$0.016)% and an overall optical loss due to scattering and absorption of just 0.185 %. Such high quality gratings, including the …
We present a novel method for opto-mechanical cooling of sub-wavelength sized nanomechanical resonators. Our scheme uses a high finesse Fabry-Perot cavity of small mode volume, within which the nanoresonator is acting as a position-dependant perturbation by scattering. In return, the back-action induced by the cavity affects the nanoresonator dynamics and can cool its fluctuations. We investigate such cavity cooling by scattering for a nanorod structure and predict that ground-state cooling is within reach.
A high-finesse suspended mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different time scales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors which erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system.
