Order Coherence Function Research Articles

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

The low frequency propagation of the fourth order coherence function through an anisotropic medium is investigated by employing 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 distance z into the medium. The expressions are valid for anisotropic media in which klH ≫ and klv2/IH ≪ 1, where k is the radiation parallel and perpendicular to the propagation direction z. Numerically, we also calculate the intensity fluctuations of a plane wave, whose propagation direction forms an arbitrary angle with the principle axes defined by IH, and lv. We find that the magnitudes of the fluctuations are very sensitive to the propagation angle. Two examples are discussed: an exponential correlation function which approximates the ocean temperature microstructure, and a Gaussian correlation function. [Work supported by NSF Contract ENG76-11812.]

Higher-order angular coherence functions

Higher-order angular coherence functions are introduced and some of their properties are discussed. The general (n, m)-th order coherence function is derived in the observation plane, in the far-field approximation, from its knowledge on a given plane. The result is applied to the case of a completely coherent field as well as to evaluate the intensity correlation at two points in the far field of a quasi-monochromatic, thermal source.

Broadening of a laser beam propagating in a turbulent atmosphere along inclined routes

Abstract : The article presents calculations of the turbulent broadening of a laser beam propagating along sloping traces in the atmosphere. The calculations are based on the solution of the equation for the coherence function of the second order, obtained in the approximation of a Markov process.

Principe d'une experience de determination de la fonction de coherence d'ordre deux d'un laser monomode

We describe an experiment which gives the coherence function of order n. The advantage of the disposal, which uses the beat signal of two independent lasers, is that it does not imply any optical delay.

Coherence properties of optical fields in a nonlinear dielectric

Coherence properties of optical fields in a nonlinear dielectric are studied taking into account their vector nature. Maxwell’ equations and a complete expansion of polarization in the electric field are used to obtain equations of propagation of coherence functions in a nonlinear dielectric. It is shown that coherence functions of order (N, M) withN≠M may be nonzero in a dielectric for fields of all the origins. A method of solving the equations of propagation of coherence functions by approximation is given. These equations are solved for the case of plane waves in an isotropic dielectric. It is shown that the intensity of second harmonic has a dependence on the fourth-order coherence functions of the fundamental. This is a generalization of the results of Beran and De Velis and of Ducuing and Bloembergen for scalar light field that the intensity of the second harmonic depends on the average square intensity of the fundamental. It is also shown that the coefficient giving nonlinear dependence of polarization on the electric field in the lowest order can be obtained from the measurements of intensity of second harmonic and fourth-order coherence functions of fundamental. The coherence function of order (1, 2) is also calculated explicitly.

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.