Abstract:
In this work, we were interested in the marriage of nonlinear optics and the photonic crystals onedimensional
(1D) and two-dimensional (2D) in semiconductor III-V. The dispersive properties of the
photonic crystals 1D and 2D are made profitable to generate effectively a wave second harmonic with
the wavelength 775nm starting from a wave fundamental with 1.55μm. During this work, numerical
tools based on the method of Finite-Difference Time-Domain (FDTD) and of the analytical methods
were developed to calculate the effectiveness of conversion of SH in arbitrary two-dimensional
structures. This enabled us to show that the photonic crystals (CPs) 1D engraved deeply in waveguides
ribbons with weak contrast of index of the type Al0.3Ga0.7As/Al0.5 Ga0.5 As are promising to obtain
effective nonlinear interactions on very short distances. By fixing the structural parameters to obtain the
condition of phase-matching and a guidance of the fundamental waves (F) and second harmonic (SH)
with weak losses, outputs of about 5% can be reached at distances as short as 5μm. These numerical and
analytical tools also have allowed us to undertake studies on the generation of SH in CPs 2D. We could
see that the condition of phase-matching can be satisfied in CPs 2D perfectly periodic and in the
waveguides consisting of a line of holes removed in a CP 2D triangular lattice of holes. In the last case,
although one benefits from a better containment of the light than in the case of the structures 1D, the
calculated outputs of conversion are lower because the covering of the modes at the frequencies F and
SH is not very good and the velocity of group of the waves being propagated at the frequencies F and
HS are not low. In the case of the structures without defect, we saw that the output of conversion
strongly depends on the coupling to the photonic modes and the velocity of group of these modes
