Interrelation between the coherence properties and the space-time structure of light beams

<title>Interrelation between reciprocity relations in spatial and temporal domains for partially-coherent beams</title>

“…In temporal domain modal weights are nondegenerate, but for two-dimensional spatial structure with minimal product of divergence angle to beam cross-section modes of decomposition have to be degenerate. Therefore for obtained coefficients form of correlation functions expansion , ,m and A, there is no set of numbers an,mi ,m2, which satisfy the equations (7).…”

Average number of coherent modes for pulse random fields

“…Under degeneration (e. g. when u i = u j ) the ambiguity arises from the fact that two different wave structures e i (t)E i (r) + e j (t)E j (r) and e i (t)E j (r) + e j (t)E i (r) produce the same correlation functions (1), (8). Strictly speaking, the modal structure of the field does not remain constant under the wave propagation, but mode mixing is comparatively low for quasimonochromatic beams with small divergence [6]. That is why the deterministic dual decomposition (5) is inherently aimed to description of laser pulses and has been first applied in nonlinear optics [9], where the partial coherence just means a high complexity of interacting waves.…”

“…Strictly speaking, the modal structure of the field does not remain constant under the wave propagation, but mode mixing is comparatively low for quasimonochromatic beams with small divergence [6]. That is why the deterministic dual decomposition ( 5) is inherently aimed to description of laser pulses and has been first applied in nonlinear optics [9], where the partial coherence just means a high complexity of interacting waves.…”

“…12, the higher moments determine a probability distribution of wave amplitude under conditions of wave mixing at a strong scatterer. The most important characteristic of field structure is an effective number of terms in decompositions (1), ( 5), ( 8) [1,6,13], which is expressed through 2nd order moment…”

“…The next principal step in the development of the modal formalism was made by Pasmanik and Sidorovich [6]. They demonstrated the spatio-temporal symmetry for decomposition (1) - (3), that leads to some important relations between spatial and temporal coherence characteristics of light waves.…”