Fourth-order Coherence Function Research Articles

Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum.

A complete asymptotic theory for the aperture-averaged orbital angular momentum (OAM) variance is developed for both weak and strong fluctuation conditions, based on the asymptotic expansions of the Feynman path-integral solution for the fourth-order coherence function of a spherical wave propagating through a random inhomogeneous medium. We show that the OAM fluctuation averaging is very different for circular-symmetric and non-circular-symmetric apertures. Aperture averaging of the OAM fluctuations does not obey the standard "square root" law, and the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined solely by the values of the scintillation index of the incident wave.

Angular and temperature dependence of photon pair rates in spontaneous parametric down-conversion from a periodically poled crystal

We present a theoretical and experimental study of the angular and temperature dependence of the photon pairs produced by spontaneous parametric down-conversion in a periodically poled KTP crystal. In the experiment, two detectors are placed at different angles in the emitted light, and the detected photon pair rate is measured as a function of one angle or of crystal temperature. In the theoretical work, exact results for the pair rates are obtained through importance-sampled numerical integration of the fourth-order coherence function over regions representing the experimental integration parameters. Conditions studied range from well-resolved results in which detector angular and filter bandwidth integration effects are negligible, to other cases in which such effects are large and pair rates exceed ${10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Throughout these cases, good agreement is often seen between experimental and theoretical results, while some differences that are noted provide insight into the actual crystal quasi-phase-matching function.

Fourth-order mutual coherence function in oceanic turbulence.

We have recently expressed the structure constant of atmospheric turbulence in terms of the oceanic turbulence parameters, which are the ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of kinetic energy per unit mass of fluid, rate of dissipation of the mean-squared temperature, wavelength, Kolmogorov microscale, and link length. In this paper, utilizing this recently found structure constant and the fourth-order mutual coherence function of atmospheric turbulence, we present the fourth-order mutual coherence function to be used in oceanic turbulence evaluations. Thus, the found fourth-order mutual coherence function of oceanic turbulence is evaluated for the special case of a point source located at the transmitter origin and at a single receiver point. The variations of this special case of the fourth-order mutual coherence function of oceanic turbulence against the changes in the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of the mean-squared temperature, the wavelength, and the Kolmogorov microscale at various link lengths are presented.

Beam scintillations for ground-to-space propagation Part I: Path integrals and analytic techniques

We extend our theory of on-axis beam scintillations [Waves Random Media 4, 243 (1994)] for the case of propagation on slant turbulent paths, where turbulence is concentrated in a relatively thin layer near the transmitter. Our technique is based on the parabolic equation for optical wave propagation and the Markov approximation for the calculation of statistical moments of beam intensity. This first of two companion papers presents the details of the path integral formulation of the solution for the fourth-order coherence function. We also discuss in detail two analytic techniques that can be used for the treatment of the path integrals.

Correlation effects of chaotic and phase-diffusion fields on polarization beats in a V-type three-level system

Abstract The correlation effects of fourth-order on polarization beats in a V-type three-level system (PBVTS) are investigated using chaotic and phase-diffusion models. It has been found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behaviour of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The fourth-order coherence function theory of chaotic field is of vital importance in PBVTS. The cases where the pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level splitting between two states can be achieved. Finally, the difference between the PBVTS and DeBeer's ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.

Correlation effects of chaotic and phase-diffusion fields on polarization beats in a V-type three-level system

The correlation effects of fourth-order on polarization beats in a V-type three-level system (PBVTS) are investigated using chaotic and phase-diffusion models. It has been found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behaviour of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The fourth-order coherence function theory of chaotic field is of vital importance in PBVTS. The cases where the pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level splitting between two states can be achieved. Finally, the difference between the PBVTS and DeBeer's ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.

Raman-enhanced polarization beats with phase-conjugation geometry

The Raman-enhanced polarization beats (REPB) with phase-conjugation geometry in carbon disulfide are investigated using chaotic and phase-diffusion models. The overall accuracy of using REPB to measure the resonant frequency of Raman-active vibrational mode is determined by the relaxation rates of the Raman mode and the molecular-reorientational grating. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence function. The difference between the REPB and the fourth-order coherence on ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.

Sixth-order correlation on Raman-enhanced polarization beats with phase-conjugation geometry

The correlation effects of sixth-order on the Raman-enhanced polarization beats (REPB) with phase-conjugation geometry in carbon disulfide are investigated using chaotic and phase-diffusion models. Based on two types of models, the cases that the pump beams have either narrow band or broadband linewidth are considered and it is found that the beat signal oscillates not only temporally with a 50.5 fs period but also spatially. The overall accuracy of using REPB to measure the resonant frequency of Raman-active vibrational mode is determined by the relaxation rates of the Raman mode and the molecular-reorientational grating. Moreover, the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the decay rates of the Raman mode and the molecular-reorientational grating. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence function. Furthermore, the different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The difference between the REPB and the fourth-order coherence on ultrafast modulation spectroscopy is discussed as well from a physical viewpoint. Therefore, the sixth-order coherence function theory of chaotic field is of vital importance in REPB.

Fourth-order interference on polarization beats in a four-level system

We have employed chaotic and phase-diffusion models to study the effects of laser fourth-order coherence on polarization beats with phase-conjugation geometry in a four-level system (PBFS). We found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Inasmuch as different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of phase fluctuation and amplitude fluctuation are pointed out. The cases that pump beams have either narrow-band or broadband linewidth are considered, and it is found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states that are dipolar forbidden from the ground state can be achieved. We also discuss the difference between the PBFS and ultrafast modulation spectroscopy from a physical viewpoint.

Fourth-Order Interference on Polarization Beats with Phase-Conjugation Geometry

The effect of fourth-order coherence on ultrafast modulation spectroscopy (UMS) with phase-conjugation geometry (PCUMS) in a cascade three-level system is investigated using chaotic and phase-diffusion models. It has been found that the modulation terms of the beat signal depend on the second-order coherence function, and different stochastic models of the laser field affect only the fourth-order coherence function. The difference between the PCUMS and UMS is discussed from a physical viewpoint.

Effects of fourth-order coherence on ultrafast modulation spectroscopy

The effect of fourth-order coherence on ultrafast modulation spectroscopy with phase-conjugation geometry (PCUMS) in a cascade three-level system is investigated using chaotic and phase-diffusion models. It has been found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation can be investigated in the time domain. The cases where the pump beams have either a narrow or broad band linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states can be achieved. The difference between the PCUMS and the DeBeer, UMS [D. DeBeer et al., Phys. Rev. Lett. 56, 1128 (1986)] is discussed as well from a physical viewpoint.

Precision of determination of the angular radius of an object from estimates of the fourth-order coherence function in optically homogeneous and turbulent media

A method for high-precision measurements of the angular radius of an object is proposed. It is based on determination of this radius from readings of a histogram of the first zero of the fourth-order coherence function, obtained by the spatial convolution method, in the vicinity of the most probable value. The results are confirmed experimentally. It is shown theoretically and experimentally that the estimate of the angular radius of an object is not affected by propagation of radiation in a turbulent medium.

Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment.

Using a multidimensional Gaussian approximation of the wave function for the signal and idler light generated by spontaneous parametric down-conversion, we derive analytical expressions for the second-order coherence function and the fourth-order coherence function (which is proportional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widths determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these parameters are governed by the pump-beam waist, the pump spectral width, and the crystal length. We thereby derive relations analogous to the van Cittert--Zernike theorem and the Siegert relation for thermal light. We show that the normalized photon coincidence rate decreases sharply as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrically down-converted light obtained from a ${\mathrm{LiIO}}_{3}$ crystal pumped by ${\mathrm{Kr}}^{+}$-ion laser radiation at 413 nm. \textcopyright{}1996 The American Physical Society.

Estimate of the fourth-order coherence function by a spatial convolution method and its potential applications in laser information systems

It is shown that the coherence function of the radiation scattered by an object with a Lambert surface can be determined by a method of spatial convolution of the intensity field. The results obtained by this method are not affected by time instabilities of the radiation from a transmitter. A method is suggested for measuring the angular radius of a lidar object and an estimate is given of the potential precision of the method.

Chirp and self-phase modulation in induced-grating autocorrelation measurements of ultrashort pulses

We show that induced-grating/four-wave-mixing ultrashort-pulse autocorrelation techniques that use slowly responding media offer the same phase information as interferometric second-harmonic generation. We also show that autocorrelation traces from nearly all possible induced-grating/four-wave-mixing beam geometries provide this information, with all yielding the same theoretical result, an integral of a fourth-order electric-field coherence function. Such traces clearly reveal chirp and self-phase-modulation effects without high-frequency fringes. Experiments using a two-beam-coupling arrangement in photorefractive media illustrate these effects.

Fourth-order coherence-function theory of laser-induced molecular reorientational grating and population grating

We have employed fourth-order coherence-function theory to study the influence of the partial-coherence properties of pump beams on the laser-induced gratings. First, we examine the formation of molecular reorientational grating. The different roles of phase fluctuation and amplitude fluctuation have been pointed out. A time-delayed method has been proposed to distinguish molecular reorientational grating from thermal grating. We then apply the fourth-order theory to study the Bragg reflection from a population grating. We obtain an analytic solution which enables us to make an extensive investigation on the temporal behaviour of the Bragg reflection signal. This study is especially helpful for elucidating the generation mechanism of population grating Utilisation de la theorie des fonctions de correlation au quatrieme ordre pour etudier l'influence des proprietes de coherence partielle des faisceaux pompe sur les reseaux induits par laser

Numerical solution for the fourth-order coherence function of a plane wave propagating in a two-dimensional Kolmogorovian medium

We present a numerical solution for the fourth-order coherence function of a plane wave propagating in a random medium. The random medium is taken to be two dimensional, homogeneous, and isotropic with a universal Kolmogorov (pure) power-law form. Our results differ from previous numerical calculations principally in the way in which the scintillation index approaches saturation. We display the full spatial dependence of the fourth moment and the spatial evolution of the covariance function of the intensity fluctuations. Our results are compared with previously obtained numerical results, with several asymptotic expressions, and with recent analytical methods.

Quadratic structure functions and scintillation

The quadratic structure function (QSF) approximation by itself does not imply a tilt-only medium in which log-amplitude fluctuations are absent. When the QSF is applied to the fourth-order coherence function, the signal variance has contributions from log-amplitude fluctuations and beam wander but not beam spreading. However, the use of the QSF in the log-amplitude correlation function is limited as it can result in increasing correlation functions for weak turbulence.

Propagation of the fourth-order coherence function in an anisotropic random medium

The propagation of the fourth-order coherence function through an anisotropic random medium is investigated for low frequency radiation using the parabolic approximation and perturbation techniques. Theoretical expressions are derived for the intensity fluctuations and correlations of an initial plane wave signal that has propagated a horizontal distance z into the medium. The expressions are valid for anisotropic media in which klH≫1 and kl2v/lH≪1, where k is the radiation wavenumber, lH and lV are, respectively, characteristic correlation lengths parallel and perpendicular to the propagation direction z. The results are compared to those obtained for an isotropic random medium.

Irradiance Fluctuations and the Assumption of Gaussian Statistics for a Beam Propagating in a Random Medium

In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.