Origin of the lobe structure in photorefractive beam fanning

Abstract

We show that the three enigmatic lobes or petals observed in the far-field fanning pattern of photorefractive BaTiQ3 crystals are correctly predicted by considering the piezoelectric and photoelastic contributions of crystal deformations to the photorefractive nonlinearity.PACS number(s): 42.65. Hw, 42.40.Pa, 77.65.j, 78.20.e A laser beam passing through a photorefractive medium spreads into a filamenting fan of light that arises from stimulated scattering [l]. This beam fanning is seen on one hand as an impediment to practical applications of photorefractive materials such as holographic storage, yet on the other hand it is the progenitor of such remarkable phenomena as self-pumped and mutual phase conjugation.Beam fanning is a hallmark of photorefractive nonlinearity whose qualitative physics is well understood: It consists of amplification of low-intensity spatially broadband light scattering by the primary beam as they both propagate through the medium. Roughly speaking, fanning intensity if large in a direction for which two-beam coupling gain between the primary beam and a signal beam traveling in that direction is large. Figure 1 shows an often seen far-field fanning pattern in BaTi03. The incident laser beam is extraordinarily polarized and propagates along the crystal a or b axis. The fanning is a FIG. 1. Far-field intensity distribution of amplified scattered light (fanning) for a pumping beam {X=514nm) propagating through a photorefractive crystal of BaTi03 along the a axis.Both the pump and the fanning have extraordinary polarization. The crystal c axis points to the right. The pump beam is blocked by the dark spot in the middle; the power going into the petals is about 10%% of that of the transmitted pumping beam. three-lobed structure consisting of a central lobe in the positive direction of the crystal c axis and two symmetric side lobes or petals making angles of about 55 with the central one. Figure 1 therefore suggests that the gain in the three directions corresponding to the petals is large compared with other directions. Yet the three-lobed pattern is not predicted by textbook formulas [2]: only the central lobe is qualitatively correctly predicted, whereas the flanking petals are not. The standard approaches often fail with other geometries and crystals as well.In the standard models of photorefractive interactions, the structure of fanning is primarily buried in the electro-optic tensor and dielectric tensor. Values of these tensors measured under clamped (constant strain) or unclamped (constant stress) conditions are usually used. It has recently been shown that the mechanical consequences of the photorefractive space-charge field can be substantial [3 -8]. Fanning structure should therefore also reAect the nature of the elasto-optic and piezoelectric tensors as well as the electro-optic tensor and dielectric tensor.In this paper, we show that the interplay of electrical, mechanical, and optical efFects substantially alters the qualitative nature of beam fanning. In particular, we show tha...

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