Self-focusing, breakup and trapping of Raman-shifted femtosecond pulses in homogeneous slab and weakly coupled arrays of nonlinear glass Silica waveguides Yoav Linzona, Dima Cheskisa, Iftach Ilsara, Roberto Morandottib, Stewart Aitchisonc, and Shimshon BarAda a School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel b Universite' du Quebec, Institute National de la Recherche Scientifique, Varennes, Quebec, Canada J3X 1S2 C Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada, M55 3G4 ABSTRACT We present experimental and numerical studies of pulse propagation in continuous and periodically modulated nonlinear waveguides, made of Silica glass. When intense femtosecond pulses are passed through this X3 material, a positive Kerr nonlinearity is formed. The unique characteristic of glass is accessibility to all domains of possible temporal dispersion (normal, zero and anomalous) in the spectral range of currently available femtosecond pulse sources. In particular, the anomalous dispersion regime enables simultaneous self-focusing in space (X) and time ( T) , yielding complex dynamics of the beam involving several mechanisms that couple between the X and T dimensions. We show that under certain circumstances, the combination of these mechanisms can lead to simultaneous spatial and spectral filtering in the continuous sample as well as steering of the point of break-up, and beam trapping in the periodic sample, using near-field microscopy and conventional spectroscopy. Keywords: Near-field imaging, Nonlinear waveguides, Spatio-temporal solitons, Photonic crystals, Discrete solitons 1. INTRODUCTION The propagation of short laser pulses through bulk nonlinear media, where the nonlinearity counteracts both diffraction and dispersion, is of great current interest for both fundamental reasons as well as from a practical point of view. In translationally- and rotationally-invariant homogeneous media, symmetrical Spatio-Temporal Soliton (STS) solutions of the Nonlinear Schrödinger Equation (NLSE) are predicted to exist when the dispersion is anomalous, but are also known to be unstable and susceptible to a catastrophic collapse for this 2d However, in reality this collapse is arrested by higher-order processes, which become significant as collapse is approached and energy densities increase; instead of collapse, an abrupt break-up of the pulse of observed. Thus, realization of STS still remains an important goal in the physics and engineering of solitons.2 We emphasize that although STS are not accessible in the normal dispersion regime, stable spatio-temporal propagation was also observed in this regime in the form of X-shaped extended (conical) waves representing quasi-localized peaks.3 When periodic modulations are applied to the linear index of refraction in the transverse direction (i.e. the x dimension of the dynamics), the properties of STS drastically change, to some extent due to partial breaking of the translational or rotational symmetry and an effective decrease of the system dimensionality. In particular, when neglecting temporal evolution and taking into account only the spatial dynamics in the NLSE (a plausible assumption when the dispersion is normal, yielding a chirp that is added to that induced by the positive Kerr nonlinearity, instead of being subtracted from it, with the overall outcome of monotonous spreading of the pulse) Contact information: Y.L. 's e-mail: linzonyopost.tau.ac.il, telephone: +972 3 640 6530 SB. 's e-mail: shimshonpost.tau.ac.il, telephone: +972 3 640 5321. Self-focusing, breakup and trapping of Raman-shifted femtosecond pulses in homogeneous slab and weakly coupled arrays of nonlinear glass Silica waveguides Yoav Linzona, Dima Cheskisa, Iftach Ilsara, Roberto Morandotti, Stewart Aitchisonc, and Shimshon BarAdL a School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel b Universite' du Quebec, Institute National de la Recherche Scientifique, Varennes, Quebec, Canada J3X 152 C Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada, M55 3G4 ABSTRACT We present experimental and numerical studies of pulse propagation in continuous and periodically modulated nonlinear waveguides, made of Silica glass. When intense femtosecond pulses are passed through this X3 material, a positive Kerr nonlinearity is formed. The unique characteristic of glass is accessibility to all domains of possible temporal dispersion (normal, zero and anomalous) in the spectral range of currently available femtosecond pulse sources. In particular, the anomalous dispersion regime enables simultaneous self-focusing in space (X) and time ( T) , yielding complex dynamics of the beam involving several mechanisms that couple between the X and T dimensions. We show that under certain circumstances, the combination of these mechanisms can lead to simultaneous spatial and spectral filtering in the continuous sample as well as steering of the point of break-up, and beam trapping in the periodic sample, using near-field microscopy and conventional spectroscopy. Keywords: Near-field imaging, Nonlinear waveguides, Spatio-temporal solitons, Photonic crystals, Discrete solitons 1. INTRODUCTION The propagation of short laser pulses through bulk nonlinear media, where the nonlinearity counteracts both diffraction and dispersion, is of great current interest for both fundamental reasons as well as from a practical point of view. In translationally- and rotationally-invariant homogeneous media, symmetrical Spatio-Temporal Soliton (STS) solutions of the Nonlinear Schrödinger Equation (NLSE) are predicted to exist when the dispersion is anomalous, but are also known to be unstable and susceptible to a catastrophic collapse for this 2d geometry.' However, in reality this collapse is arrested by higher-order processes, which become significant as collapse is approached and energy densities increase; instead of collapse, an abrupt break-up of the pulse of observed. Thus, realization of STS still remains an important goal in the physics and engineering of solitons.2 We emphasize that although STS are not accessible in the normal dispersion regime, stable spatio-temporal propagation was also observed in this regime in the form of X-shaped extended (conical) waves representing quasi-localized peaks.3 When periodic modulations are applied to the linear index of refraction in the transverse direction (i.e. the x dimension of the dynamics), the properties of STS drastically change, to some extent due to partial breaking of the translational or rotational symmetry and an effective decrease of the system dimensionality. In particular, when neglecting temporal evolution and taking into account only the spatial dynamics in the NLSE (a plausible assumption when the dispersion is normal, yielding a chirp that is added to that induced by the positive Kerr nonlinearity, instead of being subtracted from it, with the overall outcome of monotonous spreading of the pulse) Contact information: Y.L. 's e-mail: linzonyopost.tau.ac.il, telephone: +972 8 640 6580 SB. 's e-mail: shimshonpost.tau.ac.il, telephone: +972 3 640 5321. Topical Problems of Nonlinear Wave Physics, edited by Alexander Sergeev, Proc. of SPIE Vol. 5975, 59750T, (2006)0277-786X/06/$15 · doi: 10.1117/12.675574 Proc. of SPIE Vol. 5975 59750T-1