Spatial coherence of optical fields in longitudinally inhomogeneous media with quadratic refractive index profiles

The paraxial approximation for the scalar wave equation is used to study the spatial coherence of optical fields in media with an overall quadratic refractive index profile and an arbitrary regular longitudinal inhomogeneity. Analytic expressions are obtained for the parameters describing the spatial coherence of fields in such media, particularly for the correlation radius and the width of a partly coherent beam generated by a variety of light sources. It is shown that for certain distributions of the longitudinal inhomogeneity there is no change in the coherent properties of the field because of a matching effect. This effect is proposed as a method for ensuring a matched contact between two different graded-index waveguides. A study is made of the influence of the degree of coherence on the focusing region of the beam and it is shown that, in principle, it is possible to focus a paraxial beam with a finite initial width in a region smaller than the wavelength. It is shown that variation of the longitudinal inhomogeneity distribution can be used to control coherent properties of the radiation. The results obtained can be used in fiber-optic communication lines, integrated optics, and coherent optical data processing.