D.E. Pelinovsky and E.H. Sargent
Stable all-optical limiting in nonlinear periodic structures
II. Computations
J. Opt. Soc. Am. B 19, 1873-1889 (2002)
Abstract:
Transmission of coherent light through photonic gratings
with varying Kerr nonlinearity is modeled within a
coupled-mode system derived from the Maxwell equations.
The incident light waves are uniformly stable in
time-dependent dynamics if the photonic grating has zero
net-average Kerr nonlinearity. When the average
nonlinearity is weak but nonzero, light waves exhibit
oscillatory instabilities and long-term high-amplitude
oscillations in the out-of-phase linear gratings. We show
that a two-step transmission map between lower-transmissive
and higher-transmissive states has a narrow stability
domain, which limits its applicability for
logic and switching functions. Light waves exhibit cascades
of real and complex instabilities in the multi-stable
gratings with strong net-average Kerr nonlinearity. Only
the first lower-transmissive stationary state
can be stimulated by the incident light of small intensities.
Light waves of moderate and large intensities are
essentially nonstationary in the multistable gratings,
and they exhibit periodic generation of Bragg solitons
and blowup.
Keywords:
PERIODIC OPTICAL MATERIALS, COUPLED-MODE EQUATIONS,
INPUT-OUTPUT TRANSMISSION CHARACTERISTICS, INSTABILITIES
OF STATIONARY SOLUTIONS, EIGENVALUES, BIFURCATIONS,
FINITE-DIFFERENCE NUMERICAL APPROXIMATIONS, BLOW-UP