Single beam holographic grating recording, based on the photogalvanic coupling between orthogonal birefringent modes, is demonstrated in a photorefractive BaTiOa crystal.PACS numbers: 42.70.Nq, 42.25.Ja, In holography, two waves, signal and reference, are needed to record information about the phase and amplitude of the signal wave. This is normally accomplished using one optical beam for the signal wave and a separate beam for the reference wave.In this paper, we demonstrate both theoretically and experimentally the possibility of hologram recording using only one input beam, which is automatically split into two eigenmodes in a birefringent photogalvanic crystal. The interaction between the two orthogonally polarized eigenmodes, ordinary io) and extraordinary {e), in the crystal, via a photogalvanic current [1-5], then writes a holographic grating. This grating is subsequently read using the same single recording beam either in real time or at a later time. Consequently, the great advantage of this technique is that there are reduced restrictions on the coherence length and alignment of the incident laser light since the reference and signal beams are formed inside the crystal.The coupling between orthogonal waves inside the crystal is depicted in Fig. 1. An optical beam is incident onto a crystal at angle 0. The incident field then splits into two crystal eigenfunctions characterized by the ordinary and extraordinary wave vectors k^ and k^. In the region of overlap between the two eigenwaves in the crystal, a holographic grating is written. More formally, the electric field of the incident light in the crystal can be written as a superposition of quasiplane waves,where ?7J =^0)^ -k^-r and "5" is a sum over the ordinary and extraordinary crystal eigenmodes. In this expression, the birefringence of the photorefractive crystal is contained in the wave vector k^ and oy is the optical frequency of the incident field.The propagation of the electric field in the crystal is described by MaxwelFs wave equation:To take into account the fact that our coefficients of the expansion in Eq.(1) are time dependent we write the displacement vector asSubstituting Eqs. (1) and (3) into the wave equation, while making the slowly varying envelope approximation, we get an expression [6] for the wave amplitudes Q: (k, •¥)€,-1(0 2c ^ . 2 l(0 {5T>e ~''^'},^r {SeEe''"')t,r, (4) q = ko-ke nek' n.k^ zIlC FIG. 1. BaTiOs in crystallographic system of axes with kvector diagram.4330