Two-photon Photorefractive Crystals Research Articles

Coupling of separate solitons in a series circuit of two photon photorefractive crystals exhibiting simultaneous quadratic and linear nonlinearities

Separately coupled optical spatial solitons are shown to exist in a biased series two-photon photorefractive(TPPR) crystal circuit consisting of two TPPR crystals which have the quadratic and linear electro-optic(EO) effect present simultaneously. The space charge field in each photorefractive(PR) crystal in the circuit has been derived. We find that the space charge field in each crystal is coupled with the space charge field in the other crystal. We consider the cases of separately coupled bright, dark and grey solitons and obtain the numerical solutions for the spatial solitons’ profile. The coupling effect due to the soliton peak intensity in each crystal and the gating beam intensity is studied in detail. The light induced current causes a change in the spatial profile of the dark or grey soliton in one of the crystal which results in a change in the spatial profile and propagation of the soliton in the other crystal. We also find that the bright soliton intensity in one crystal does not affect the soliton in the other crystal. A change in the gating beam intensity in one crystal influences the soliton in the other crystal and this is true for all the three cases of dark, grey and bright separate soliton pairs.

Coherently coupled screening spatial soliton pairs due to the two-photon photorefractive effect

A theoretical study of coherently coupled spatial soliton pairs propagating along the same line in biased two-photon photorefractive crystals is presented. Our results show that coherently coupled bright–bright and dark–dark soliton pairs propagating collinearly can be supported in a steady-state regime under appropriate conditions. Moreover, the effects of the intensity ratio, the initial phase difference between two incident coherent beams, and various external bias fields on the existence conditions and properties of these soliton pairs have been discussed in detail. The stability of these soliton pairs has also been discussed by means of beam propagation methods. Finally, the temperature dependence of the dark irradiance and diffusion process on the intensity profiles and self-deflection of coherently coupled bright–bright soliton pairs are also analyzed.

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.

双光子光折变介质中基于两种电光效应的相干耦合孤子对

双光子光折变介质中基于两种电光效应的相干耦合孤子对

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

Different from the cases discussed preciously, nonlinear changes of refractive index in the photorefractive materials are influenced by both the linear and quadratic electro-optic effect simultaneously now. Here we present the evolution equations of one-dimension incoherently coupled spatial soliton families due to two-photon effect in biased photorefractive crystals with both the linear and quadratic electro-optic effect and discuss their existence conditions and properties in detail. Our analysis indicates that these soliton families can exist in all three possible realizations: dark-dark, bright-bright and dark-bright provided that the incident beams have the same polarization, wavelength and are mutually incoherent. Finally, the stabilities of these soliton families have been discussed by means of beam propagation methods.

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

Abstract The evolution equation of one-dimension spatial optical solitons resulting from two-photon effect in biased photorefractive crystals with both the linear and quadratic electro-optic effect is presented theoretically. Under appropriate conditions, our analysis indicates that bright, dark photorefractive spatial solitons can exist in the steady-state regime. The analytical solutions in the low amplitude regime are also obtained. Moreover, we theoretically discuss the self-deflection of bright solitons by taking the diffusion effect into account. Both the self-deflection effects follow a cubic polynomial of the applied bias field, and increase considerably at higher values of applied bias field. Relevant examples are provided.

Effects of temperature on the dynamic evolution of two-photon photorefractive screening spatial solitons

We investigate theoretically the temperature effects on the evolutions of both bright and dark screening spatial solitons in biased two-photon photorefractive crystals. For a stable bright or dark two-photon screening spatial soliton originally formed in a crystal at a given temperature, when the crystal temperature changes, it will evolve into another stable screening soliton if the temperature change is quite small, while it will become unstable or break down if the temperature change is large enough. The spatial shape of a stable two-photon screening spatial soliton can be changed by appropriately adjusting the crystal temperature.

Incoherently coupled spatial soliton families in centrosymmetric two-photon photorefractivecrystals

It is shown theoretically that incoherently coupled dark, bright and bright–dark hybridsoliton families can exist in centrosymmetric two-photon photorefractive crystals understeady-state conditions. These soliton families can be established provided that theincident optical beams share the same polarization and frequency, and are mutuallyincoherent.

双光子光折变晶体中两分量矢量空间孤子

To study the vector spatial solitons in biased two-photon photorefractive crystals, the dynamical evolution equation and the numerical solution of the vector spatial solitons are established. The bright-bright and dark-dark self-coupled vector solitons are predicted by using numerically methods. The dynamical evolutions of the bright-bright self-coupled vector spatial solitons are analyzed numerically. The results indicate that these self-coupled vector solitons can be obtained by using simple numerical integration procedures and their formation are irrespective to the ratio of the intensities of the two optical components. The bright-bright and dark-dark self-coupled vector spatial solitons exist steadily in two-photon photorefractive crystals.

External field-controlled photovoltaic symbiotic spatial soliton pairs in two-photon photorefractive crystals

We report the existence of incoherently coupled bright–bright steady state photovoltaic (PV) soliton pairs in biased two-photon photorefractive (TPPR) materials that arise due to the TPPR effect. A remarkable finding is that, with the application of electric field, it is possible to generate solitons and control them in such media, where soliton formation was actually prohibited hitherto. The present analysis indicates the existence of a plethora of bright–bright soliton pairs with dynamical properties controllable by the application of an external electric field of appropriate polarity and magnitude. We have identified two different power regimes in which the effect of external electric field is opposite. We have undertaken linear stability analysis which shows that these solitons are stable.

Steady-state bright–dark vector spatial solitons in biased two-photon photorefractive crystals

We show that bright–dark vector solitons are possible in biased two-photon photorefractive crystals under steady-state conditions. The analytical solutions of these vector solitons can be obtained if the intensities of the two vector components are approximately equal. When the intensities of the two vector components differ, the vector soliton pair solutions can be determined using simple numerical integration procedures. The stability of the bright–dark vector solitons has been investigated numerically.

Separate spatial soliton pairs in an unbiased series two-photon photorefractive crystal circuit

Dark (bright) steady-state spatial solitons are predicted in one dimension for a series circuit consisting of two two-photon photorefractive crystals of which at least one must be photovoltaic. Each crystal can support a spatial soliton. The two solitons are known collectively as separate spatial soliton pairs with three types: dark–dark, bright–dark and bright–bright. In the limit in which the optical wave has a spatial extent much less than the width of the crystal, the dark soliton can affect the other soliton by light-induced current, but the bright soliton cannot affect the other soliton in the soliton pair.

Incoherently coupled spatial soliton pairs in two-photon photorefractive media

The coupling of two mutually incoherent optical beams with the same polarization and wavelength in two-photon photorefractive crystals is studied. It is shown that incoherently coupled dark-dark, bright-bright, and bright-dark soliton pairs are possible due to two-photon photorefractive effect.