Soliton dynamics in a nonlocal medium
JOSA B, Vol. 16, Issue 2, pp. 236-239 (1999)
http://dx.doi.org/10.1364/JOSAB.16.000236
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Abstract
The nonlinear response of various materials extends beyond the illuminating beam. We present what is to our knowledge the first analytically tractable model for the dynamics of beams in partially nonlocal media. As far as an isolated beam is concerned, propagation is qualitatively the same, independently of the radius of nonlocality.
© 1999 Optical Society of America
OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
Citation
D. John Mitchell and Allan W. Snyder, "Soliton dynamics in a nonlocal medium," J. Opt. Soc. Am. B 16, 236-239 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-2-236
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References
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- A. W. Snyder and D. J. Mitchell, [Opt. Lett. 22, 16 (1997)] describe the mighty morphing spatial solitons and bullets that are characteristic of a highly saturating medium. The ln I law had been introduced previously, unbeknown to us, in a different context. See, for example, I. Bialynicki-Birula and J. Mycielski, Phys. Scr. 20, 539 (1979). But no one seems to have recognized its relevance to optical spatial solitons, possibly because of its singularity at I=0. However, Gausian beams in a ln I medium induce parabolic index waveguides, which are a standard model in linear optics. Coming at the problem, as we do, from the linear perspective shows from the outset that ln I is, like the parabolic index fiber, a good approximation.
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- We substitute ψ=B exp(ax^{2}) or ψ=B exp(ar^{2}) into the Schrödinger equation. Taking B=b^{−1/2} exp(iΦ) in two dimensions or B=b^{−1} exp(iΦ) in three dimensions, where Φ=(k/2n_{0})∫[n^{2}(0, z)−n_{0}^{2}]dz, and using Eq. (5), we find that a=ikn_{0}(db/dz)/(2b) and 2ikn_{0}(da/dz)+4a^{2}− (k^{2}Δ/ρ_{w}^{2})=0. Now the radius is given by 1/ρ^{2}= −2 Re(a). Thus, after a little algebra, we obtain d^{2}ρdz^{2}+1n_{0}^{2}ρ Δρ^{2}ρ_{w}^{2}−1k^{2}ρ^{2}=0. Equation (4) follows immediately.
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