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

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:


  1. 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]

  2. 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]