Polarization Coherence Theorem in Birefringent Nonlinear Single-Mode Optical Fibers

Recently, Eberly et al. [1] introduced the polarization coherence theorem (PCT):
$P^{2}=V^{2}+D^{2}$
, where the polarization
$P$
, visibility
$V$
, and distinguishability
$D$
are joined. In this work, we study the PCT in birefringent nonlinear single-mode optical fibers by considering circularly polarized input light fluctuating in amplitude. We analyze the behavior of the output PCT as a function of the linear birefringence and average input power. We demonstrate that the output light field undergoes a reduction of
$P$
and
$V$
but an increase of
$D$
when the linear birefringence approaches a critical value defined by the average input power; otherwise,
$P$
,
$V$
, and
$D$
remain unaffected. We also show how the average input power impacts
$P$
,
$V$
, and
$D$
by enhancing the linear birefringence.