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Annual Meeting Optical Society of America

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

Putcha Venkateswarlu, H. Jagannath, M. C. George, Alan Miahnahri

Published Jan 1, 1987• 0 citations

Abstract

BaTiO3 crystal is self-pumped by coherent beams A1 and A2 from a multilongitudinal-mode Ar+ laser. The self-pumped A 1 * and A 2 * 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, A 1 * and A 2 * coexist and are stable with minor coherent pulsations. When coexisting, A 2 * and A 1 * 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 A 2 * shows a sharp intensity drop and similarly the D1 of A 1 * , 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.

DOI: 10.1364/oam.1987.mf3

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BaTiO3 crystal is self-pumped by coherent beams A1 and A2 from a multilongitudinal-mode Ar+ laser. The self-pumped A 1 * and A 2 * 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, A 1 * and A 2 * coexist and are stable with minor coherent pulsations. When coexisting, A 2 * and A 1 * 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 A 2 * shows a sharp intensity drop and similarly the D1 of A 1 * , 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.

Optical bistability and hysteresis in BaTiO3 have been observed in a self-pumped ring resonator (SPRR). The SPRR can be controlled with an additional He–Ne laser erasing beam that makes an angle with the ring pump beam. The erasing beam could be coherent or incoherent with the pump beam. By injecting the erasing beam into the crystal in such a way as to partially erase the index grating and/or take energy from the pump beam, the coupling strength is modified. In either case, the output of the ring shows bistability and hystersis in the complete cycle of the on-off-on operation by monitoring the intensity of the erasing beam. The intensity change and the time interval between each change step of the erasing beam have effects on the hysteresis behavior. The hysteresis observed when it is controlled by a coherent erasing beam is more than the one by an incoherent erasing beam. Some fluctuations exist in the hysteresis loop when the coherent erasing beam is used.

We report our observations of optical bistabilities and hysteresis1 in photorefractive passive phase conjugate resonators with BaTiO3, caused by grating erasure effects between two resonators in three different configurations. Bistable oscillations have been observed between two semilinear oscillators, two ring resonators, and also between a ring and a semilinear resonator. In the experimental arrangement used for bistability studies, a single-mode argon ion laser beam (4880 Å) entered the crystal in a face appropriate for self-pumped phase conjugation. However, the orientation is kept in such a way that no self-pumped phase conjugation is observable if none of the resonators is in operation. In this geometry, bistability and hysteresis were observed in the signal intensity of one resonator as the reflectivity of the variable beam reflector in the second resonator was increased and then decreased in a cycle. Bistability was also seen in the signal intensity of a single resonator as a function of the reflectivity of the external mirror.

Bistable oscillations have been observed in BaTiO(3) pumped by a single-mode 30-mW (488-nm) argon-ion laser, which is used simultaneously as a ring passive phase conjugator (RPPC) and as a unidirectional ring resonator (UDRR). Strong oscillations in the UDRR increase the threshold coupling strength required for oscillation in the RPPC. The oscillations in the RPPC reduce the fanning in the crystal necessary for the startup of oscillation in the UDRR. Auxiliary resonators pumped by the RPPC are also bistable with the UDRR. Similar bistable oscillations have been observed when the crystal is used simultaneously as a RPPC and as a linear passive phase conjugator.

When two mutually incoherent light beams are used as simultaneous inputs to a crystal of BaTiO(3), a spontaneously generated loop of light is created that provides a coupling mechanism between the two input beams, resulting in two phase-conjugate outputs. This behavior is discussed, and the phase-conjugate reflectivities are presented as a function of the ratio of input-beam intensities. A simple theory is developed to describe this phenomenon, and the predictions are compared with experimental data.

Kwang and Yariv(1) used a single domain BaTiO3 crystal to form a ring passive phase conjugator (RPPC) and auxiliary resonators pumped by a multi-mode Ar+ laser at 4880Å. The auxiliary resonators were bistable. Jagannath et. Al(2) from this laboratory, reported the operation of a unidirectional ring resonator (UDRR) in addition to the RPPC and found bistability between the two. They also observed a linear passive phase conjugator (LPPC) which is bistable with the RPPC. It was found that auxiliary oxci nations between the crystal and a mirror are bistable separately with the UDRR and the LPPC.