Temporal instabilities in single-grating photorefractive four-wave mixing

Błędowski, A.; Królikowski, Wiesław; Kujawski, Adam

doi:10.1364/josab.6.001544

Cited by 32 publications

(17 citation statements)

References 13 publications

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“…For the case in which yl is real, the steady-state analysis predicts no self-oscillation.' 8 Our present analysis, however, shows unstable regions. The minimum coupling coefficient that will give instability is lyll = 2v when r = exp(± 7-).…”

Section: Io Iocontrasting

confidence: 54%

“…Cronin-Golomb and co-workers 5 6 extended this treatment to include time-varying signals with arbitrary Fourier frequency components. Other studies in 4WM were undertaken by Papen et al and Zozulya et al 7 and by Bledowski and co-workers, 8 and in 2WM they were performed by Feinberg and Anderson 9 and others. 1 0 l" More recently, Vachss 2 calculated the grating buildup for the 2WM process and obtained a de-pendence of the grating buildup on the coupling constant.…”

Section: Introductionmentioning

confidence: 98%

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Time-dependent behavior of photorefractive two- and four-wave mixing

1991

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A theoretical and experimental study of the temporal response of photorefractive two-and four-wave mixing processes is given. We examine the buildup and the decay of the output signal and the gratings when the input signal beam is turned on and off. For two-wave mixing we have performed an analysis that includes the depleted-pump regime. The experiment was done with a BaTiO 3 crystal. The buildup-and-decay behavior is strongly dependent on the coupling constant and the ratio of the signal and pump intensities. From these measurements we obtain the crystal time constant, which was found to have an intensity dependence with a power of-0.7. The coupling constant is extracted from the data of the whole dynamic process of buildup and erasure and not only from the steady-state point, as is usually done. This is the first analytic study, to the best of our knowledge, for the four-wave mixing decay and buildup. We find that the solution for time-dependent fourwave mixing processes (the phase-conjugate mirror and the double phase-conjugate mirror) with undepleted pumps is identical to that for two-wave mixing with unidirectional optical feedback circuits. This similarity provides a direct way to study the stability properties of the devices. We find, for example, that in the unstable regime of four-wave mixing a self-pulsation of the output corresponds to the frequency detuning of the unidirectional two-wave mixing oscillator.

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Section: Io Iocontrasting

confidence: 54%

Section: Introductionmentioning

confidence: 98%

Time-dependent behavior of photorefractive two- and four-wave mixing

1991

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“…= n 43 π, s 43 = (−1) n 43 , I m = 1 2 e i(ϕ e − π/2) f 2 12 sin 2(u − C 12 ) − f 2 43 sin 2(u + C 43 ) , n 12 , n 43 ∈ Z, (9) in terms of the real solution u of a damped sine-Gordon equation [18,4,5],…”

Section: Introductionmentioning

confidence: 99%

Explicit solutions of the four-wave mixing model

Conte¹,

Bugaychuk²

2009

J. Phys. A: Math. Theor.

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The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lowerdimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painlevé test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time τ , the complex response constant γ. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (ℜ(γ) = 0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (ℜ(γ) = 0), we display strong similarities with the cubic complex Ginzburg-Landau equation.

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“…The non-steady-state FWM in a medium with a nonlocal response is described by the following system in the approximation of slowly varying amplitudes of plane waves [1][2][3][4][5]16]:…”

Section: The Determination Of the Dynamic Grating Structurementioning

confidence: 99%

“…In spite of many years' study of FWM, some of its features are still unexplained, such as many-valued solutions and bistability occurring in a photorefractive medium with a strong response [1,2,[6][7][8][9]; a clear definition of ranges of interaction parameters, in which there are oscillations and the chaotic of output wave intensities [10][11][12][13][14][15][16]; the influence of input intensity ratio on the value of FWM diffraction efficiency [17] and experimental observation of instabilities for output waves [18,19]. All these are factors which limit the applications of FWM in photorefractive media.…”

Section: Introductionmentioning

confidence: 99%

Analytical Description of Partially Coherent Optical Systems for Optimization of Numerical Aperture and Degree of Coherence

Watanabe

1994

Jpn. J. Appl. Phys.

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Recording of localized transmission gratings by four-wave mixing in non-local photorefractive media with strong response is considered. The input conditions to record dynamic gratings with a stable grating amplitude distribution as well as grating amplitude oscillations are defined. They are determined both by intensities and by a phase difference of input waves. The influence of fluctuations of wave phases on stability of the recorded gratings is considered. Methods of optical control of both the grating amplitude localization degree and the grating amplitude location are defined.

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Temporal instabilities in single-grating photorefractive four-wave mixing

Cited by 32 publications

References 13 publications

Time-dependent behavior of photorefractive two- and four-wave mixing

Time-dependent behavior of photorefractive two- and four-wave mixing

Explicit solutions of the four-wave mixing model

Analytical Description of Partially Coherent Optical Systems for Optimization of Numerical Aperture and Degree of Coherence

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