Waveguides and waveguide arrays formed by incoherent light in photorefractive materials

We report on experimental observations of nonlinear optical waveguides and waveguide arrays formed by incoherent light in photorefractive materials. Such waveguides are made possible by creating partially spatially incoherent solitons in a noninstantaneous self-focusing photorefractive medium. In addition to planar, Y-junction, and circular waveguides, we report the first demonstration of pixel-like spatial solitons from partially incoherent light. An array of as many as 56 56 soliton pixels is readily realized by launching a spatially modulated incoherent beam into the selffocusing photorefractive medium. These solitons are stable and robust, forming a steady-state two-dimensional waveguide array in which optical coupling and control of local waveguide channels can be achieved. These experiments bring about the possibility of controlling high-power laser beams with low-power incoherent light sources as well as the possibility for optically inducing three-dimensional reconfigurable photonic lattices in a bulk medium. 2002 Elsevier Science B.V. All rights reserved. Optical spatial solitons are considered to be among the prime candidates for controlling light by light. Since the demonstration of Kerr-type spatial solitons and their ability to guide and switch other beams [1,2], there has been an increasing interest in soliton-induced waveguides and their applications. In particular, recent work on self-trapping and light guiding in various 3D saturable nonlinear materials [3] has opened up several avenues for possible applications of spatial solitons in optical interconnects, optical communications, and other areas. For instance, spatial switching with quadratic solitons [4] and directional couplers based on photorefractive solitoninduced waveguides [5] have been demonstrated, and soliton-induced waveguides have even been employed to achieve high efficiency frequency conversion in nonlinear vð2Þ photorefractive media [6]. In addition to oneor two-waveguide structures, which involve only a few solitons, spatial soliton pixels and soliton-based waveguide arrays have been proposed for applications in signal processing and information technology [7]. Recently, pixel-like spatial solitons have been demonstrated in a semiconductor microcavity and in a cavityless optical parameteric amplifier [8]. In all those previous studies, spatial soliton arrays were generated with coherent light waves. For decades, solitons have been exclusively considered to be coherent entities, and optical solitons have been studied only with intense coherent light beams. Nature, however, is full of Corresponding author. E-mail address: [email protected] (Z. Chen). 0925-3467/03/$ see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-3467(02)00295-1 Optical Materials 23 (2003) 235–241 www.elsevier.com/locate/optmat incoherent radiation sources. Can incoherent light also form a soliton and thus induce a waveguide? This intriguing and challenging question has recently motivated several experiments [9,10] on selftrapping of incoherent light. By now, a series of experimental and theoretical studies [9–12] has clearly demonstrated that incoherent spatial solitons are indeed possible in slow-responding nonlinear media such as biased photorefractives. This brings about the interesting possibility of using low-power incoherent light beams to form solitons that can guide and control other high-power coherent laser beams. This is simply because the light-induced variation of the refractive index associated with either bright or dark incoherent solitons can form a waveguide structure in the selftrapped region, and a probe beam can be guided at much higher power level as long as it has a less photosensitive wavelength [13–15]. In this paper, we review our experimental work on waveguides induced by incoherent dark solitons. These induced waveguides allow optical guidance of other beams that may be coherent or incoherent. In addition, we report the first experimental observation of pixel-like two-dimensional spatial soliton arrays from partially spatially incoherent light. Optical waveguide arrays are of particular interest because of their potential applications as well as their collective behavior of nonlinear wave propagation that exhibits many intriguing phenomena found also in other nonlinear discrete systems. Yet, it has always been a challenge to create or fabricate two-dimensional waveguide arrays in bulk media. We create a 2D waveguide array induced by as many as 56 56 pixel-like spatial solitons by launching a spatially modulated incoherent beam into a self-focusing photorefractive nonlinear crystal. These spatial solitons are stable and robust, provided that the coherence of the beam and the strength of nonlinearity are set at an appropriate value. If the coherence is too high or the nonlinearity is too strong, the beam tends to break up into disordered patterns rather than ordered soliton structures. Once the soliton pixels form in steady state, they induce a two-dimensional waveguide array capable of guiding an intense probe beam of a longer wavelength. Optical waveguiding and control of nearby waveguide channels in the array are demonstrated in experiments. These soliton pixels may find particular applications in image transmission and information encoding, as there is no or only weak correlation among the various pixels on the soliton array due to the nature of incoherent light. In our experiments, we first convert a coherent beam from an argon ion laser (k 1⁄4 514 nm) into a quasi-monochromatic spatially incoherent light source by passing it through a rotating diffuser [9,10]. The laser beam is focused by a lens onto the diffuser, and the scattered light from the diffuser is collected by another lens. The rotating diffuser provides random phase fluctuations, thus turning the beam into partially spatially incoherent. The spatial degree of coherence of this beam is revealed by the average size of the speckles borne on it. One can actually trace the temporally varying speckles with a fast camera, or, as we do here, monitor the beam when the diffuser is stationary. We then launch the speckled beam onto a phase or an amplitude mask, and redirect the reflected dark beam onto the input face of a photorefractive crystal in a way similar to that previously followed in generating coherent dark screening solitons [14,16]. The photorefractive crystal used here is a 12-mm-long SBN grown at Stanford using the Vertical Bridgeman method. We first generate a 1D incoherent dark stripe from a phase mask (odd initial conditions) [14]. When the diffuser is stationary, what the crystal ‘‘sees’’ is the speckled pattern shown in Fig. 1a. However, as the diffuser rotates at a time scale much faster than the response time of the crystal, the crystal ‘‘sees’’ a dark stripe superimposed on a smooth intensity profile (Fig. 1b) rather than the speckled pattern. This illustrates that our photorefractive crystal responds to the time-averaged envelope and not to the instantaneous speckles. By providing an appropriate bias field, we obtain selftrapping of the incoherent dark stripe. We then launch a cylindrically focused probe beam from a HeNe laser (k 1⁄4 633 nm) into the soliton to test its waveguide properties. Fig. 2 shows typical experimental results. At input, the dark beam has a coherence length (estimated from the average speckle size) of 15 lm. The incoherent dark soliton is 18 lm (FWHM) wide, generated at a bias field of 950 V/cm. In the absence of nonlinearity, the probe 236 Z. Chen, H. Martin / Optical Materials 23 (2003) 235–241