Elsevier

Optics Communications

Volume 278, Issue 1, 1 October 2007, Pages 187-193
Optics Communications

Spatial coherence of an optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability

https://doi.org/10.1016/j.optcom.2007.06.002Get rights and content

Abstract

We report the experimental observation of the dynamic pattern formation of a broad coherent light beam in a biased photorefractive crystal due to the spatiotemporal modulation instability. When the nonlinearity exceeds a specific threshold, the coherent light beam not only breaks up into light spots due to the modulation instability but also fast fluctuates both spatially and temporally, forming an optical turbulent beam, which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. We investigate the spatial coherence property of an optical turbulent beam from the visibility of the averaged double-slit interference fringe. We also numerically demonstrate the visibility variation of the instantaneous interference fringe of an optical turbulent beam.

Introduction

Several important reports of pattern formation due to the modulation instability in spatially incoherent light beams [1], [2], [3], have attracted again many research interests in photorefractive nonlinear optics since 2000. Modulation instability is a nonlinear process, in which small amplitude and phase perturbations (due to the noise) grow rapidly under the combined effects of the nonlinear self-focusing effect and the light diffraction. Thus, as illustrated in Fig. 1, a broad optical beam has a tendency to disintegrate into filaments or break up into light spots during propagation. In the report of the incoherent modulation instability [1], the nonlinearity threshold for pattern formation to occur spontaneously from noise was found to depend on the coherence property of the incoherent beam. The filaments that emerge from the incoherent modulation instability process are actually trains of almost ideal incoherent solitons [4], [5]. The key nature for the incoherent solitons to occur is that the nonlinear material within which the light propagates must be “noninstantaneous”, i.e., the material gives rise to the nonlinear refractive index basing on the time-averaged intensity profile and not on the instantaneous rapidly varying speckled intensity pattern. In other words, the material is indifferent to any rapid local intensity fluctuation that is faster than the material can respond. Therefore, given that the intensity variation of the light beam is much faster than the charge re-distribution process, the photorefractive screening nonlinearity is of course noninstantaneous, allowing the spatially and temporally incoherent solitons to occur [6].

In order to investigate how a partially incoherent soliton reacts in the medium that somewhat can respond to the spatially fluctuating intensity of the soliton beam, we have studied experimentally and numerically with the bicomponent solitons in dynamic soliton-like modes [7] and with the swinging solitons [8]. Motivated by the reports of the incoherent modulation instability, we are very interested again in exploring how a spatially and temporally varying optical spatial soliton beam behaves in a somewhat instantaneous nonlinear medium.

In a previous paper [9], we have ever reported another series of experiments on the pattern dynamics [10] due to the modulation instability by launching a very broad coherent CW light beam uniformly onto a biased photorefractive strontium barium niobate crystal (SBN:60, n = 2.35 and r33 = 280 pm/V). When the external voltage or the incident light intensity exceeds a specific threshold, we observe that the modulation instability breaks into a novel optical turbulence[11], which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. This spatiotemporal chaotic behavior reveals that, with nonlinearity magnitude large enough or nonlinearity relaxation time short enough, the medium can respond not only to the spatially fluctuating light intensity, but also to the temporally fluctuating light intensity due to the noise.

In this paper, we intend to further investigate the spatial coherence property of an optical turbulent beam [12], which also behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. The beam size is as broad as 200 μm around, and is about 10 times larger than that of an ordinary optical spatial soliton formed in a biased photorefractive crystal. We adopt the strategy of measuring the double-slit-interference fringes [13] of the broad optical turbulent beam. The equivalent experimental methods and results could also be found in other fields of optical physics [14].

Turbulence is of large importance in many fields. In addition to the turbulent flow in ordinary fluids, the quantum turbulence was also studied in superfluid helium-4 or helium-3 at very low temperatures [15]. It implies that a turbulent flow might be not solely a classical phenomenon. How the quantum effects affect an optical turbulent beam in a biased photorefractive crystal could become a new research issue in the future. The non-classical coupling or interaction between the dynamic multi-quasi-solitons and the fast-moving soliton-induced multi-waveguides of quasi-photonic-crystal structure for an optical turbulent beam in a biased photorefractive crystal will also probably attract again many research interests.

In classical fluid dynamics, one can measure the pressure gradients associated with the turbulent flow in a tube and the forces on the obstacles which the turbulent flow passes [15]. The vortex lines exhibit the presence of viscosity or mutual frictional interaction. One can obtain the density of vortex lines or the vorticity in flows through the measurement of mutual friction. Another important measurement of the pressure fluctuations, which is related to the fluctuations in turbulent flow velocities, can be used to obtain the turbulent energy spectral distribution over different eddy sizes. These techniques or approaches will also inspire us to pursue deeper understanding of the optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability in the future.

Section snippets

Observing the spatiotemporal pattern formation of an optical turbulent beam

The experimental setup for observing an optical turbulent beam is shown in Fig. 2, and is similar to the typical setup for observing a photorefractive optical spatial soliton. At first, to produce a broad turbulent beam, a TEM00 extraordinarily polarized signal laser beam (wavelength at 532 nm) is focused by a lens of 1000-mm focal length and then launched into the SBN crystal along the 7-mm-long crystalline a-axis, with the 195-μm-wide (FWHM) minimum beam waist located at the crystal input

Measuring the spatial coherence of an optical turbulent beam

Next, as shown in Fig. 4, to elucidate the spatial coherence property of the turbulent signal beam due to the modulation instability, we perform a series of measurements on the optical interference fringes of the turbulent signal beam by a double-slit plate of 40-μm slit width and 250-μm slit separation. This double-slit plate is placed at the original position (the image plane of the imaging lens) of the slightly withdrawn CCD camera, and corresponds to 4.6-μm slit width and 28.7-μm slit

Conclusion

In conclusion, we have experimentally explored the spatiotemporal modulation instability and the pattern formation dynamics by the use of a broad coherent light beam incident in a biased photorefractive crystal. As the external voltage or the incident light intensity exceeds a threshold, the light beam forms filaments spontaneously from noise, and further breaks up into arrays of light spots at higher voltage or incident light intensity. When the external voltage or the incident light intensity

Acknowledgement

We acknowledge the financial support from the National Science Council, Taiwan, through Projects NSC-89-2112-M-002-060 and NSC-95-2112-M-415-004.

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