D. E. Edmundson, "Unstable halo states of a three-dimensional
nonlinear Schroedinger equation," Physical Review A, submitted
The generalized nonlinear Schroedinger equation (GNLSE) governs the
propagation of a 3-dimensional plane-polarized optical envelope in a
bulk anomalously dispersive medium possessing an arbitrary
intensity-dependent refractive index. The GNLSE supports "halo state"
solitary waves comprised of a bright central core surrounded by a number
of spherical shells. For a saturable nonlinearity where the zeroth
order state is known to be stable, a linear stability analysis of
spherical harmonic modes Y(l,m) predicts the upper bound states to
be transversely unstable, and, in contrast to the situation in
2-dimensions, families of eigenmodes are found to possess the same
growth rate. These predictions are corroborated by direct simulation of
Email comments to dEdmundson@bigfoot.com.