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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.
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  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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