Spatial solitons in biased two-photon photorefractive crystals with both the linear and quadratic electro-optic effect

Incoherently coupled spatial soliton families in biased two-photon photorefractive crystals with both the linear and quadratic electro-optic effect

“…Similarly, when the incident optical beams contain only one component, Eq. 1are equivalent to that of the single soliton case already discussed previously [32] . Moreover, incoherently coupled dark-bright hybrid soliton families can be supported in our configuration when the peak values of the total intensity of bright beams and that of the dark ones are approximately equal.…”

“…Through numerical analysis we can get that dark soliton family due to two-photon effect is possible only when α 1 < −2α [32] 2 . In other words, such dark soliton families own their existence to both the linear and quadratic electro-optic term in the meantime.…”

“…However, some types of two-photon photorefractive materials that have large electro-optic effect, including both the linear and quadratic electrooptic effects near the phase-transition temperature have been found, such as ferroelectric KTa x Nb 1−x O 3 (KTN) crystals [29,30] , LiNbO 3 single crystals [15,25,31] and so on. Very recently, we have demonstrated that photorefractive spatial solitons can also be supported in biased two-photon photorefractive crystals involving both the linear and quadratic electro-optic effect in steady-state regime [32] . Study on photorefractive soliton pairs and soliton families have been gradually developed [33−35] .…”

“…Only the one-dimensional nonlinear diffraction will be taken into account in our configuration by assuming that the variables vary much more rapidly in the x direction. In the steady-state regime, the envelopes U i of the N beams then satisfy the following dynamical evolution equations [32] :…”

“…Through numerical calculation we can conclude that Eq. (6) can support bright solitons only when α 1 > −α 2 /6 [32] . It is easy to see that the sign of α 1 and α 2 also can be different by altering the polarity of the external bias electric field as long as α 1 > −α 2 /6, which is quite different from the cases presented previously.…”