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Second harmonic generation: the solution for an amplitude-modulated initial pulse |
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| Authors: | H. Steudel Carla Figueira de Morisson Faria M. G. A. Paris A. M. Kamchatnov O. Steuernagel |
| Affiliation: | a Institut für Physik der Humboldt-Universität, Arbeitsgruppe “Nichtklassische Strahlung”, Rudower Chaussee 5, D-12484 Berlin, Germany b Max-Born Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Rudower Chaussee 6, D-12484 Berlin, Germany c Dipartimento di Fisica ‘Alessandro Volta' dell'Universitá degli Studi di Pavia, Istituto Nazionale di Fisica della Materia, Unitá di Pavia, via Bassi 6, I-27100 Pavia, Italy d Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 142092, Moscow Region, Russia e Department of Chemistry, Princeton University, Frick Chemical Laboratory, Washington Road and William Street, Princeton, NJ 08544, USA |
| Abstract: | We address the initial value problem for one-dimensional second harmonic generation starting from a purely amplitude-modulated fundamental wave. A general method to solve the problem in terms of a Schrödinger equation is presented, in which the initial pulse-shape is taken as a potential. Several examples with the complete solution given in analytical form are discussed. A much broader class of solutions can be found with the help of a single numerical integration. In particular, solutions with incident pulses approximating a sech-shape have been obtained. |
| Keywords: | Second harmonic generation Laser pulses Light modulation Partial differential equations Nonlinear equations Integration Approximation theory Problem solving Amplitude modulated initial pulses Initial value problems Amplitude modulated fundamental waves Schrodinger equation Liouville equation Ultrashort optical pulses |
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