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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 2111–2121

Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures

Giuseppe D’Aguanno, Marco Centini, Michael Scalora, Concita Sibilia, Mario Bertolotti, Mark J. Bloemer, and Charles M. Bowden  »View Author Affiliations

JOSA B, Vol. 19, Issue 9, pp. 2111-2121 (2002)

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Using a first-order multiple-scale expansion approach, we derive a set of coupled-mode equations that describe both forward and backward second-harmonic generation and amplification processes in nonlinear, one-dimensional, multilayered structures of finite length. The theory is valid for index modulation of arbitrary depth and profile. We derive analytical solutions in the undepleted pump regime under different pumping circumstances. The model shows excellent agreement with the numerical integration of Maxwell’s equations.

© 2002 Optical Society of America

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(230.4170) Optical devices : Multilayers

Giuseppe D'Aguanno, Marco Centini, Michael Scalora, Concita Sibilia, Mario Bertolotti, Mark J. Bloemer, and Charles M. Bowden, "Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures," J. Opt. Soc. Am. B 19, 2111-2121 (2002)

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  19. The numerical calculations were performed by use of a fast Fourier transform beam-propagation method that integrates the equations of motion in the time domain, as outlined in Ref. 1. Incident pulses are assumed to be 2 ps in duration and have the following intensity profile in time: Ĩ(pump)(t)=I(peak) exp[−(t2/2σ2)], where I(peak) is the peak intensity of the pump. A comparison with plane-wave results by use of pulses is possible because the spatial extension of these pulses is nearly 3 orders of magnitude greater than the structure length. As far as the structure is concerned, this incident pulse is nearly monochromatic, and the dynamics yield results that are nearly identical to the plane-wave results, provided the intensity of the plane wave is properly averaged over the pulse width. The average intensity of an incident plane-wave pump field is defined as I(pump)=I(peak)4σ −∞+∞ exp−t22dt=(π/8)1/2I(peak).
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  22. P. M. Lushnikov, P. Lodahl, and M. Saffman, “Transverse modulational instability of counterpropagating quasi-phase-matched beams in a quadratically nonlinear medium” Opt. Lett. 23, 1650–1652 (1999), and references therein. [CrossRef]

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