Optical Parametric Amplification of Narrow Beams under Subdiffractive Propagation in Photonic Crystals

Parametric amplification of extremely narrow beams is problematic. Essentially there are two basic mechanisms limiting the gain of the optical parametric amplification of narrow beams (of the width of few wavelengths): (i) The first mechanism is the phase mismatch between the pump waves and spatial Fourier components of the narrow signal waves with different transverse components of the wavevector, which means that they (different transverse components) can never be simultaneously matched with- and amplified by the pump beam. This leads to the filtering of spatial Fourier components, which results in a diffusive spatial broadening of the signal beam, (ii) The second mechanism is the diffraction, working also without the parametric amplification (linear propagation). The narrow signal beams spread rapidly, which results in a diffractive broadening of the beam as a whole and thus its top intensity decreases during the propagation. In this communication we show that the two mechanisms mentioned above can be eliminated under non-diffractive (self-collimation) regimes of light propagation in the materials with refractive index periodically modulated in space, the so called photonic crystals. This leads to increasing of the efficiency of parametric amplification in such PCs with respect to the OPA in homogeneous materials. Here we study the degenerate OPA process under regimes of self-collimation of the narrow subharmonic beams when the two dimensional (2D) PCs structure is formed at subharmonic wavelength (but not at the pump one).