Birefringent Mirror Research Articles

Effects of mirror birefringence and its fluctuations to laser interferometric gravitational wave detectors

Effects of mirror birefringence and its fluctuations to laser interferometric gravitational wave detectors

Characterization of the Vacuum Birefringence Polarimeter at BMV: Dynamical Cavity Mirror Birefringence

We present the current status and outlook of the optical characterization of the polarimeter at the birefringence magnetique du vide (BMV) experiment. BMV is a polarimetric search for the quantum electrodynamics predicted anisotropy of vacuum in the presence of external electromagnetic fields. The main challenge faced in this fundamental test is the measurement of polarization ellipticity on the order of $ {10^{-15}}$ induced in linearly polarized laser field per pass through a magnetic field having an amplitude and length $ {B^{2}L=100~\mathrm {T}^{2}\mathrm {m}}$ . This challenge is addressed by understanding the noise sources in precision cavity-enhanced polarimetry. In this paper, we discuss the first investigation of dynamical birefringence in the signal-enhancing cavity as a result of cavity mirror motion.

Polarisation dynamics of a birefringent Fabry–Perot cavity

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 for the phase difference between the two orthogonal polarisation components introduced by the combination of the two cavity mirrors (equivalent wave-plate). The theoretical formulas and the experimental data agree well showing that the consequences of the mirror birefringence must be taken into account in this and in any other similar experiment.

Precision Interferometric Measurements of Mirror Birefringence in High-Finesse Optical Resonators.

High-finesse optical resonators found in ultrasensitive laser spectrometers utilize supermirrors ideally consisting of isotropic high-reflectivity coatings. Strictly speaking, however, the optical coatings are often non-uniformly stressed during the deposition process and therefore do possess some small amount of birefringence. When physically mounted the cavity mirrors can be additionally stressed in such a way that large optical birefringence is induced. Here we report a direct measurement of optical birefringence in a two-mirror Fabry-Pérot cavity with R = 99.99 % by observing TEM00 mode beating during cavity decays. Experiments were performed at a wavelength of 4.53 μm, with precision limited by both quantum and technical noise sources. We report a splitting of δν = 618(1) Hz, significantly less than the intrinsic cavity linewidth of δcav ≈ 3 kHz. With a cavity free spectral range of 96.9 MHz, the equivalent fractional change in mirror refractive index due to birefringence is therefore Δn/n = 6.38(1) × 10-6.

Birefringence-induced frequency beating in high-finesse cavities by continuous-wave cavity ring-down spectroscopy

By analyzing the decaying intensity, leaking out a high-finesse cavity previously ``filled'' by a cw laser source (using the cavity ring-down spectroscopy technique), we observed frequency beating between what we think are two orthogonal eigenpolarization states of the intracavity electromagnetic field. The time decay (ring down) is analyzed by varying the angle of the polarization analyzer located in front of the detector. A full modeling of the observed signal is proposed. It is based on the Jones matrix formalism required for modeling the cavity behavior following a rotated phase shifter. The full transfer function is first established in the frequency domain, and then Fourier transformed to recover the temporal response. The same optical cavity, i.e., constituted of the same set of mirrors, is used at two different wavelengths ($\ensuremath{\sim}800$ and $\ensuremath{\sim}880$ nm). It demonstrates the differences in behavior between a high-finesse cavity $(\ensuremath{\sim}400\phantom{\rule{0.16em}{0ex}}000)$ and a lower finesse cavity $(\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}000)$. Beating frequency, characteristics time, and beat amplitude are mainly discussed versus the analyzer angle. A cavity birefringence of $\ensuremath{\sim}1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ rad, resulting from the mirror birefringence is suggested. If the current analysis is in agreement with pulsed CRDS experiments (polarimetry) obtained in an isotropic moderate-finesse cavity, it differs from a recent work report on a high-finesse cavity associated with a source mode locking [Phys. Rev. A 85, 013837 (2012)].

Cavity stabilization using the weak intrinsic birefringence of dielectric mirrors

We demonstrate a universal cavity stabilization scheme that exploits the intrinsic birefringence of dielectric multilayer mirrors. Homodyne locking using weak mirror birefringence of even an empty Fabry-Perot-type cavity requires neither frequency modulation nor mixing and allows us to generate an error signal that is comparable to more widely used heterodyne stabilization schemes.

Shot-noise-limited measurement of sub–parts-per-trillion birefringence phase shift in a high-finesse cavity

We report on a promising approach to high-sensitivity anisotropy measurements using a high-finesse cavity locked by optical feedback to a diode laser. We provide a simple and effective way to decouple the weak anisotropy of interest from the inherent mirror's birefringence whose drift may be identified as the key limiting parameter in cavity-based techniques. We demonstrate a shot-noise-limited phase shift resolution previously inaccessible in an optical cavity, readily achieving the state-of-the-art level of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ rad.

Birefringence of interferential mirrors at normal incidence

In this paper we present a review of the existing data on interferential mirror birefringence. We also report new measurements of two sets of mirrors that confirm that mirror phase retardation per reflection decreases when mirror reflectivity increases. We finally developed a computational code to calculate the expected phase retardation per reflection as a function of the total number of layers constituting the mirror. Different cases have been studied and we have compared computational results with the trend of the experimental data. Our study indicates that the origin of the mirror intrinsic birefringence can be ascribed to the reflecting layers close to the substrate.

Measurement of mirror birefringence at the sub-ppm level: Proposed application to a test of QED

We present detailed considerations on the achievable sensitivity in the measurement of birefringence using a high finesse optical cavity, emphasizing techniques based on frequency metrology. Alternative approaches of laser locking and cavity measurement techniques are discussed and demonstrated. High-precision measurements of the cavity mirror birefringence have led to the interesting observations of photorefractive activities on mirror surfaces.

MIRROR BIREFRINGENCE IN A FABRY-PEROT CAVITY AND THE DETECTION OF VACUUM BIREFRINGENCE IN A MAGNETIC FIELD

Quantum electrodynamics (QED) theory predicts that vacuum under the influence of a strong magnetic field is birefringence. Recently, several groups have proposed to used a high finesse Fabry—Perot cavity to increase the average path length of the light in the magnetic field. This together with the state-of-the-art dipole magnets, should bring the effect within reach of observation. However, the mirrors used in the FP are known to have intrinsic birefringence which is of orders of magnitude larger than the birefringence of the vacuum. In this letter, we analyze the effect of uncontrollable variations of mirror birefringence on two recently proposed optical schemes. The first scheme,1 which we called the frequency scheme, is based on measurement of the beat frequency of two orthogonal polarized laser beams in the cavity. We show that mirror birefringence contributes to the detection uncertainties in first order, resulting in a high susceptibility to variations of its value. In the second scheme, which we called the polarization scheme, laser polarized at 45° relative to the B-field is injected into the cavity. The ellipticity and polarization rotation of the light exiting the cavity is measured.2 Under this scheme, mirror birefringence contributes as a correction of the QED effect, greatly reducing its sensitivity to the undesirable changes.

Laser stabilization at the millihertz level

The main task of this paper is to identify a number of physical problems that must be successfully addressed to achieve stabilized laser linewidths well below 1 Hz. After presentation of the basic stability characteristics of available laser sources, it is shown that if any of these lasers were optimally locked to a high-finesse Fabry-Perot cavity it would be theoretically possible to obtain a laser linewidth in the millihertz domain. Problems of optical feedback, modulation waveform errors, mechanical support and isolation of the reference cavity, thermal stabilization of the environment, etc. are considered, and interim solutions are discussed. Experimentally, locking accuracy to successive cavity orders of less than 0.00002 linewidths (+ or - 1.5 Hz) was achieved; mirror birefringence pulled the lock point approximately 10-fold more. Relative phase coherence between two independent lasers locked onto adjacent cavity orders was preserved for 8 sec, corresponding to a linewidth of each optical source of about 50 mHz.

Birefringent Laser Mirrors

Narrow band mirrors composed of a polarizer, a stack of lossless birefringent crystals, and a conventional mirror are described. Curves showing the reflectance characteristics of the mirrors are included. Design data are tabulated for narrow band mirrors that have appreciable between-peak reflectances because of the Gibbs phenomenon as well as for slightly broader band mirrors with lower between-peak reflectances. Computations are presented in a series of graphs to demonstrate sensitivity of the response to the angular adjustment of the crystal elements. Electric tuning of the birefringent mirror is possible and can be enhanced by a double element design. The choice of electrooptic birefringent materials and the temperature sensitivity of the mirror's peak wavelength are discussed along with applications. An appendix provides computational aids for the synthesis of birefringent filters.