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Hermite Coherent States for Quadratic Refractive Index Optical Media

  • Zulema Gress
  • Sara Cruz y CruzEmail author
Chapter
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

Ladder and shift operators are determined for the set of Hermite–Gaussian modes associated with an optical medium with quadratic refractive index profile. These operators allow to establish irreducible representations of the su(1, 1) and su(2) algebras. Glauber coherent states, as well as su(1, 1) and su(2) generalized coherent states, were constructed as solutions of differential equations admitting separation of variables. The dynamics of these coherent states along the optical axis is also evaluated.

Keywords

Hermite–Gaussian modes Ladder operators Coherent states Self-focusing media Paraxial beams Ermakov equation 

Notes

Acknowledgements

The financial support of CONACyT, Mexico (Project A1-S-24569 and grant 257292 for ZG), Instituto Politécnico Nacional, Mexico (Project SIP20180377), the Spanish MINECO (Pro. MTM2014-57129-C2-1-P), and Junta de Castilla y León, Spain (VA137G18) is acknowledged. The authors are indebted to Prof. J. Negro for enlightening comments and to the anonymous referee for valuable suggestions. Z. Gress is grateful to the Valladolid University for kind hospitality.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidad Autónoma del Estado de HidalgoCiudad del ConocimientoHidalgoMexico
  2. 2.Instituto Politécnico NacionalUPIITACiudad de MéxicoMexico

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