Nonlinear localized modes in photonic crystals and photonic
crystal waveguides
Sergei F. Mingaleev
and
Yuri S. Kivshar
Nonlinear Physics
Group,
Research School of Physical Sciences and Engineering,
The Australian National University,
Canberra ACT 0200, Australia
Rowland A. Sammut
School of Mathematics and
Statistics,
Australian Defence Force Academy, University of New South Wales, Australia
ABSTRACT:
Photonic crystals are usually viewed as an optical analog of
semiconductors that modify the properties of light similarly
to a microscopic atomic lattice that creates a semiconductor
band-gap for electrons. It is therefore believed
that by replacing relatively slow electrons with photons as
the carriers of information, the speed and band-width of
advanced communication systems will be dramatically
increased, thus revolutionizing the telecommunication
industry. However, to employ the high-technology potential of photonic
crystals, it is crucially important to achieve a dynamical
tunability of their properties. This idea can be realized by changing
the light intensity in the nonlinear photonic
crystals.
Here, we develop the theory of nonlinear localised modes in two-dimensional
photonic crystals and photonic-crystal waveguides.
We demonstrate that such nonlinear localised modes can be accurately
described by a new type of discrete nonlinear Schroedinger equation with
long-range interactions.
Using this approach, we consider different geometries of the photonic-crystal
waveguides created by an
array of nonlinear dielectric rods embedded
into an otherwise perfect linear two-dimensional photonic crystal;
we reveal the existence of different types of nonlinear guided mode
and describe their unique properties, including bistability.
We also predict stabilisation of the two-dimensional nonlinear localised
modes near the band edge of a reduced-symmetry
photonic crystal with a Kerr nonlinearity.
More information about our research on nonlinear photonic crystals can be found on the page:
http://wwwrsphysse.anu.edu.au/nonlinear/research/photonic
References:
-
Self-trapping and stable localized modes in nonlinear photonic crystals
S. F. Mingaleev and Yu. S. Kivshar,
Phys. Rev. Lett. 86, 5474-5477 (2001).
[Abstract]
[Full-text PDF (231 Kb)]
[Online]
-
Long-range interaction and nonlinear localized modes in photonic crystal waveguides
S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut,
Phys. Rev. E 62, 5777-5782 (2000).
[Abstract]
[Full-text PDF (588 Kb)]
[Online]