Origin of Gap Solitons in Gaussian Apodized Centro-Symmetrical Non-linear KLTN Lattices

Optical spatial gap solitons are investigated in biased centrosymmetric photorefractive media exhibiting the Kerr nonlinearity with an embedded photonic lattice. A Gaussian apodized lattice is considered and the photonic lattice band structure is found using the Floquet-Bloch theory. The photorefractive nonlinearity enabled the formation of soliton inside the photonic band gaps where usually transmission of light is forbidden. The paraxial Helmholtz equation is solved along with the Bloch wave solution to obtain the soliton states in both band gaps. We observe, for the first time, various types of soliton solutions, i.e., single hump, double hump, and multi hump in both the band gaps. A detailed investigation has been conducted on the existence and properties of the gap solitons. The stability of the spatial gap solitons against linear perturbations is examined by utilizing both numerical techniques and the Vakhitov-Kolokolov criterion.