Analytical Studies of Nonlinear Partial Differential Equations of Interest in Nonlinear Optics
Final rept. 1 Mar 1991-31 Mar 1992
COLUMBIA UNIV NEW YORK DEPT OF APPLIED PHYSICS
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We use the time-dependent Hartree approximation to obtain solutions to a quantized higher-order nonlinear Schroedinger equation. This equation describes pulses propagating, in nonlinear optical fibers and, under certain conditions, has femtosecond soliton solutions. These solitons travel at velocities that differ from those of the picosecond solitons obtained from the standard quantized nonlinear Schroedinger equation. Furthermore, we find that quadruple-clad fibers are required for the propagation of these solitons, unlike the solitons of the standard nonlinear Schroedinger equation which can propagate in graded-index optical fibers. From the quantum solution, we find that the soliton experiences phase-spreading and self-squeezing as it propagates.
- Numerical Mathematics
- Nuclear Physics and Elementary Particle Physics