Eur. Phys. J. B 24, 323-326 (2001)
https://doi.org/10.1007/s10051-001-8681-6

Nonlinear frequency conversion in 2D x⁽²⁾ photonic crystals and novel nonlinear double-circle construction

¹ Institute of Physics, Academia Sinica, PO Box 603, Beijing 100080, PR China
² CCAST (World Laboratory), PO Box 8730, Beijing 100080, PR China and Institute of Physics, Academia Sinica, PO Box 603, Beijing 100080, PR China

Corresponding author: ^a guby@aphy.iphy.ac.cn

Received: 19 April 2001
Published online: 15 December 2001

Abstract

The analytic solution to the wave equation for small-signal sum-frequency process is derived in 2D x⁽²⁾ photonic crystals with use of the Green function method. It is predicted that the sum-frequency electrical field at quasi-phase matching (QPM) resonance is proportional to the angle-dependent effective crystal length. This implies that multiple wavelength QPM frequency conversion with controllable intensity output can be realized in a single 2D x⁽²⁾ photonic crystal. It is revealed that efficient frequency conversion requires both the QPM and the proper structure matching. A novel double-circle construction, different from the conventional Ewald construction, is presented to reflect important QPM processes. It is also shown that the QPM resonance tuning of second-harmonic generation can operate over the whole transparent wavelength range of crystals.