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Physical Review A

Coherent optical oscillator with periodic zero- π phase modulation

Aleksandr Shumelyuk, A. Hryhorashchuk, Serguey G. Odoulov

Published Aug 22, 2005• 18 citations
Publisher

Abstract

The four-wave-mixing coherent optical oscillator is described, which is emitting light wave with regular alternation of its phase between two discrete values zero and $\ensuremath{\pi}$. Such a periodic self-modulation is a consequence of competition of photorefractive gratings formed by movable charge species of two different signs. The period of modulation depends on overthreshold coupling strength and on decay time of slow photorefractive grating. It falls to few seconds range for ${\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ crystals at ambient temperature but it can go down to microsecond range for photorefractive semiconductors.

DOI
10.1103/physreva.72.023819

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The four-wave-mixing coherent optical oscillator is described, which is emitting light wave with regular alternation of its phase between two discrete values zero and \ensuremathπ\ensuremath{\pi}\ensuremathπ. Such a periodic self-modulation is a consequence of competition of photorefractive gratings formed by movable charge species of two different signs. The period of modulation depends on overthreshold coupling strength and on decay time of slow photorefractive grating. It falls to few seconds range for Sn2P2S6{\mathrm{Sn}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}Sn2​P2​S6​ crystals at ambient temperature but it can go down to microsecond range for photorefractive semiconductors.
Periodic anharmonic modulation of output intensity is studied for semilinear coherent oscillator with photorefractive crystal that possesses two types of movable charge carriers. The pulse amplitude and modulation frequency are shown to depend considerably on grating spacing of photorefractive grating. We calculate these dependences within the model proposed earlier [A. Shumelyuk, A. Hryhoraschuk, S. Odoulov, Phys Rev. A, 72, 023819 (2005)] and show satisfactory agreement with the experimental data.
The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the pi /2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included.>
Two-wave mixing in photorefractive crystals has been shown to combine coherently a modulated optical signal beam with a strong pump optical field.’ For a phase-modulated signal beam, the induced index of refraction phase grating inside the crystal yields a coupling of the optical fields of the pump and signal so that subsequent intensity detection results in apparent intensity modulation of the transmitted signal or pump beams. This provides an easy way to detect phase differences between two optical beams. Some of the advantages the above scheme offers over commonly used coherent optical phase detection schemes are: no loss of 3 dB in the signal beam intensity at the 50/50 beam splitter (used to combine signal and local oscillator fields); automatic alignment of the index of refraction grating with the two incident optical wavefronts; insensitivity to slow random changes in the phases of both beams. Experimental results are given, and a new definition for the resulting mixing gain for the phase-modulated beam is introduced, through which optimal conditions for input beam intensity ratios can be found. Applications to coherent homodyne detection are discussed.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.