Theoretic analysis of mode-couple equation in all-fiber polarization transformer

The variably coupled-mode equation in all-fiber polarization transformer (AFPT) is theoretically analyzed and an optimal profile of variably spun rate to get better performance for AFPT samples is proposed as Q(z) = 0.5tan{arcsin[(z/L)sin(arctan2Q(L))]} where Q(z) is the normalized spun rate by beat length L_B along the spinning section of AFPT with total length L. Then, in accordance with this specific intrinsic structure of AFPT, we found that there exists a set of strictly analytic solution for the variably coupled-mode equations of AFPT. It is also found that the linear polarized exact eigen-modes of AFPT at the un-spun end are not parallel but with a slight angle relative to the birefringence axes of the un-spun fiber. The difference of phase factor and amplitude between the exact analytic solution and the asymptotic solution is compared and discussed. The analysis has referential values to the design, fabrication and evaluation of AFPT samples.