Spectral Changes in Focused Partially Coherent Wave Fields

Abstract

When light is focused, there are several mechanisms which may cause spectral changes. Among them are diffraction, the state of coherence of the light [1], and propagation through a linear time-invariant system [2]. The focusing configuration is depicted in Fig. 1, it being assumed that f ≫ a ≫ λ. The cross-spectral density function of a field U ⁽⁰⁾ of arbitrary state of coherence on a reference sphere [3] is given by the expression [4, Sec.4.3.2]

$$ {{W}^{{\left( 0 \right)}}}\left( {{{Q}_{1}},{{Q}_{2}},v} \right) = {{W}^{{\left( 0 \right)}}}\left( {{{\rho }_{1}},{{\rho }_{2}},v} \right) = \left\langle {{{U}^{{\left( 0 \right)*}}}\left( {{{\rho }_{1}},v} \right){{U}^{{\left( 0 \right)}}}\left( {{{\rho }_{2}},v} \right)} \right\rangle . $$

(1)