Power-dependent polarization of optical pulses

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Abstract
The theory of the power dependence of the polarization of optical pulses in birefringent optical fibers with Kerr-like nonlinearity is presented in detail. Fundamental discussions are given of the nature of the polarization, and the coupled Schrödinger equations satisfied by the components of the polarization are derived in detail from first principles. It is shown how the Cartesian and circularly polarized field representations relate to each other and to the existing literature. Extensions that include self-steepening and applications to twisted fibers are also given. It is argued that, since high-order solitons evolve on a much shorter length scale, relative to the soliton length, than lower-order solitons, a more useful indication of the significance of dispersion is given by some pulse-compression distance based on the initial compression rate of the pulse, owing to self-phase modulation. This evidence is presented numerically for an initial condition using a 100-W pulse for a fiber having αp = 1.8 × 10−9 as its nonlinear coefficient and assuming an initial pulse width of 3.3 psec. The effect of dispersion and birefringence on a nonlinear pulse with the power equally distributed between the fast (y) and slow (x) axes of a birefringent optical fiber is given for a fiber with an intrinsic birefringence that gives a beat length of 20 m. In the evolution of the fields for zero group-velocity dispersion, it is shown that a portion of the power transfers from the fast axis the slow axis and back and continues to oscillate back and forth between the two. The evolution in the presence of dispersion (〈β″〉 = 5 × 10−26) without any intrinsic birefringence shows that this case is close to the standard N = 3 soliton case. In both of the above cases, the structure of the pulse evolves as it travels down the z axis, but there is no overall breakup of the pulse. If both dispersion and the assumed birefringence are present, splitting into two separate pulses is seen, with, in addition, some permanent transfer of energy from the fast to slow mode.