Light-bullet modes in self-induced-transparency media with refractive-index modulation
JOSA B, Vol. 19, Issue 6, pp. 1376-1379 (2002)
http://dx.doi.org/10.1364/JOSAB.19.001376
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Abstract
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
Citation
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)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-6-1376
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References
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- These bullets can be guided in the presence of a different refractive-index modulation given by n(x)=1−½C^{2} (−1+ ½ sech ^{2} Θ_{1} +½sech ^{2} Θ_{2} +tanh Θ_{1} tanh Θ_{2}), with C, Θ_{1}, and Θ_{2} as defined in Ref. 13.
- 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=α^{2} /(α^{2} +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} +n^{2} E _{τ} +ikE +i(1−n^{2})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 n^{2} (x)=1−β^{2} [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+Θ_{0}. Thus these solutions are localized in τ and x, but at a fixed τ they are not localized in z.
- 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≡x^{2} +y^{2} 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:n^{2} (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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- 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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