Manakov solitons in photorefractive crystals with both the linear and quadratic electro-optic effects due to the two-photon photorefractive effect

We have first investigated Manakov solitons in biased two-photon photorefractive crystals in which refractive index changes are governed by both the linear and quadratic electro-optic effects simultaneously. Our results show that Manakov soliton pairs can be supported in all three possible realizations: dark-dark, bright-bright and dark-bright under steady-state conditions provided that the total intensity of the two mutually inherent beams is much lower than that of dark irradiance. It is also found that these Manakov solitons owe their existence to the co-effect of the linear and quadratic electro-optic effect where PR effect may be enhanced, weakened or even counteracted with each other. Moreover, the intensity full widths at half maximum of these Manakov solitons are inversely proportional to the square root of the quadratic polynomial of the external bias field, so the width can also be adjusted by altering the polarity besides changing the strength of the external biased field.