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Beam coupling, bistability, and commutative and noncommutative behavior of self-pumping beams in BaTiO3

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Abstract

BaTiO3 crystal is self-pumped by coherent beams A1 and A2 from a multilongitudinal-mode Ar+ laser. The self-pumped A1* and A2* with a 4800-Å laser showed oscillations whose frequency increases with laser intensity. They are bistable and do not coexist. With 5145 and 4765 Å, A1* and A2* coexist and are stable with minor coherent pulsations. When coexisting, A2* and A1* are strong with a 5145-Å laser while they are very weak with 4765 Å. A mutually consistent fanning occurs so that a component of each fanned beam (A1 and A2) is incident on the other beam’s grating at the correct Bragg angle to undergo total internal reflection and get into the reverse direction of the other. Thus when A1 is shut off the detector D2 of A2* shows a sharp intensity drop and similarly the D1 of A1*, when A2 is off. The counterparts of the images at D1 and D2 are seen outside the crystal between the outgoing directions of A1 and A2. When the beams A1, and A2 with 5145 Å are incoherent, the sequence A1 + A2 does not commute with A2 + A1.

© 1987 Optical Society of America

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