Effect of depolarization on temporal coherence within a focused supercontinuum

Under the conditions of vectorial diffraction, an increase in refraction at the extremities of the lens rotates the incident polarization state which transfers energy from the initial state to the orthogonal transverse field and the longitudinal field, which is known as depolarization. Since the field is a vectorial field containing three polarization components, the theory for the degree of coherence is first extended to incorporate cross-correlation effects within these vectorial components which are calculated through a coherency matrix. The use of this matrix provides an insight into interesting correlation effects between copropagating vectorial fields such as the coupled modes (linear polarized modes) of the supercontinuum generated by a photonic crystal fiber. An investigation is presented on the coherence times for the supercontinuum field generated by cross coupling into the photonic crystal fiber. The coherence times under cross-coupling conditions show that the degree of coherence of the two coupled modes from the fiber are different, which is due to the differences in phase. For a supercontinuum with a linear polarization state, the coherence times along the x, y, and z axes are different, with the most significant change occurring along the optical axis (z) where the coherence time changes by an order of magnitude when the numerical aperture is increased from 0.1 to 1.