Optimal pulses for arbitrary dispersive media

M. A. Alonso; T. SetÃ¤lÃ¤; A. T. Friberg

doi:10.2971/jeos.2011.11035

Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Optimal pulses for arbitrary dispersive media

M. A. Alonso, T. SetÃ¤lÃ¤, A. T. Friberg

Abstract

A variational procedure is given for finding the pulses for which the initial temporal rms width and the rate of increase of this width are jointly minimized for propagation in non-absorbing media with arbitrary dispersive properties. We show that, while in linearly dispersive media the optimal pulses are Gaussian, in other situations such as a hollow metallic waveguide or for purely cubic dispersion departures from Gaussian behavior become evident. An interpretation of the results in terms of suitable phase-space representations is also given.

Full Text: PDF

Citation Details

Cite this article

References

A. E. Siegman, "New developments in laser resonators" Proc. SPIE 224, 2-14 (1990).

P. A. Bélanger, Y. Champagne, and C. Paré, "Beam propagation factor of diffracted laser beams" Opt. Commun. 105, 233-242 (1994).

P. A. Bélanger, "Beam propagation and the ABCD ray matrices" Opt. Lett. 16, 196-198 (1991).

A. E. Siegman, "Defining the effective radius of curvature for a nonideal optical beam" IEEE J. Quantum Elect. 27, 1146-1148 (1991).

H. Weber, ed., Special Issue on Laser Beam Quality, Opt. Quant. Electron. 24, no. 9 (1992).

S. A. Ponomarenko, and G. P. Agrawal, "Phase-space quality factor for ultrashort pulsed beams" Opt. Lett. 3, 767-769 (1989).

B. H. Kolner, and M. Nazarathy, "Temporal imaging with a time lens" Opt. Lett. 14, 630-632 (1989).

B. H. Kolner, "Space-time duality and the theory of temporal imaging" IEEE J. Quantum Elect. 30, 1951-1963 (1994).

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Second Edition, Wiley, New York, 2007).

G.-C. Lin, C.-H. Sui, and Q. Lin, "Non-Gaussian pulse propagation and pulse quality factor using intensity moment method" Chinese Phys. Lett. 16, 415-417 (1999).

G. Rousseau, N. Mcgarthy, and M. Piché, "Description of pulse propagation in a dispersive medium by use of a pulse quality factor," Opt. Lett. 27, 1649-1651 (2002).

J. C. Petruccelli and M. A. Alonso, "Phase space distribution tailored for dispersive media," J. Opt. Soc. Am. A 27, 1194-1201 (2010).

P. Loughlin, and L. Cohen, "A Wigner approximation method for wave propagation" J. Acoust. Soc. Am. 118, 1268-1271 (2005).

P. Loughlin, and L. Cohen, "Approximate wave function from approximate non-representable Wigner functions" J. Mod. Opt. 55, 3379-3387 (2008).

J. Vanderlinde, Classical Electromagnetic Theory (Wiley, New York, 1993).

G. P. Agrawal, Nonlinear Fiber Optics (Second Edition, Academic Press, San Diego, 1995).

N. G. R. Broderick, "Method for pulse transformations using dispersion varying optical fibre tapers" Opt. Express 18, 24060-24069 (2010).

G. B. Arfken, and H. J. Weber, Mathematical Methods for Physicists (Sixth Edition, Elsevier, Amsterdam, 2005).