22 February 2008 Analytical solutions for nonlinear waveguide equation under Gaussian mode approximation
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Critical power, nonlinear guided stationary mode and transient dynamics in nonlinear waveguides are studied analytically. Under Gaussian mode approximation, critical power for nonlinear self-focus is derived analytically and is found to be independent of waveguide parameters. Nonlinear guided stationary mode is found to be the stable solution of nonlinear waveguide below critical power for nonlinear self-focus and has a reduced mode size dependent on optical power and V value of the waveguide. Equation governing transient dynamics of the nonlinear waveguide modes is also found. Transient dynamics scale with Rayleigh Raleigh range similar to that in bulk media. Mode is found to evolve adiabatically towards the local stationary mode in a fiber below self-focus limit. Mode will collapse to a singular point at a self-focus distance at and above critical power. Larger V value increases transient and self-focus distance. The self-focus distance becomes proportional to square root of optical power at higher power level and independent of V value. B integral are calculated for various amplifiers considering the impact of gradual collapse of beam size along the amplifier.
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Liang Dong, Liang Dong, } "Analytical solutions for nonlinear waveguide equation under Gaussian mode approximation", Proc. SPIE 6873, Fiber Lasers V: Technology, Systems, and Applications, 68730V (22 February 2008); doi: 10.1117/12.774052; https://doi.org/10.1117/12.774052


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