Abstract
Chirped Hermite–Gaussian functions shows outstanding potentialities in mathematical models for linear and non linear pulse propagation in optical fibers. We propose three generalized subclasses of Hermite–Gaussian functions as natural extension to the complex domain. We exemplify the properties of these subclasses by analyzing some relevant cases of pulse oscillatory dynamics governed by nonlinear Schrödinger equation with constant or periodic coefficfients.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M. and I.A. Stegun. Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables, 1974.
Agrawal, G.P. Nonlinear fiber optics, San Diego, Academic Press, 1995.
Barthélé my, A., B. Bourliaguet, C. De Angelis, F. Gringoli and G.F. Nalesso. Opt. Commun. 171 345, 1999.
Bracewell, R.N. The Fourier Transform and its Applications, McGraw Hill, 1986.
Cohen-Tannoudji, C., B. Diu and F. Laloe. Quantum Mechanics, John Wiley and Sons, 1977.
Daubechies, I. IEEE Trans. Inform Theory 34 605, 1988.
Haus, H.A. and Y. Chen. J. Opt. Soc. Am. B, 16(6) 889 1999.
Kodama, Y. Physica D. 123 255, 1998.
Lakoba, T.I. and G.P. Agrawal J. Opt. Soc. Am. B, 16(9), 1332, 1999.
Lakoba, T.I. and D.J. Kaup, El. Lett. 34(11) 1124, 1998.
Lazaridis, P. G. Debarge and P. Gallion. Opt. Lett. 22(15), 685, 1997.
Lushnikov, P.M. Opt. Lett. 25(16) 1144, 2000.
McCord Morse P. and M. Feshback. Methods of Theoretical Physics, McGraw Hill, 1953.
Tonello, A. J. Opt. A: Pure Appl. Opt. 2(1–6), 2000.
Tonello, A., A.D. Capobianco, S. Wabnitz and S.K. Turitsyn. Opt. Commun. 175(1–3) 103, 2000.
Turitsyn, S.K. and E.G, Shapiro J. Opt. Soc. Am. B 16(9) 1321, 1999.
Turitsyn, S.K., T. Schäfer and V.K. Mezentsev, Opt. Lett., 23(17) 1351, 1998.
Turitsyn, S.K., T. Schäfer and V.K. Mezentsev. Phot. Tech. Lett. 11(2) 203, 1999.
Wolf K.B. Integral Transforms in Science and Engineering, Plenum Press New York, 1979.
J. Opt. Soc. Am. A 3 4, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cariolaro, G., Fregolent, M., Tonello, A. et al. Generalized Hermite–Gaussian functions and pulse propagation in optical fiber systems. Optical and Quantum Electronics 36, 853–880 (2004). https://doi.org/10.1007/s11082-002-9393-8
Issue Date:
DOI: https://doi.org/10.1007/s11082-002-9393-8