Ray-optical theory of broadband partially coherent emission

We present a rigorous formulation of the effects of spectral broadening on emission of partially coherent source ensembles embedded in multilayered formations with arbitrarily shaped interfaces, provided geometrical optics is valid. The resulting ray-optical theory, applicable to a variety of optical systems from terahertz lenses to photovoltaic cells, quantifies the fundamental interplay between bandwidth and layer dimensions, and sheds light on common practices in optical analysis of statistical fields, e.g., disregarding multiple reflections or neglecting interference cross terms.

Figure 1

Physical configuration of a general multilayered formation, with an embedded source and a far-field observation point. Two different rays $s$,$s^{\prime }$, originating at the source and interfering in the observation point, are depicted.

Figure 2

Physical configuration of a symmetrical biconvex lens with radius $R$ and thickness $d$. A plane wave parallel to the $z$ axis impinges the lens from the left, and the angle between the far-field observation point and the $z$ axis is $\theta$. Ray tracing of two rays $s$, $s^{\prime }$ with different numbers of internal reflections, which interfere at the observation point, is presented.

Figure 3

Effect of coherence length on angular distribution of power in the far field, for impinging parallel paraxial rays, and four coherence length values: infinite coherence length (thick dashed red line), $L_c=50\mathrm{mm}$ (solid black line), $L_c=5\mathrm{mm}$ (dash-dotted green line), and $L_c=1\mathrm{mm}$ (dashed blue line). For comparison, the direct ray contribution (dotted black line), obtained by neglecting all internal reflections in the lens, is presented as well.

Figure 4

Definitions of $d_{\nu }$ and ${\rho }_{\nu }$ demonstrated using a representative ray tracing of the lens, corresponding to Fig. 2.

Figure 5

Auxiliary lines for optical path calculation, demonstrated using a representative ray tracing of the lens, corresponding to Fig. 2.