Mechanism of shape formation of optical structures in a nonlinear Fizeau interferometer as the mirror is shifted and the beam dimensions are varied

The article is concerned with the study of shape formation in a nonlinear Fizeau interferometer with two-dimensional feedback. In a preceding study [1], an approach was presented by means of which it is possible to elucidate the mechanism underlying the formation of the simplest optical structures for particular values of the parameters of the interferometer and the input optical beam. In the present article, an attempt is undertaken to account for the production of shear instability type structures and structures that arise as the beam dimensions in the feedback loop are varied. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 67–72, July, 1997.     

Asymmetric moving localized structures in a wide-aperture nonlinear interferometer

The existence of a branch of asymmetric solitary localized radiation structures moving in the transverse direction with a constant velocity is demonstrated for the slit (transversely one-dimensional) scheme of a wide-aperture interferometer with a threshold nonlinearity which is excited by external coherent radiation. This branch is shown to split off the branch of symmetric motionless structures at a certain bifurcation value of the external-radiation intensity. The generalization to other schemes, for which the existence of dissipative optical solitons is known, is discussed.     

菲索干涉仪中精确移相的实现

为了实现移相式菲索干涉仪对光学元件面形的高精度测量,建立了干涉仪同步采集移相系统,并对精确移相方法进行了研究。介绍了移相系统的构成和工作原理,计算了测量过程中移相器的速度。针对PZT移相器在移相过程中会引入离焦误差,并存在加速段和减速段的问题,详细设计了移相器的行进过程。最后,对移相器的性能进行了标定。在改造后的干涉仪上开展了重复性验证实验,结果表明：干涉仪可以获得λ/11 340的RMS测量重复性。对改造后干涉仪与Zygo公司生产的Verifire XP/D干涉仪的测量精度做了比对实验,结果显示：相同元件下两者测量结果的面形RMS之差约为0.9 nm,表明提出的移相系统及移相方法在重复性和准确度方面都能满足纳米级面形测量的要求,为研制高精度移相干涉仪奠定了基础。     

Optical structures formed by combined field transformations in a nonlinear interferometer

By means of a numerical experiment, an investigation was carried out of the characteristics for generating optical structures in a Fizeau interferometer with Kerr nonlinearity under the effect of combined large-scale transformation of the optical field in the feedback profile by: shifting the interferometer mirror, rotation of the optical field, and compression (expansion) of the laser beam. New types of structures are predicted. From the scale of these listed effects it is established that the combined effect of all three factors is not limited to the sum of their effects. An explanation for the specific structure formations is proposed. Analogs to these rules can be found in the results of actual experiments.Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 20–22, February, 1995.     

Mechanism of formation of simple optical structures in nonlinear fizeau interferometry

Explanations are suggested for the specific shapes of simple structures, generated in nonlinear interferometry. This is done within the mathematical model of dynamics of nonlinear phase clamping, developed by A. S. Akhmanov and M. A. Vorontsov. The basis of the analysis is an estimate of the contributions of diffusion and relaxation effects, as well as that of the Kerr effect, to the rates of phase dynamics.Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 77–81, June, 1995.     

Motion of localized structures in the case of oblique incidence of radiation on a nonlinear interferometer

For wide-aperture interferometers filled with a medium with threshold nonlinearity and excited by external radiation, the transverse profile of the field of localized structures in the form of solitons and dissitons is found when taking spatial filtering into account. The drag coefficient determining the velocity of transverse motion of a single dissiton in the case of oblique incidence of external radiation is analytically calculated.     

Polymerization shrinkage of a dental resin composite determined by a fiber optic Fizeau interferometer

A fiber optic sensing method based on a Fizeau-type interferometric scheme was employed for monitoring linear polymerization shrinkage in dental restoratives. This technique offers several advantages over the conventional methods of measuring polymerization contraction. This simple, compact, non-invasive and self-calibrating system competes with both conventional and other high-resolution bulk interferometric techniques. In this work, an analysis of the quality of interference signal and fringes visibility was performed in order to characterize their resolution and application range. The measurements of percent linear contraction as a function of the sample thickness were carried out in this study on two dental composites: Filtek P60 (3M ESPE) Posterior Restorer and Filtek Z250 (3M ESPE) Universal Restorer. The results were discussed with respect to others obtained employing alternative techniques.     

Simultaneous demodulation technique for a multiplexed fiber Fizeau interferometer and fiber Bragg grating sensor system

We propose a demodulation technique for a multiplexed fiber Fizeau interferometer (FFI) and fiber Bragg grating (FBG) sensor system using the discrete wavelet transform with signal processing enhancements. This simple and flexible demodulation technique determines the cavity length of FFI and the Bragg wavelength of FBG simultaneously and is especially suited for quasi-static measurements. We demonstrate this demodulation technique by performing some strain measurements, and a strain resolution of 1.0 microepsilon and an accuracy of 2.6 microepsilon are obtained. The maximum cross-talk of the sensor system is 6% of the applied strains.     

Switching behaviour of a nonlinear Mach-Zehnder interferometer

In the present paper, a detailed investigation on the switching behaviour of a nonlinear Mach-Zehnder interferometer (NMZI) has been carried out using beam propagation method (BPM). A thorough investigation on input vs. output characteristic has been carried out by varying different parameters like length of the arms, refractive index of the linear/nonlinear arm, wavelength of the input beams and nonlinear coefficient of the material of the nonlinear arm. The input vs. output characteristic has also been investigated by shifting the balance point of the NMZI. The present paper provides a physically intuitive understanding of the effect of change in different parameters of the NMZI on its switching behaviour.     

Hysteresis and nonlinear thermooptic waves in a semiconductor Fabry-Perot interferometer

We propose and demonstrate the existence of temperature hysteresis phenomena in a Fabry-Perot interferometer, resulting from a change in the refractive index of the interferometer material when heated by laser radiation. We also demonstrated theoretically that temperature multistability in the distributed interferometric system may cause the emergence of nonlinear thermooptic switching waves and found an approximate expression for the propagation velocity of such waves. We present the results of experimental observations of temperature multistability and thermooptic switching waves in a germanium Fabry-Perot interferometer illuminated by CO₂-laser radiation.     

Single- and multi-pulse formation of surface structures under static femtosecond irradiation

Femtosecond surface structure modifications are investigated under irradiation with laser pulses of 150 fs at 800 nm, on copper and silicon. We report sub-wavelength periodic structures formation (ripples) with a periodicity of 500 nm for both materials. These ripples are perpendicular to the laser polarization and can be obtained with only one pulse. The formation of these ripples corresponds to a fluence threshold of 1 J/cm² for copper and 0.15 J/cm² for silicon. We find several morphologies when more pulses are applied: larger ripples parallel to the polarization are formed with a periodicity of 1 μm and degenerate into a worm-like morphology with a higher number of pulses. In addition, walls of deep holes also show sub-wavelength and large ripples.     

Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer

A Fizeau interferometer based set up for measurement of surface forms of plane optical surfaces has been discussed. Phase shifting interferometry has been applied using polarization phase shifter. A linearly polarized (632.8 nm) He–Ne laser has been used as the source. Light reflected from the object and the reference/master surfaces are made circularly polarized in opposite senses by means of two properly oriented quarter wave retardation plates placed at appropriate positions, one inside and other outside the interference cavity of the interferometer, and phase shifts are introduced between the object and the reference/master waves by varying angular orientation of a polarizer/analyzer. Final result is made free from any residual wave-front aberrations introduced by the (intra-cavity) wave plate by subtracting phase values obtained by PSI technique between a high optical quality master surface and the reference surface from that obtained for the test object surface with respect to the same reference surface for each point of the interference field. Results are shown for a plane surface.Advantages of the technique presented are linearity and high accuracy in phase stepping, no perturbation of the interference cavity during the phase shifting and possibility of real time or dynamic interferometry.     

Angular interferometer using calcite prism and rotating analyzer

An interferometer using a calcite prism and rotating analyzer is proposed for angular displacement determinations. The calcite prism senses the angular displacements and the rotating analyzer transfers the interference signals from dc-type into ac-type. Compact optical setup and using low-cost devices are thus the advantages of the interferometer. The theory of the interferometer is first demonstrated. A setup constructed to realize the interferometer and the results of using this setup are then presented.     

Quantum fluctuations of spatial dissipative solitons in a nonlinear interferometer

A quantum Langevin equation is derived that makes it possible to study the radiation field in a large-aperture nonlinear interferometer excited by external classical radiation. This equation is linearized in the vicinity of the solution for a stationary soliton. A mathematical formalism for obtaining a spectral representation of the solution to the linearized problem is constructed. It is shown that, in general, the excitation spectrum of a soliton consists of three branches, two of which belong to a continuous spectrum, while the third branch is discrete. The spectral representation obtained makes it possible to rigorously define the operator of soliton coordinate fluctuations, since, as is shown in the study, the traditional definition of this operator leads to a divergence in the vicinity of the solution. A new type of dissipative soliton is found, which is a natural generalization of a stationary soliton and takes into account its motion. A relation is found between this soliton and the contribution to the solution for field fluctuations from the discrete spectrum expansion. The mean squares of fluctuations of the soliton coordinate and momentum are calculated. A range of parameters is determined where the momentum of the soliton can always be measured with a spread smaller than the standard quantum limit. This possibility is related to the occurrence of states squeezed with respect to the soliton momentum. A scheme is proposed for the experimental observation of these states.     

Quantum effects of a nonlinear interferometer with a Kerr cell

With the help of the optical Kerr effect we can produce phase fluctuations caused by intensity fluctuations. For this effect we present an exact solution in the Heisenberg picture. Interference of such a light beam with a reference beam produce enhanced bunching as well as antibunching of weak fields.     

Theory, design, and evaluation of the rotating polarizer interferometer

We present the results of modeling the response of a Rotating Polarizer Interferometer (RPI), an actual design and the evaluation of it. The RPI was introduced almost 10 years ago by Erickson [1] and since then it has not received too much attention from the millimeter wave community despite its very attractive characteristics, this is perhaps due to a lack of proven designs to encourage potential users. Here we show that with proper design equations a predictable result can be achieved and that a working device with a low-loss dielectric filling (Teflon) is feasible     

Measurement of surface figure of plane optical surfaces using Fizeau interferometer with wedge phase-shifter

A Fizeau interferometer-based set-up for measurement of surface figure of plane optical surfaces has been discussed. Phase-shifting interferometry has been applied using wedge phase shifter. Technique for elimination of system aberrations has been described. Results are shown for a plane surface.