Coherence of the electromagnetic field in dielectric waveguides

An investigation is made of the coherence of the electromagnetic field in a plane dielectric waveguide excited by an external field with specific coherence properties. The quantum theory of an electromagnetic field in one-dimensionally inhomogeneous media is employed to derive an expression which relates the correlation functions of the field inside the waveguide to the external field. This expression is used to study the variation of the coherence of the radiation at various distances z from the area where the radiation is coupled into the waveguide. If the external field has a finite line width, the spatial coherence is a periodic function of z when z≪z_cr and tends to a constant value when z≫z_cr. When z≪z_cr, the temporal coherence is the same as for the external source, whilst when z≫z_cr, the temporal coherence as a function of τ has maxima which move away from the point τ = 0 with increasing z. It is found that the coherence tunes τ₁ and τ₂ determined following Wolf and Mandel behave differently when z≫z_cr: τ₁² increases quadratically with increasing z, whereas τ₂ tends to a constant value. The form of the radiation modulation spectrum is deduced. Curves are plotted for the spatial and temporal coherence by way of a specific example.