Gap Solitons Supported by Cosine Apodized Optical Lattices in Centrosymmetric Photorefractive Crystals

The study investigates optical spatial gap solitons in a photorefractive crystal with Kerr nonlinearity and an embedded photonic lattice, where the crystal is biased and centrosymmetric. The band structure of the photonic lattice is analyzed using the Floquet-Bloch theory. The photorefractive nonlinearity enables the formation of solitons within the photonic band gaps where light transmission is typically not allowed. The soliton solutions are obtained by solving the paraxial Helmholtz equation with the Bloch wave solution, resulting in single hump and double hump solitons in each forbidden band gap. The soliton width and intensity vary depending on the frequency and location within the band gap. The stability of these solitons is studied through the Vakhitov-Kolokolov criterion and numerical techniques.