Mutual spatiotemporal coherence of optical fields in an amplitude-splitting interferometer

We have considered cross correlations of wave perturbations formed by optical fields at different points of space at the exit of an interferometer with the splitting of the amplitude of the initial wave field. Expressions for the longitudinal spatiotemporal cross-correlation function of perturbations on the optical axis of a Michelson interferometer have been obtained and analyzed. We have determined spatial and temporal intervals in which the wave fields excite mutually coherent perturbations in the exit channel of the interferometer in the free space and in the image space of the lens system. We have found that, in the free space, mutually correlated perturbations arise simultaneously in identical longitudinal intervals, whereas, in the image space, they arise at different times in spatial and temporal intervals varying along the optical axis of the lens. The influence of cross correlations of the wave fields on the interferometer signal has been analyzed.

     

Coherence in the output spectrum of frequency shifted feedback lasers

We present a detailed theoretical analysis, using correlation functions, of the coherence properties of the output from a frequency shifted feedback (FSF) laser seeded simultaneously by an external seed laser and by spontaneous emission (SE). We show that the output of a FSF laser is a cyclostationary process, for which the second-order correlation function is not stationary, but periodic. However, a period-averaged correlation function can be used to analyze the optical spectrum. From the fourth-order correlation function of the output of a Michelson interferometer we obtain the essential characteristics of the radio-frequency (RF) spectrum, needed for describing the use of the FSF laser for optical-ranging metrology. We show that, even for a FSF laser seeded by SE, the RF spectrum comprises a sequence of doublets, whose separation gives directly a measure of the length difference between the interferometer arms. This doublet structure is a result of the correlation of interference terms of individual components of the cyclostationary stochastic process. It is not seen in the optical spectrum of the FSF laser but is observable in the RF spectrum. We analyze the competition between SE and continuous wave (CW) seeding to obtain an analytical expression for the ratio of power in the discrete CW signal to the background continuum spectrum from SE. We show that, unlike mode competition in conventional lasers, where there occurs exponential selectivity, here there is a balance between the two fields; the power in the fields is related linearly, rather than exponentially, to the control parameters.     

Shot noise in a double-quantum-dot Aharonov-Bohm interferometer under the perturbation of ac fields

We have investigated the shot noise spectral density in the parallel double-quantum-dot (DQD) interferometer threaded with an Aharonov-Bohm (AB) flux under the perturbation of ac fields. The derivations are based on the nonequilibrium Green’s function (NGF) technique in the Coulomb blockade regime. The AB flux and the perturbation of ac fields together provide a photon-assisted AB interferometer for controlling the shot noise efficiently. The signature of the shot noise reflects the intrinsic microstructure of the DQD system, which plays important roles for the enhancement and suppression of shot noise. The versatile resonant structures of shot noise, Fano factor have been revealed to exhibit the sub-Poissonian and super-Poissonian types of shot noise by adjusting the gate voltages sequentially.     

Quantum interference of multimode two-photon pairs with a Michelson interferometer

We perform the second-order quantum interference experiment with the multimode photon pairs produced via an optical parametric oscillator far below threshold in a Michelson interferometer, measure the second-order correlation function in different cases. We find when the interferometer is highly unbalanced, the shape of the second-order correlation function is clearly dependent on the path length difference between two interfering beams. On the contrary, when the interferometer is nearly balanced, beside its height, the shape of the second-order correlation function is independent on the small path length difference. The second-order correlation function shows a multipeaked structure in both cases. All experimental results agree very well with the theoretical predictions.     

Multi-Particle Interference in an Electronic Mach–Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach–Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach–Zehnder interferometer.     

A Near-Infrared Diode Laser Spectrometer of High Resolution and Wide Scanning Range

We have constructed a simple and inexpensive diode laser spectrometer in which the source is locked to and tracked by a scanning Fabry-Perot interferometer and in which absolute frequency measurements are made by markers generated by a further Fabry-Perot interferometer, itself locked either to a selected spectral line of the sample or to the saturated absorption of a D2 line in atomic Rb at 780 nm. With this technique we have been able to obtain near-continuous spectra stretching over the range from 12 640 to 12 780 cm⁻¹ at Doppler-limited resolution. In this paper we describe the principles of the spectrometer along with absolute frequency measurements of a number of overtone rovibrational transitions in two isotopomers of acetylene. The combination relations formed by these transitions demonstrate the accuracy of our measurements to be typically ±0.0002 cm⁻¹.     

Increase in the correlation length of nonmonochromatic radiation during propagation in a single-mode optical fiber containing random inhomogeneities and the influence of this increase on the operation of a fiber ring interferometer

An analysis is made of the conditions under which the coupling of orthogonal polarization modes at random inhomogeneities in single-mode optical fibers leads to an increase in the correlation length of a source of nonmonochromatic radiation. It is shown that when long-base fiber ring interferometers with a single-mode fiber ring system possessing weak linear birefringence are used, the correlation length of the nonmonochromatic radiation at the interferometer exit is increased, which means that the interference pattern can have satisfactory visibility even when there is an appreciable difference between the interferometer arms as a result of the Sagnac effect due to the Earth’s rotation. The calculations were made by mathematical modeling of random inhomogeneities in the fiber. Zh. Tekh. Fiz. 69, 140–143 (July 1999)     

In-plane electronic speckle pattern shearing interferometry

An analysis of the out-of-plane shearing interferometer has been performed which shows that production of in-plane strain partial derivatives is possible, which are not affected by out-of-plane displacement function components. The in-plane data are represented as subtraction correlation fringes. This interferometer employs a single diverging illumination beam and is applicable to object plane stress and plane strain loading conditions. The interferometer was tested and compared using a compact tension crack specimen and the results are correlated with finite element software predictions of strain distributions across modelled specimens. This experimental validation was chosen because we had an existing test rig and finite element models which had been independently verified.     

Spatial coherence properties of azimuthally polarized laser modes

Understanding of coherence properties of optical fields is of basic importance both in classical optics and in quantum physics. Coherence properties of electromagnetic laser modes are only now beginning to be explored and have not yet been tested experimentally, except in the simplest cases. In this paper, we first study theoretically the coherence properties of azimuthally polarized laser modes and we clarify the distinction between coherence and correlations in stochastic electromagnetic fields, a distinction which has up to now not been fully understood and has, in fact, been a subject of controversy. Our analysis clearly illustrates the distinction between these two concepts. After elucidating theoretically the coherence properties of radially polarized laser modes, we describe an experimental study of their properties, made by the use of a recently introduced reversed-wavefront Young’s interferometer. A good agreement between theory and experiment has been found.     

透过检测中的准直镜精度容限

在干涉检验过程中,被检元件的面形误差检测精度受到干涉仪系统结构的影响,从而降低测量结果的可靠性。为了得到较高的检测精度,必须对检测系统进行分析,建立测量误差和系统结构的关联度。根据菲涅耳衍射近似理论,就菲佐干涉仪中的准直镜和标准镜面形误差对透过检测的影响进行了研究。通过对波前相位传递情况的分析,得出波前误差和系统结构参量的相关性,去除空腔系统误差,优化结构参量,并建立准直镜误差容限表达式。经计算得出,当被检面形变误差为0.2λ时,测试误差可以达到0.02λ,而对准直镜的面形误差要求只需0.8λ。     

Polarimetric and spectral changes in random electromagnetic fields

Beginning with a recently formulated unified theory of coherence and polarization for random electromagnetic fields, we show how partially polarized light can be generated through correlation of unpolarized components. The effect is demonstrated by use of a Mach-Zehnder interferometer, showing the possibility of producing light with adjustable spectral density and an adjustable degree of polarization.     

Eikonal equation for partially coherent fields

Coherence is the study of the amplitude correlations of optical fields. Its physical features can be obtained from the cross-spectral density function W(x₁,x₂,γ) which satisfies two coupled Helmholtz equations. In this article, we describe the amplitude of the optical field using the angular spectrum model. With this representation we calculate the propagation of the correlation function emerging from a transmittance plane. We show that the cross-spectral density function, can be described by just one Helmholtz equation. The treatment permits us to associate directional features to the coherence phenomena. This implies the existence of extremal trajectories of correlation, which are characterized by an eikonal equation, and the existence of a function for media fluctuations, which we term the correlation refractive index. Experimental results are shown for the synthesis of partially coherent focusing regions, which are described by an ensemble of extreme correlation trajectories.     

A Novel Method to Calculate the Initial Phase Difference between the Two Fibre Arms of Laser Homodyne Iuterferometer

We suggest a novel method to calculate the initial phase difference between two fibre arms of a laser homodyne interferometer. Put the two fibre arms in a temperature controller, whose short term stability is 0.02° C （measured in an hour）, then measure the interference photocurrent and the photocurrents from the two fibre arms at a fixed temperature. With these three photocurrents we can calculate the value of the initial phase difference. We set up a simple laser homodyne interferometer to test the theory. The experimental results are repeatable and the measurement precision is about 0.04°. It is theoretically and experimentally proven that this method is potentially easy and practical.     

Absorption interferometer of two-sided cavity

We propose a scheme in which an arbitrary incidence can be made perfectly reflected/transmitted with a phase modulator. We analyze the variation of intracavity field as well as output field with closed-loop phase φ1 of the control fields and relative phase φ2 of the probe beams. With two phases, medium absorption and light interference can be controlled so that photon escape from the cavity can be manipulated, thus an intensity switching based on phase modulation can be realized. And the condition for perfect transmitter or reflector is obtained. Then based on the transmission/reflection analysis,the total absorption of this system can be investigated. Therefore our scheme can be used as an absorption interferometer to explore the optical absorption in some complicated system. The state delay of the output light intensity, which is dependent on φ1 or φ2, can be applied in the realization of quantum phase gate and subtle wave filter. And based on this scheme, we implement the state transfer between perfect transmitter/reflector and non-perfect coherent photon absorber via relative-phase modulation.     

Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line

We report on the generation of a type-I multimode two-photon state on a rubidium D(2) line (780 nm) using periodically poled KTiOPO(4) crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function; the cross correlation between two photons shows a cavity bandwidth of about 7.8 MHz. We also use a Fabry-Perot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retrieval of narrow-band photons in Rb atomic ensembles, which is important for long-distance quantum communication.     

Acoustic impedance measurements with a sound intensity meter

Acoustic impedance measurements have been made by evaluating, with a sound intensity meter, sound pressure and normal velocity close to absorbing material samples.Measurements have been made both in a Kundt interferometer and in the free field. With the Kundt interferometer the same results are achieved as with the classical Kundt interferometer but the present method is much faster and easier to implement.Free field measurements are accurate for frequencies high enough to allow one to neglect the finite dimension effect of the absorbing material sample.     

Fourier-domain low-coherence interferometry for light-scattering spectroscopy

We present a novel method for obtaining depth-resolved spectra for determining scatterer size through elastic-scattering properties. Depth resolution is achieved with a white-light source in a Michelson interferometer with the mixed signal and reference fields dispersed by a spectrograph. The spectrum is Fourier transformed to yield the axial spatial cross correlation between the signal and reference fields with near 1-microm depth resolution. Spectral information is obtained by windowing to yield the scattering amplitude as a function of wave number. The technique is demonstrated by determination of the size of polystyrene microspheres in a subsurface layer with subwavelength accuracy. Application of the technique to probing the size of cell nuclei in living epithelial tissues is discussed.     

Scheme for direct measurement of the Wigner characteristic function of traveling fields

We present a proposal to measure field states for traveling modes. The scheme leads, in a simple and direct way, to the characteristic function of the state, yielding the determination of the Wigner function without a demanding data analysis. We employ a Mach-Zehnder interferometer including an auxiliary nonlinear medium in one arm. Analogies with other proposals to reconstruct states of stationary fields and trapped atoms are discussed.     

Measurement of the spatial correlation function of phase fluctuating Bose-Einstein condensates

We measure the intensity correlation function of two interfering spatially displaced copies of phase fluctuating Bose-Einstein condensates. It is shown that this corresponds to a measurement of the phase correlation properties of the initial condensate. Analogous to the method used in the stellar interferometer experiment of Hanbury Brown and Twiss, we use spatial intensity correlations to determine the phase coherence lengths of elongated condensates. We find good agreement with our prediction of the correlation function and confirm the expected coherence length.     

Adaptive gain interferometry: a new mechanism for optical metrology with speckle beams

We describe, for the first time to our knowledge, the use of a saturable laser gain medium to implement an adaptive gain interferometer for performing optical metrology with speckle-distorted beams. We show that interferometric formation and replay of a saturable gain hologram permit coherent extraction of fast vibrational information about an object in real time and removal of slowly varying spatial distortion. An experimental characterization of the frequency response of the adaptive gain interferometer is made by use of a diode-pumped solid-state laser amplifier, and a new theoretical formulation of the gain interferometer is also developed for the first reported time.