Theoretical analysis of two-step holographic recording with high-intensity pulses

Abstract

We develop a full numerical as well as an approximate analytic solution for two-step holographic recording with high intensity pulses in LiNbO3 :Fe crystals. We find the unknown material parameters by fitting the numerical solution to the experimental results. The two important parameters that were unknown so far and found in this work are the bulk photovoltaic coefficient and absorption cross section for the excitation of the electrons from small polarons in LiNbO3 with infrared light. We show that the approximate analytic solution agrees very well with the numerical solution ~as well as the experimental results! for most practical applica- tions. We use the analytic solution to explain the experimental observations that were not understood before. Photorefractive crystals are excellent candidates for vol- ume holographic storage @1-3#. A major obstacle in making practical read/write holographic memory systems has been nonpersistence ~or destructive readout! of the stored informa- tion. Thermal fixing@4# and electrical fixing @5# are the two major nonoptical methods for obtaining persistence. How- ever, they require heating the sample or applying large elec- tric fields. All-optical methods for persistent holographic re- cording include frequency-difference holograms @6#, readout with wave-vector spectra @7#, and gated recording @8,9#. Among all the methods proposed, gated recording is the most promising one for obtaining persistent read/write holo- graphic memories. Gated holographic recording relies on the existence of two sets of traps ~shallower and deeper traps! with energy levels in the band gap of the recording crystal. These traps can be due to doping by impurities ~for example, LiNbO3 :Fe:Mn crystals @9#! or ~at least one set of traps! can be due to intrinsic traps @8 #~ polarons, bipolarons, etc.! .W e refer to recording using the former as ''two-center record- ing'' and to that using the latter as ''two-step recording,'' since intrinsic defects can occur in a very high concentration enabling direct charge transfer between the shallower and the deeper traps. Recording is performed by the simultaneous presence of a sensitizing ~or gating! beam of shorter wave- length ~higher photon energy! and two recording beams of longer wavelength ~lower photon energy!. Electrons are ini- tially in the deeper traps ~shallower traps are initially empty!. Sensitizing light causes the electron transfer from the deeper traps to the shallower traps. The hologram is recorded by the recording beams using the electrons from the shallower traps. The final hologram is imprinted in the deeper traps, and persists against readout with the light of longer wave- length ~same as recording wavelength!. In this paper, we mainly consider two-step holographic recording in LiNbO 3 :Fe crystals with green pulses for sensitization and infrared pulses for recording. Most of the initial two-step holographic recording experi- ments were performed with high intensity pulses in congru-