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• W2739944841 abstract "We develop an asymptotic method for the calculation of spatial correlation function of the radiation field in statistically irregular open waveguides with an arbitrary profile of the refractive index in the transverse cross section. It is shown that the spatial correlation function of the field at large distances from the region of entry of the radiation into the waveguide is determined only by the distribution of the average power over the modes. In the case of multimode waveguide, this function can be determined by solving an equation of the Einstein~Fokker type for the density distribution of the rays. In the case of planar waveguides, this function is determined by expanding asymptotically the correlation function of the field with respect to a small quasiclassicity parameter. We consider a concrete example of open waveguide with random curvatures of the axis. Irregularities in open waveguide channels in practice lead not only to a loss of power in a wave propagating in the channel, but also to an impairment of its spatial coherence~ The theoretical analysis of this characteristic of the wave in an irregular waveguide is hindered by the regular dependence of the refractive index of the medium on the transverse coordinates, and by its random variation along the waveguide axis. The correlation function of the wave can be calculated rigorously only for a statistically irregular waveguide with a quadratic dependence of the refractive index on the transverse coordinates [1-3]. The statistical characteristics of the normal modes of the waveguide field can be studied for a wide class of randomly inhomogeneous waveguides with a power-law profile of the unperturbed refractive index [4-6]. The mode analysis of spatial coherence of the wave field in a statistically irregular waveguide [7-9] shows that the intermode correlation is attenuated after the passage of a wave through a critical distance. The spatial correlation function of the wave field is determined only by the distribution of the average power over the modes. However, a further analysis is met with difficulties associated with the solution of a boundary-value problem for the proper waves in a waveguide with an arbitrary profile of the refractive index in the transverse cross section, and because of the calculation of a sum of large number of terms. It is therefore expedient to use numerical calculations. The method of calculation developed in the present work makes it possible to avoid the above difficulties. It is based on an asymptotic expansion of the spatial correlation function of the field in a multimode waveguide in terms of a small quasiclassicity parameter [i0, ii]. Below, this method is used to obtain closed analytical expressions for the spatial correlation function of the field in a planar multimode statistically irregular open waveguide at a sufficientlylargeseparation from the region of entry of the radiation. We note that the case of closed waveguide channels coincides with the case considered in [io]. I. Principal Equations We consider a two-dimensional waveguide channel. Let us suppose that the direction of the z axis coincides with the direction of propagation of the wave, and x is a coordinate transverse to the z axis. We assume that in the plane z = 0, the waveguide is excited by a monochromatic wave beam E0(x) of frequency ~ (we assume a harmonic time dependence exp(iwt)). The refractive index of the medium n = n(x, z) will be represented in the form" @default.
• W2739944841 created "2017-08-08" @default.
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• W2739944841 date "1986-01-01" @default.
• W2739944841 modified "2023-09-27" @default.
• W2739944841 title "STATISTICALLY IRREGULAR WAVEGUIDES" @default.
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