Effective lensing effects in parametric frequency conversion

We show that, in the high wave-vector-mismatch (cascading) limit, the well-known paraxial description of parametric frequency conversion in quadratic media entails effective lensing effects, which can have a self-focusing or a self-defocusing nature, critically depending on the mismatch sign, the selected wave, and the launching condition (second-harmonic generation or downconversion). Numerical and experimental evidence of this behavior is reported.

[1]  Michael Canva,et al.  Quadratic spatial soliton generation by seeded downconversion of a strong harmonic pump beam , 1997 .

[2]  David J. Hagan,et al.  χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons , 1996 .

[3]  M. Segev,et al.  Steady-state spatial screening solitons in photorefractive materials with external applied field. , 1994, Physical review letters.

[4]  Dmitry V. Skryabin,et al.  Optical Solitons Carrying Orbital Angular Momentum , 1997 .

[5]  Liejia Qian,et al.  Generation of Optical Spatiotemporal Solitons , 1999 .

[6]  Günter,et al.  Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect. , 1995, Physical review letters.

[7]  Lluis Torner,et al.  Observation of topological charge pair nucleation in parametric wave mixing , 1998 .

[8]  Claude Fabre,et al.  Observation of Pattern Formation in Optical Parametric Oscillators , 1999 .

[9]  C De Angelis,et al.  Observation of quadratic spatial solitons in periodically poled lithium niobate. , 1999, Optics letters.

[10]  Charles H. Townes,et al.  Self-trapping of optical beams , 1964 .

[11]  Buryak,et al.  Self-trapping of light beams and parametric solitons in diffractive quadratic media. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[12]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[13]  L. A. Ostrovskiĭ.  Self-action of Light in Crystals , 1967 .

[14]  H A Haus,et al.  Nonlinear Schrödinger equation for optical media with quadratic nonlinearity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[15]  Boris A. Malomed,et al.  7 - Optical Solitons in Media with a Quadratic Nonlinearity , 2000 .

[16]  Parametric spatial solitary waves due to type II second-harmonic generation , 1997 .

[17]  Yu. N. Karamzin,et al.  Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters , 1974 .

[18]  Frank W. Wise,et al.  Generation of Optical Spatiotemporal Solitons , 1999 .

[19]  Fischer,et al.  Spatial solitons in photorefractive media. , 1992, Physical review letters.

[20]  Properties of type II quadratic solitons excited by imbalanced fundamental waves. , 1997, Optics letters.

[21]  C. Conti,et al.  Focusing versus Defocusing Nonlinearities due to Parametric Wave Mixing , 2001 .

[22]  Pelinovsky,et al.  Instability of solitons governed by quadratic nonlinearities. , 1995, Physical review letters.

[23]  Trillo,et al.  Stability of Three-Wave Parametric Solitons in Diffractive Quadratic Media. , 1996, Physical review letters.

[24]  A. Andreoni,et al.  TWO-DIMENSIONAL SPATIAL SOLITARY WAVES FROM TRAVELING-WAVE PARAMETRIC AMPLIFICATION OF THE QUANTUM NOISE , 1998 .

[25]  Algis S. Piskarskas,et al.  Observation of temporal solitons in second-harmonic generation with tilted pulses , 1998, Nonlinear Guided Waves and Their Applications.

[26]  Stefano Trillo,et al.  Focusing versus defocusing nonlinearities in self-trapping due to parametric frequency conversion , 2001, QELS 2001.

[27]  Curtis R. Menyuk,et al.  Solitary waves due to ?^(2): ?^(2) cascading , 1994 .

[28]  S. Minardi,et al.  Observation of Optical Vortices and J 0 Bessel-Like Beams in Quantum-Noise Parametric Amplification , 1998 .

[29]  F. Wise,et al.  Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  G. Stegeman,et al.  Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system. , 2001, Physical review letters.

[31]  S. Wabnitz,et al.  Two-wave mixing in a quadratic nonlinear medium: bifurcations, spatial instabilities, and chaos. , 1992, Optics letters.

[32]  George I. Stegeman,et al.  SPATIAL MODULATIONAL INSTABILITY AND MULTISOLITONLIKE GENERATION IN A QUADRATICALLY NONLINEAR OPTICAL MEDIUM , 1997 .

[33]  L. Torner,et al.  Stationary trapping of light beams in bulk second-order nonlinear media , 1995 .

[34]  Di Trapani P,et al.  Observation of quadratic optical vortex solitons , 2000, Physical review letters.

[35]  J. Aitchison,et al.  All-optical switching based on nondegenerate phase shifts from a cascaded second-order nonlinearity. , 1993, Optics letters.

[36]  Stegeman,et al.  Observation of two-dimensional spatial solitary waves in a quadratic medium. , 1995, Physical review letters.

[37]  Stegeman,et al.  One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  S. Herminghaus,et al.  Nonlinear optics of Bessel beams. , 1993, Physical review letters.

[39]  Yuri S. Kivshar,et al.  MULTISTABILITY OF THREE-WAVE PARAMETRIC SELF-TRAPPING , 1997 .

[40]  Luc Bergé,et al.  Wave collapse in physics: principles and applications to light and plasma waves , 1998 .

[41]  C. B. Clausen,et al.  Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media , 1997 .