Second-order Coherence Function Research Articles

Time-delayed Raman-enhanced nondegenerate four-wave mixing with a broadband laser source.

We report an experiment of the time-delayed Raman-enhanced nondegenerate four-wave mixing (RENFWM) with a broadband laser in carbon disulfide (${\mathrm{CS}}_{2}$). We studied the RENFWM signal intensity as a function of the relative time delay \ensuremath{\tau} between two beams which originate from a single broadband laser source. Our results indicate that the temporal behavior of the RENFWM is asymmetric with the maximum of the signal shifted from \ensuremath{\tau}=0. Furthermore, unlike the corresponding coherent Stokes Raman scattering (CSRS) no coherent spike appears at \ensuremath{\tau}=0. From our experimental results the relaxation time of the Raman mode can be extracted directly. We present a second-order coherence function theory to elucidate the physics of the basic features of the time-delayed RENFWM. We also discuss the difference between the RENFWM and the CSRS from a physical viewpoint.

Two-photon atomic transitions with a squeezed cavity field and Stark shift

The problem of a single atom making two-photon transitions in the presence of a cavity field that is initially in the general squeezed state or squeezed vacuum state is studied. Closed expressions for the atomic inversion, the second-order coherence function, and the quadrature variances are derived under the assumption of a large initial average photon number and a squeezed field input. The effects of Stark shift on these quantities are analyzed and discussed. We see collapses and revivals of atomic inversion and the second-order coherence function with a general squeezed input, but none are apparent when the input is in the squeezed vacuum state. Perodic revivals of squeezing are seen.

Analysis of a multiphoton Jaynes-Cummings model with squeezed inputs.

An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.

Multiphoton ionisation in the presence of pre-Gaussian light

The authors present exact solutions for N=1 and 2 N-photon off-resonance ionisation in the presence of a fluctuating radiation field with pre-Gaussian statistics. These pre-Gaussian fluctuations are composed of n independent two-state jump processes (telegraphs). Such telegraph-type fluctuations have a second-order intensity coherence function g that is normalised and bounded such that 1<or=g<or=2. In the limit n to infinity the pre-Gaussian noise converges to chaotic light with the well known g=2!. The authors show that an exact discussion of the N-photon ionisation rate can be given for such pre-Gaussian fluctuations.

Propagation of Partially Coherent Light Pulses

The propagation of light pulses with partial spatial and temporal coherence is analysed. It is shown that the introduction of the second-order coherence function enables the description of both spatial and temporal radiation characteristics to be described in the angular spectrum approach. A strong correlation between the spatial and temporal parameters is obtained.

Propagation of laser radiation in an instantaneous-response nonlinear medium

An equation is derived for the second-order coherence function applicable to propagation of laser radiation over long distances in an instantaneous-response nonlinear medium where an exponential growth of perturbations in a wave changes to a regime of saturated fluctuations. An analysis of this equation is made on the basis of a self-similar solution.

Coherence of neutron fields

Glauber's definition of quantum coherence is used for neutron fields under the assumption that the complete occupation number space is a direct product of Fermi subspaces. As a result, completely coherent microfields are obtained which define a density operator in full analogy to Glauber's $P$ representation of boson fields. For better physical significance, a transformation from the $P$ representation to a momentum representation is performed. It is proved that the second-order coherence function in this representation is equivalent to Wolf's second-order coherence function of a classical Dirac field. Finally, the results of the theory are used to calculate explicitly the second-order coherence function and the coherence time of an ideally collimated neutron beam.

Propagation of laser radiation in a moving delayed-response nonlinear medium

A derivation is given of the second-order coherence function for the propagation of laser radiation in a moving delayed-response nonlinear medium. A solution of this equation is used in an asymptotic analysis of fluctuations of the radiation in the case of propagation over long distances.

Operator methods for time-dependent waves in random media with applications to the case of random particles

The random medium is represented by the operator, constructed from the characteristic functional of the medium, and this representation is shown to considerably facilitate the formulation of various equations of waves in random media, as well as obtaining the physical insight into the equations. A specific application is made to waves in the medium of random particles, and the equations obeyed by the characteristic functional of wave are derived with the aid of the effective medium method. Here, the optical condition is exhibited by the condition of an operator in space and time. Independent of this operator method, the general theory is extended, in an unperturbative way, for the equations of the second-order coherence functions, being given in form of the Bethe–Salpeter equation, and the coherent potential equations are formulated for the basic matrices of two kinds appeared in the equations. The explicit expressions of these matrices are obtained, on utilizing the coherent potential approximation, and are shown to be exactly the same as those obtained by the effective medium method, in both cases of weak-scattering limit and of random particles. Finally, on employing the appropriate Fourier representations in space and time, the theory is presented in a few different forms, one being particularly suited to derive the equations of multifrequency coherence functions.

Canonical Extension of a Problem in Parametric Frequency Up-conversion with Stochastic Pumping

A canonical model for the frequency up-conversion process with stochastic coupling function is proposed. Based on it the first-order coherence functions, the time dependence of the mean photon numbers and the second-order coherence functions are found and compared with the corresponding results already available in the literature. It is shown that the total photon number, as a function of time, has a turning point. The antibunching effect is predicted regardless of the mean photon numbers available in the process.

Phase determination of second-order coherence function

By making use of recent calculations on the third-order intensity correlations, we suggest a method for the numerical computation of the phase of the normalized second-order coherence function. The method is applicable for a laser working well below its threshold of oscillation.

On an investigation of Tatarskii into the relationship between coherence theory and the theory of radiative transfer*

In an investigation into the foundations of the theory of radiative energy transfer, Tatarskii (1971) postulated a certain relationship between the specific intensity of radiation and a second-order coherence function of the wavefield. It is shown in the present paper that for propagation in free space, Tatarskii’s assumption restricts the validity of his theory to fields that are statistically homogeneous.

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.

Estimation of Optical Field Mean Intensities from Photocount Correlations

An extremely simple procedure is given for estimating the mean intensity of each component of a twocomponent optical field from measurements of the number of photocounts recorded over counting intervals of T sec duration spaced tau sec apart. The only a priori knowledge required about each component is the functional form of the first- and second-order coherence functions and an order of magnitude estimate of their coherence times.

Intensity interferometry by two-photon excitation of fluorescence

Two-photon fluorescence traces used for picosecond pulse-width measurement are analyzed and described by intensity correlation functions, also known as second-order coherence functions. The correlation functions and the fluorescence traces are discussed for three special types of light emission and calculated in detail for a three-mode laser model in free-running, mode-locking, and FM-like operation. A rigorous calculation for the fluorescence intensity excited by a laser oscillating in a large number of modes with arbitrary amplitudes and phases is also given. The shapes of the fluorescence traces are found to be essentially the same for both, free-running and ideally mode-locked emission, but with different contrast ratios of 1.5 : 1 and 3 : 1, respectively.

Measurements of Photon Correlations in Partially Coherent Light

Measurements have been made of the distribution in time of arrival of photons produced in a low-pressure ${\mathrm{Hg}}^{198}$ discharge. Sufficient calibration was done so that the measurements could be directly compared with the predictions of a calculation of ${G}^{(2)}({x}_{1},{x}_{2},{x}_{2},{x}_{1})$, the second-order coherence function. Correlations were observed in a mixture of light from two independent sources and between orthogonally polarized components of a beam initially in a pure polarization state.

Degree of Higher-Order Optical Coherence

In this paper we define the normalized coherence function of arbitrary order (m, n), in a manner which seems to be a natural generalization of that defined for the second-order coherence function. Both classical and quantized optical fields are considered and the results are compared. It is shown that for classical fields and also for quantized optical fields having nonnegative definite diagonal coherent state representations of the density operator, the modulus of these normalized coherence functions is bounded by the values 0 and 1. This definition differs from the one recently given by Glauber for quantized optical fields, where the normalized coherence functions may take arbitrarily large values even for fields having nonnegative definite diagonal representations of the density operator. Conditions for ``complete coherence,'' i.e., those under which the modulus of the normalized coherence function attains the limiting value 1, are discussed. Some consequences of stationarity and quasi-monochromaticity are also discussed.