Publications (122) View all
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Article: Self-trapping threshold in disordered nonlinear photonic lattices.
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ABSTRACT: We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average propagation constant allows for a generalized definition of the threshold power for the onset of soliton localization. When compared to perfectly ordered systems, this threshold is found to decrease in the presence of coupling disorder.Optics Letters 05/2013; 38(9):1518-20. · 3.40 Impact Factor -
Article: Dynamic localization in Glauber-Fock lattices.
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ABSTRACT: Glauber-Fock lattices refer to a special class of semi-infinite tight-binding lattices with inhomogeneous hopping rates which are found in certain simple solid state, quantum optics and quantum field theoretical models. Here it is shown that dynamic localization, i.e. suppression of quantum diffusion and periodic quantum self-imaging by an external sinusoidal force (Dunlap and Kenkre 1986 Phys. Rev. B 34 3625), can be exactly realized in Glauber-Fock lattices, in spite of inhomogeneity of hopping rates and lattice truncation.Journal of Physics Condensed Matter 12/2012; 25(3):035603. · 2.55 Impact Factor -
Article: Biphoton generation in quadratic waveguide arrays: A classical optical simulation
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ABSTRACT: Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.Scientific Reports 08/2012; 2:562. -
Article: Optical Analogues for Massless Dirac Particles and Conical Diffraction in One Dimension
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ABSTRACT: We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized. One-dimensional conical diffraction is also observed for the first time in this work. The Dirac wave equation, formulated in 1928 by Dirac [1], represents one of the great breakthroughs of theoreti-cal physics. This equation unifies the principles of quan-tum mechanics and special relativity, suggesting in particular a new form of matter: antimatter, that predated its experimental discovery [2]. Importantly, the Dirac theory does not only describe massive particle-antiparticle pairs but also potentially massless fermions, such as neu-trinos and anti-neutrinos [3]. However, direct experimen-tal observation of such entities is highly intricate since such particles do only weakly interact with matter [4]. Classical optical emulators of the Dirac equation recently received a great deal of interest since, with their help, various relativistic phenomena can be experimentally observed in tabletop experiments [5–9]. In all of these demonstrations, a biatomic superlattice waveguide array was used to simulate the spinor-type wave function of the Dirac equation. However, this carries the intrinsic draw-back that a band gap opens between the two minibands, which is physically equivalent to a mass in the emulated Dirac equation leading to the fact that only massive Dirac particles can be simulated. To date, the only known optical realization of a massless Dirac equation is in the two-dimensional (2D) setting of honeycomb photonic lattices [10,11] that consists of two shifted hexagonal lattices. Therefore, this structure represents a superlattice with identical waveguides and, hence, without a gap between the bands of eigenmodes. The honeycomb structure, which resembles the geometry of electronic graphene, can consequently be used for realizing optical simula-tions of the 2D versions of Klein tunneling [12] and Zitterbewegung [13]. It is usually believed that gapless superlattices exist only in settings with two transverse dimensions, and one-dimensional (1D) superlattices always exhibit an interband gap. However, 1D systems are particu-larly useful in isolating certain phenomena associated with the Dirac equation that may be too intricate to generate in systems with higher dimensions. As it is commonly known, the band structure of a mass-less Dirac equation features a particular conical intersec-tion point between the two minibands—the Dirac point (also called ''diabolic'' point). These points, that were first described by Hamilton in the context of biaxial crystals [14], are characterized by their singularity; i.e., no uniquely defined group velocity exists at such points. Importantly, this gives rise to the peculiar phenomenon, amongst others, of conical diffraction [14], where a light beam, launched into a biaxial crystal at the direction of the diabolic points, spreads in a conical fashion. The light forms a thin ring with an increasing radius during propa-gation, but the thickness of the ring stays constant over the whole propagation distance. Following Hamilton's predic-tion, conical diffraction was first experimentally observed by Lloyd [15] and is, therefore, the first theoretically predicted physical phenomenon ever. Interestingly, conical diffraction attracts attention until today [16–21]. Even though this concept was introduced in the field of crystal optics, it can be transferred to other fields of physics, where such diabolic points exist. This became particularly clear in the work of Peleg et al. [10], where conical diffraction was associated with the diabolic points in the honeycomb structure, although the physical origin is slightly different in that system. To date, diabolic points have never been realized in a 1D structure, and—consequently—conical diffraction has never been observed in a 1D geometry. In our work, we present the first experimental imple-mentation of the 1D massless Dirac equation that exhibits a conical intersection in the band structure. We demonstrate the optical analogue to a massless relativistic particle and its antiparticle moving away from each other. Additionally, we draw a connection from this phenomenon to 1D conical diffraction, a surprising result that emphasizes the closePhysical Review Letters 07/2012; 109(2):023602. · 7.37 Impact Factor -
Article: Optical analogues for massless dirac particles and conical diffraction in one dimension.
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ABSTRACT: We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized. One-dimensional conical diffraction is also observed for the first time in this work.Physical Review Letters 07/2012; 109(2):023602. · 7.37 Impact Factor
