Summary form only given. In this paper we report the outcome of our comprehensive investigations to study the dynamics of the beam trapping in both bulk crystals and optical planar waveguides made of quadratic nonlinear media in second-harmonic generation configurations. We address and discuss the suitable experimental conditions required to form spatial solitary waves in critical phase-matching and quasi-phase-matching settings.Peer ReviewedPostprint (published version

Menyuk, C

Stegeman, G

Torner Sabata, Lluís

Torruellas, W

Wright, E

English

Summary form only given. In this paper we report the outcome of our comprehensive investigations to study the dynamics of the beam trapping in both bulk crystals and optical planar waveguides made of quadratic nonlinear media in second-harmonic generation configurations. We address and discuss the suitable experimental conditions required to form spatial solitary waves in critical phase-matching and quasi-phase-matching settings.Peer Reviewe

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Trapping of light beams and formation of spatial solitary waves in quadratic nonlinear media

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178 I QELS'96 THURSDAY MORNING 2. K. L. Vodopyanov, H. Graener, C. C. Phillips, Phys. Rev. B 47, 6831 (1993). QThD6 11:45 am impulsive stimulated Raman excitation of coherent phonons in antimony G. A. Garrett, T. E Albrecht, J. T. Whitaker, R. Merlin 500 East University, University of Michigan, Ann Arbor, Michigan 48109-1120 The excitation of coherent phonons in semimetals with femtosecond laser pulses has recently been investigated by several groups and accounted for by an excitation mechanism called displacive excitation of coherent phonons (DECP). DECP is considered to be different from conventional Raman processes in that it only launches fully symmetric A-pho- nons and that these oscillations have a cosine behavior rather than the sine be- havior that is expected for impulsive stimulated raman scattering (ISRS). In this work we re-investigated the ex- citation of phonons in Antimony using both time-resolved and cw-Raman tech- niques. The time-resolved experiments were carried out with a simple femtosec- ond pump-probe setup in reflection, us- ing a self-modelocked Tisapphire laser at 810 nm as the pulse source. Our results agree with previous studies in that the response at room temperature is domi- nated by the 150 cm-' A,-mode, whereas contributions from the E,-phonon at 112 cm-' are negligible. This is illustrated in Fig. la, which shows the oscillating con- tribution to the transient reflection at room temperature after subtraction of a slowly varying background. The data can be fitted with a single-frequency damped oscillation. Below 200 K however, the E,- - -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 E O  45' 5 I 1 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Time (PS) QThD6 Fig. 1 Oscillatory part of femtosecond ISRS-experiments on Sb. (a) At 300 K only the A,-phonon mode is visible. (b) At 8 K, the E,-phonon causes a beating structure that changes with angle between the pump and probe polarizations. phonon becomes readily observable and causes a beat structure in the transient, as can be seen in Fig. lb. Experimental re- sults at 8 K are shown for different po- larization angles, +, between the pump and probe pulses. While the fully sym- metric A,-phonon is independent of 9, the amplitude of the E,-component ex- hibits a cos(29) behavior. These findings are in agreement with Raman selection rules. Our experiments show that the fre- quency, linewidth, and polarization selec- tion rules for both phonons are consistent with results found in spontaneous Ra- man scattering obtained with the same excitation wavelength. We developed a theory that relates DECP to ISRS by con- sidering a complex Raman tensor. The limiting case of a purely real, nonreso- nant, or complex, strongly resonant, Ra- man tensor then corresponds to ISRS or DECP, respectively. The phase of the ex- cited phonons then depends on the fre- quency dependence of the Raman tensor. The theory predicts that the relative ratio of the intensities of the E, and A, modes need not be the same between sponta- neous and impulsive Raman scattering, as observed in our experiments. QThE 10:30 am Room 82 Self-Trapping in Quadratic Media and Instabilities George I. Stegeman, University of Central Florida, Presider QThEl (Invited) 10:30 am Trapping of light beams and formation of spatial solitary waves in quadratic nonlinear media Lluis Tomer, William E. Tonuellas,* George I. Stegeman,' Curtis R. Menyuk," Ewan M. Wright,t Department of Signal Theory and Communications, Polytechnic University of Catalonia, Barcelona, ES 08034, Spain Self-focusing and self-trapping of light have been investigated since the early days of nonlinear optics.' Interest in this field has been maintained by the fasci- nating range of new phenomena encoun- tered and their potential applications. Until very recently such effects have been pursued by use of the optical Kerr effect in third-order, or cubic, nonlinear media and the photorefractive effect. However, self-trapping of light also occurs in quad- ratic nonlinear media and both temporal and spatial solitons form through the mutual focusing of the waves paramet- rically interacting in the medium. Self-focusing effects in quadratic non- linear processes were long known to be possible under specific conditions, but the full extent of their implications was not fully appreciated until recently, after the so-called "cascading of second-order nonlinearities" was identified as a poten- tial new approach for the control of light by light? A remarkable exception is the work of Karamzin and Sukhorukov 20 years ago: who investigated the mutual focusing of beams in parametric pro- cesses and identified its implications for the formation of solitons. Recently, spa- tial soliton propagation has been ob- served experimentally in second-har- monic generation settings in bulk potassium titanyl phosphate (KTP)' and in planar waveguides made of lithium niobate (LiNb03)? In this paper we report the outcome of our comprehensive investigations to study the dynamics of the beam trapping in both bulk crystals and planar wave- guides made of quadratic nonlinear me- dia in second-harmonic generation con- figurations. We address and discuss the suitable experimental conditions required to form spatial solitary waves in critical phase-matching and quasi-phase-match- ing settings. We discuss the properties and stability of the relevant known families of unidi- mensional and two-dimensional station- ary solitary waves, their evolution in the presence of small perturbations and losses, and we explore the dynamics of the excitation of spatial solitary waves under different material and excitation conditions. We show how the mutual trapping occurs in a wide variety of con- ditions, not necessarily close to those given by the stationary solitary waves so- lutions of the governing equations. Soli- tary waves emerge with inputs that fall very far from those solutions indeed. We speafically show the dynamics of the beam trapping with only the fundamen- tal beam at the input face of the nonlinear crystal. We discuss the mutual beam dragging of the fundamental and second harmonic waves that occurs in the pres- ence of linear walk-off or spatial phase modulation of the input beams, beam steering, collisions, and interaction of sol- itary waves, break-up and self-deflection of beams, and their potential applica- tions. 'CREOL, University of Central Florida, Orlando, Florida 32826 **Department of Electrical Engineering, University of Maryland, Baltimore, Maryland 21228 toptical Sciences Center, University of Arizona, Tucson, Arizona 85721 1. 2. 3. 4. 5. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964). G. I. Stegeman et al., in Novel Optical Materials and Applications, I. C .  Khoo and F. Simoni, eds. (Wdey, NY, 1996), in press. Yu. N. Karamzin, A. P. Sukhorukov, Sov. Phys. JET 41, 414 (1976). W. E. Torruellas et al., Phys. Rev. Lett. 74, 5036 (1995). R. Schiek et al., to appear in Phys. Rev. E (1996). 

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Trapping of light beams and formation of spatial solitary waves in quadratic nonlinear media

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