VOLUME 83, NUMBER 23 PHYSICAL REVIEW LETTERS 6DECEMBER 1999 Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations R. Morandotti,* U. Peschel, † and J. S. Aitchison Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G128QQ, United Kingdom H. S. Eisenberg and Y. Silberberg Department of Physics of Complex Systems, The Weizmann Institute of Science, 76100 Rehovot, Israel (Received 1 July 1999) We experimentally demonstrate the occurrence of optical Bloch oscillations in a waveguide array with linearly growing effective index of the individual guides. We monitored the output profiles for varying propagation lengths and observed a periodic transverse motion of the field and a complete recovery of the initial excitation. The action of the focusing nonlinearity leads to a loss of recovery, symmetry breaking, and power-induced beam spreading. PACS numbers: 42.82.Et, 42.65.Sf, 42.65.Wi Discrete systems such as semiconductor superlattices, molecular chains, waveguide arrays, or coupled pendula share a lot of interesting and somehow intriguing features. One of the most remarkable is the occurrence of Bloch oscillations [1]. For example, if a static electric field is applied perpendicularly to a semiconductor superlattice, charged particles do not react on the electric force as ex- pected. An oscillating current is generated in contrast to the dc flow observed in bulk materials [2]. Because of the fundamental relevance of discreteness in nature we expect to find similar effects in other systems of quite dif- ferent origin. In fact, Bloch oscillations occur in molecu- lar chains [3] and were experimentally observed for atoms captured by optical potentials [4]. Similar evolution equa- tions in optics and quantum mechanics indicate the rele- vance of Bloch oscillations in optical systems under appropriate conditions. It was shown that the transmis- sion spectrum of certain layer structures [5] or chirped fiber gratings [6] reproduces the spectral properties of bi- ased semiconductor superlattices, which are characterized by series of equidistant peaks, the so-called Wannier-Stark ladder. In particular, the two cases above are simply the Fourier representation of Bloch oscillations with respect to either the angle of incidence [5] or the wavelength [6]. Recently, it was suggested that waveguide arrays with a varying effective index of the individual guides are an ideal environment to observe optical Bloch oscillations in the space domain [7]. Here we use arrays of AlGaAs waveguides to demonstrate this goal. In addition to the test of the linear properties this material system enables us to investigate the influence of nonlinearity on the field evolution. The nonresonant instantaneous cubic nonlin- earity in semiconductors operated below half the band edge is analog to a pointlike scattering of interacting par- ticles in quantum mechanics [8]. Therefore we can study dephasing effects with the tools of nonlinear optics on an accessible, i.e., millimetric, scale. Besides this fundamen- tal interest, the practical importance of waveguide arrays is quite obvious. It was suggested that a linearly grow- ing effective refractive index induced via the electro- or thermo-optical effect might be used to steer signals into a desired output channel. Further, waveguide arrays are basic components of high power semiconductor lasers, where the onset of nonlinearly induced filamentation and self-focusing can cause a basic limitation of the achiev- able output power. As we will show here the field in an array with linearly increasing effective index spreads due to the action of a focusing nonlinearity, therefore avoiding filamentation to a certain extent. The sample under investigation consisted of 25 ridge waveguides (for a schematic drawing see top of Fig. 1). It was etched 1.2 mm deep on top of an AlGaAs slab waveguide composed by a 1.5 mm thick guiding layer of Al 0.18 Ga 0.82 As, sandwiched between two layers of Al 0.24 Ga 0.76 As. These upper and lower claddings were 1.5 and 4.0 mm thick, respectively. To obtain a linear increase of the effective index the rib width was varied from 2 to 3.4 mm, corresponding to an index difference of dn  1.275 3 10 24 between adjacent guides. To ensure constant coupling also the spacing between the guides was varied from 6.6 to 3.3 mm (see top of Figs. 1 and 2). Finally, the sample was cleaved into pieces of different length varying from 3 to 18 mm to allow for an insight into the field evolution. To measure the optical response of the sample the setup described in [9] was used. Light pulses of 180 fs duration were generated at a wavelength of l  1.53 mm, which is well below half the band gap resulting in the suppression of two photon absorption. We used an elliptically shaped input beam with a width varying from 3 to 20 mm. The image of the output field was recorded with an infrared camera. To compare the results obtained from samples of different length special care was taken to keep the initial conditions constant. To adjust the output images the initial beam was tilted to illuminate the array boundaries. Additionally, the geometrical properties of the array, which guarantee a symmetric intensity distribution for an excitation of the central guide, were used to identify the central guide in the 4756 0031-9007 99  83(23)  4756(4)$15.00 © 1999 The American Physical Society