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D. Pelinovsky, J. Sears, L. Brzozowski, and E.H. Sargent

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Stable all-optical limiting in nonlinear periodic structures

I. Analysis

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J. Opt. Soc. Am. B 19, 43-53 (2002)

**Abstract:**

We consider propagation of coherent light through a
nonlinear periodic optical structure consisting of
two alternating layers with different linear and
nonlinear refractive indices. A coupled-mode system
is derived from the Maxwell equations and analyzed
for the stationary transmission regimes and linear
time-dependent dynamics. We find the domain for
existence of true all-optical limiting when the
input-output transmission characteristic is monotonic
and clamped below a limiting value for output intensity.
True all-optical limiting can be managed by compensating
the Kerr nonlinearities in the alternating layers,
when the net-average nonlinearity is much smaller than
the nonlinearity variance. The periodic optical structures
can be used as uniform switches between lower-transmissive
and higher-transmissive states if the structures are
sufficiently long and out-of-phase, i.e. when the linear
grating compensates the nonlinearity variations at each optical
layer. We prove analytically that true all-optical limiting for zero
net-average nonlinearity is marginally stable in time-dependent
dynamics. We also show that weakly unbalanced out-of-phase
gratings with small net-average nonlinearity exhibit local
multistability while strongly unbalanced gratings with large
net-average nonlinearity display global multistability.

**Keywords**:

PERIODIC OPTICAL MATERIALS, COUPLED-MODE EQUATIONS,
INPUT-OUTPUT TRANSMISSION CHARACTERISTICS