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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 6 — Jun. 1, 2002
  • pp: 1376–1379

Light-bullet modes in self-induced-transparency media with refractive-index modulation

Miriam Blaauboer, Gershon Kurizki, and Boris A. Malomed  »View Author Affiliations

JOSA B, Vol. 19, Issue 6, pp. 1376-1379 (2002)

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We predict the existence of a new type of spatiotemporal soliton (so-called light bullets) in two-dimensional self-induced-transparency media with refractive-index modulation in the direction transverse to that of pulse propagation. These self-localized guided modes are found in an approximate analytical form. Their existence and stability are confirmed by numerical simulations, and they may have advantageous properties for signal transmission.

© 2002 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

Miriam Blaauboer, Gershon Kurizki, and Boris A. Malomed, "Light-bullet modes in self-induced-transparency media with refractive-index modulation," J. Opt. Soc. Am. B 19, 1376-1379 (2002)

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  26. These bullets can be guided in the presence of a different refractive-index modulation given by n(x)=1−½C2 (−1+ ½ sech 2 Θ1 +½sech 2 Θ2 +tanh Θ1 tanh Θ2), with C, Θ1, and Θ2 as defined in Ref. 13.
  27. As an example of another type of 2D guided-LB mode, one can find a family of LBs that correspond to α=∞ in Eq. (2d). Their velocity, given by the expression v=α2 /(α2 +1), takes the maximum possible value, v=1. These solutions are obtained by substitution of a plane wave (in z) ansatz E (τ, z, x)=E (τ, x)exp (−ikz), P (τ, z, x)=P (τ, x)× exp (−ikz), and W(τ, z, x)=W(τ, x), with an arbitrary real constant k, into Eqs. (1). The equation for the field then becomes −iE xx +n2 E τ +ikE +i(1−n2)E −P =0, with the equations for P and W given by Eqs. (1b) and (1c). If the RI in the medium is modulated as n2 (x)=1−β2 [tanh 2 (βx)−sech 2 (βx)]+kβ, the LB solution to Eqs. (1) can be approximated by Eq. (2), with Θ(τ, z) replaced by τ+Θ0. Thus these solutions are localized in τ and x, but at a fixed τ they are not localized in z.
  28. A guided LB similar to that in Eq. (2) can be found in a 3D SIT medium embedded in a cylindrical waveguiding structure. The medium is described by Eqs. (1), with E xx → E rr +(1/r)E r, where r≡x2 +y2 is the transverse radial coordinate. Searching for an axisymmetric solution of these 3D equations, we arrive at an approximation of the same form as Eqs. (2) but with x replaced by r, and a corresponding cylindrical RI modulation:n2 (r)=1−ββ[1−2 sech 2 (βr)]−tanh (βr) r, for |βr|≪1. Comparison with results of simulations of the cylindrically symmetric 3D equations by use of the analytical approximation as an initial ansatz again shows good agreement (with a deviation of <2%). In practice, however, such 3D guided-LB and waveguiding structures are probably much harder to realize than their 2D counterparts.
  29. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999). [CrossRef]
  30. See J. P. Dowling, H. Everitt, and E. Yablonovitch, “Photonic band-gap bibliography,” http://home.earthlink.net/~jpdowling/pbgbib.html.
  31. C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. W. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999). [CrossRef]
  32. R. E. Slusher, “Self-induced transparency, experiment,” in Progress in Optics, by E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 76–85.

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