Sum frequency generation in photonic crystals

Lasha Tkeshelashvili and Kurt Busch

Institut für Theorie der Kondensierten Materie,
Universität Karlsruhe,
76128 Karlsruhe, Germany

Progress in photonics is closely connected to the development of optical materials with tailor made properties. In the context of nonlinear optical phenomena, Photonic Crystals (PCs) carry this principle to a new level in that the tailoring of the dispersion relation and mode structure allows to explore regimes for parameters such as group velocities, group velocity dispersion and effective nonlinearities which have hitherto been virtually inaccessible.

Any succesfull experimental exploration of the huge parameter space provided by PCs has to be accompanied by a quantitative theoretical analysis in order to identify the most interesting cases and to help interpret the data. To date, only a few works along these lines has been carried out for either Kerr-nonlinearities [1] or sum-frequency and second harmonic generation [2]. Moreover, the approximations involved seriously limit the applicability of these theories to real PCs. For instance, the study of Kerr-nonlinearities in two-dimensional PCs [1] has been limited to the nearly free photon case, i.e., weak modulations in the linear index of refraction. Similarly, the recent investigation of second harmonic generation in two-dimensional PCs [2] failed to reproduce the well-known results for the limiting case of a homogeneous material.

In this presentation, we will apply the multi-scale analysis to the case of sum-frequency generation in two-dimensional PCs and discuss some of the most interesting results. In particular, we show how the PC allows to access experimentally a parameter range that has been considered theoretically by Zakharov [3]. For instance, as there are no stable soliton solutions in two dimensions, a two-dimensional PC would allow the complete radiation conversion from one wavelength to another through nonlinear interactions. This may have important applications for wavelength shifters in telecommunication technology.


  1. N. Aközbek and S. John, Phys. Rev. E 57, 2287 (1998).
  2. K. Sakoda and K. Ohtaka, Phys. Rev B 54, 5742 (1996).
  3. A. Zakharov, Sov. Phys. Dokl. 21, 322 (1976).