Space-Charge Wave Effects in Photorefractive Materials

Abstract

This chapter provides the first systematic description of the basic properties of low-frequency space-charge waves (SCWs) in photorefractive materials, and the effects caused by these weakly damped eigen-modes. The basic properties incorporate the dependences of the wave frequency and damping on the wavevector, and the restrictions on the material parameters necessary to ensure weakness of the wave damping. The unifying feature of the SCW effects is their resonant character. These effects include the known DC and AC enhancement of the photorefractive response (treated as the linear resonance), the subharmonic generation (treated as parametric excitation of SCWs), the low-frequency peculiarities of the nonlinear response, and also a number of effects caused by the joint action of the optical and material nonlinearities. While an exposition of the concepts lies at the center of this chapter, it also gives a review of experimental studies relevant to the subject matter and a historical sketch.

Feedback-Controlled Photorefractive Beam Coupling

“…with G 0 ¼ E 0 The dependence G(V) exhibits a resonant behavior [35,42]. When V v K , the rate coefficient G becomes real and its value is enhanced by a factor of Q ¼ jv K j=g K ) 1 as compared to the value relevant to the static case (V ¼ 0).…”

“…In certain special cases, it possesses a relatively large imaginary part which means the presence of weakly-damped space-charge waves [34,35,41]; Eq. (6.7) can be restricted there to the values of light contrast m ( 1.…”

“…The upper and lower signs correspond to the photo-excitation of electrons and holes, respectively. For many fast PR materials (including the sillenites) and the transmission case, it will be sufficient to set F ¼ ÀE 0 À iE D and t À1 r ¼ g K À iv K , and accept that jv K j ) g K within a certain range of E 0 and K. This range is relevant to the presence of weakly damped space-charge waves [35,41] and to the resonant enhancement of the PR response [2,42]. The necessary relations for the reflection geometry can be found in Section 6.5.3.…”

“…The resonant response: This case is relevant to the sillenite crystals [2,35]. The actual values of the applied field E 0 are much higher here than E D (typically E 0 ¼ 6 À 10 kV=cm and E D &1 kV=cm) and t À1 r ¼ g K À iv K (see Section 6.3.1).…”

“…Second, we enter a new physical domain. The combination of the small grating periods with the possibility to apply extremely high electric fields (up to 650 kV/cm, see [33]) meets the condition for the resonant excitation of low-frequency eigen-modes (spacecharge waves) in slow PR materials like LiNbO 3 and LiTaO 3 [34,35]. Third, the diffraction efficiency cannot achieve here the ultimate value h ¼ 1 owing to counter-propagation of the interacting light waves.…”