Dispersive properties of a truncated 1-dimensional photonic crystal

Crina Cojocaru, Jordi Martorell, and R. Vilaseca
Universitat Politècnica de Catalunya, Departament de Física i Enginyeria Nuclear,
08222 Terrassa (Barcelona), SPAIN
E-mail: jordi.martorell@upc.es

In recent years, nonlinear interactions between light and matter have been considered in photonic crystals of one-, two- or three-dimensions. The particular dispersive behavior of the index of refraction of these type of structures [1], may lead in certain configurations to a phase matching mechanism that makes this type of materials of great interest for designing optical systems based on the quadratic nonlinear interaction [2]. In photonic crystals with a low contrast between the indexes of refraction of the layers, the phase matching condition is achieved both inside and just outside of the gap [2,3].

However, in a periodic quarter-wave structure with a high contrast between the refractive indexes of the layers, resonant at the fundamental or SH wavelengths, the phase matching condition is achieved only inside of the gap. In principle, this type of photonic crystals can not be used since either the fundamental or the SH can not propagate through the structure. However, if a defect is introduced in such type of structure, the light at the frequency of the defect can propagate through the structure and then phase matching between the two waves is possible.

In the present paper, we consider a truncated 1-D photonic crystal, made by two l0/4 multiple stack of dielectric layers, highly reflecting at the fundamental wavelength (l0) and separated by a defect filled with a nonlinear material. This defect introduces within the Bragg reflection band a high transmission resonant state at l0 ,with an index of refraction that coincides with the index of the SH field. When an intense SH field is send simultaneous to a weak fundamental field, the cascaded nonlinear interaction can strongly modify the dispersion curve w (k) at the fundamental frequency resulting in a change of both the effective index of refraction (phase velocity) as well as the slope of the dispersion curve (group velocity) in the neighborhood of the resonant state. The later change, that can only by obtained in structures with a high modulation of the index of refraction, is the main responsible for the active change induced by the presence of the SH in the reflectivity of the fundamental beam on a this type of structure. For certain conditions of input phase difference between the two incident beams, this slope increase at wavelengths near the resonant state may lead to an induced reflectivity changes that can be from 0% when the SH is turn off up to 90% when the SH is turn on [4].

[1] I.Inanç Tarhan, Martin P. Zinkin and George H. Watson, Optics Lett. 20 1571 (1995)
[2] Jordi Martorell, R. Corbalan, Optics Comm. 108, 319 (1994)
[3] Jordi Martorell, R. Vilaseca, R. Corbalan, Appl. Phys. Lett. 70, 702 (1997)
[4] Crina Cojocaru, Jordi Martorell, R. Vilaseca, J. Trull and Eugenio Fazio, Appl. Phys. Lett. 74, 504 (1999)