TY - JOUR
T1 - Illumination-dependent densities of modes in non-linear photonic crystals
AU - Vigneron, Jean-Pol
AU - Lousse, Virginie
PY - 2002
Y1 - 2002
N2 - When the unit cell of the photonic crystal contains material which undergoes an optical Kerr effect, internal illumination will change the refractive index distribution without modifying the crystal periodicity and induce significant modifications of the dispersion relations. We describe these modifications by a self-consistent computation of the band structure where the occupation of a photon mode with specific frequency, Brillouin-zone vector and polarization is kept fixed. This requires to solve a sequence of ordinary, linear, photonic band structure problems. The resulting non-linear photonic band structure explicitly depends on the mode occupation, itself determined by the level of illumination. We carry out specific non-linear band structure calculations for the woodpile structure where rods are considered experiencing refractive index changes according to various types of illumination. It is shown that, for positive Kerr coefficient, a strong illumination moves the photonic band gap to lower frequency while slightly modifying its width. The use of different illumination polarizations and frequencies results in modifications of the band structure and the spectral location of the Van Hove singularities in the density of states.
AB - When the unit cell of the photonic crystal contains material which undergoes an optical Kerr effect, internal illumination will change the refractive index distribution without modifying the crystal periodicity and induce significant modifications of the dispersion relations. We describe these modifications by a self-consistent computation of the band structure where the occupation of a photon mode with specific frequency, Brillouin-zone vector and polarization is kept fixed. This requires to solve a sequence of ordinary, linear, photonic band structure problems. The resulting non-linear photonic band structure explicitly depends on the mode occupation, itself determined by the level of illumination. We carry out specific non-linear band structure calculations for the woodpile structure where rods are considered experiencing refractive index changes according to various types of illumination. It is shown that, for positive Kerr coefficient, a strong illumination moves the photonic band gap to lower frequency while slightly modifying its width. The use of different illumination polarizations and frequencies results in modifications of the band structure and the spectral location of the Van Hove singularities in the density of states.
U2 - 10.1117/12.463882
DO - 10.1117/12.463882
M3 - Article
SN - 0277-786X
VL - 4655
JO - Proceedings of SPIE - The International Society for Optical Engineering
JF - Proceedings of SPIE - The International Society for Optical Engineering
ER -