Enhanced frequency conversion in periodic structures

The study of wave propagation in periodic dielectric materials is essential to the development of various photonic devices such as distributed feedback lasers, Bragg grating filters, wavelength demultiplexers, and fiber based sensors. The transmission through a one-dimensional periodic structure is characterized by the appearance of stop bands when the Bragg conditions are satisfied. At frequencies close to the stop band, there is strong dispersion, and the fundamental field is larger than the fundamental field observed in a homogeneous medium of the same length. Introduced here is the concept of band-edge phase matching, when the fundamental frequency is close to the edge of the first stop band, causing the forward-backward wave coupling to be resonant, thus enabling enhanced frequency conversion. This is distinct from other forms of phase matching studied earlier, such as quasi-phase matching and birefringent phase matching. In quasi-phase matching the material periodicity is of the order of its coherence length, while in band-edge phase matching it is of the order of a wavelength. The analytical results obtained here using the method of multiple scales show that the use of band-edge phase matching can result in the enhanced conversion of both the second and third harmonics.