J. Eur. Opt. Society-Rapid Publ. 22, 19( 2026) 177
Fig
. 6. Degree of coherence for a sZegö source across a plane in the far zone relative to a point located at( a) v 2 =( 0, 0);( b) v 2 =( 0.16, 0);( c) v 2 =( 0.32, 0); and( d) v 2 =( 0.48, 0). Absolute value is represented on the vertical axis, and the phase is coded in a color scale. The first 100 modes were considered in the calculation.
Fig. 7.( a) OAM degree of coherence o S( m 1, m 2);( b) degree of orbitalization O S( m) for a far field radiated by sZegö source.
1 �ðq W T ðq 1; q 2; 0Þ ¼I 1 q 2 Þ N e iNðu 1�u 2 Þ
0; 1 � q 1 q 2 e iðu 1�u 2 Þ ð0 q 1; q 2 < 1Þ: ð39Þ
Spectral density and degree of coherence across the source plane turn out to be, from equations( 15) and( 16),
1 � q 2N S T ðq; 0Þ ¼I 0 circðqÞ; ð40Þ 1 � q2 and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 � q 2
1Þð1 � q 2 2Þ l T ðq 1; q 2; 0Þ ¼ ð1 � q 2N
1 Þð1 � q 2N
2 Þ 1 �ðq 1q 2 Þ N e iN ð u 1�u 2 Þ circðq 1 � q 1 q 2 e i ð u 1�u 2 Þ 1 Þ circðq 2 Þ; ð41Þ
Fig. 8. Spectral density at the source( normalized to the maximum) for a truncated sZegö CSD with N = 1, 2, 3, 5, 10, 20.