Solitons in Nonlocal Media

LIST OF FIGURES
3.2 (a,b) Perturbation profiles versus ξ for 〈ξ〉 = 0.5, 0.63, 0.76 and 0.9 (solid
line, squares, stars and triangles, respectively) for (a) ω = 0.001 and (b)
ω = 0.09. The profile in (a) is very similar to the Green function, as
the soliton is much narrower than the sample width. (c) Calculated
α (squares) and α s for 〈ξ〉 = 0.54 (no symbols), 〈ξ〉 = 0.72 (stars)
and 〈ξ〉 = 0.86 (triangles), respectively, versus normalized waist ω. (d)
Calculated α g for the same set of soliton positions. . . . . . . . . . . . . 40
3.3 Calculated V ξ m(ξ) for ω = 0.02 and 〈ξ〉 = 0.5(solid line), ω = 0.02 and
〈ξ〉 = 0.75 (asterisks), ω = 0.1 and 〈ξ〉 = 0.5 (triangles), ω = 0.1 and
〈ξ〉 = 0.75 (squares), respectively. The numerical results are in complete
agreement with the theoretical approximation. (b, c) Calculated degree
of nonlocality along x and (d) along t for 〈ξ〉 = 0.5 (circles), 〈ξ〉 = 0.54
(solid line), 〈ξ〉 = 0.68 (squares) and 〈ξ〉 = 0.81 (triangles), respectively. 45
3.4 Perturbation profiles for (a,c) ω = 0.01 and (b,d) ω = 0.1 for (a,b)
〈ξ〉 = 0.5 and (c,d) 〈ξ〉 = 0.75. The dashed (solid) lines correspond
to profiles along υ(ξ − 〈ξ〉). The profiles are chosen such to contain
the perturbation peak. Squares (triangles) are the corresponding values
computed with a full numerical approach, which completely agree with
the theoretical predictions from eq. (3.20). . . . . . . . . . . . . . . . . . 46
3.5 Calculated figure of nonlocality αx for Gaussian intensity profiles (curves
for αt and α g/s
x/t are nearly identical) versus ω for 〈ξ〉 = 0.5 and (a,b)
µ/κ = 102 or (c,d) µ/κ = 104 . In this range for µ/κ, the nonlocality
does not depend on beam position. When αx = 1, perturbation and
excitation have the same profile, i.e. the medium is local. (b) - (d):
perturbation profile along υ(symbols) and ξ−〈ξ〉(solid line) for µ/κ = 10 2
and µ/κ = 10 4 , respectively, when ω = 0.035 and 〈ξ〉 = 0.5; in both cases
the perturbation possesses radial symmetry. In (b) the perturbation is
wider due to a higher ratio µ/κ. . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Plots of g1 (a,d) and g2 (b,e) for 〈ξ〉 = 0.5. The corresponding profiles
are plotted in (c) and (f) versus ξ (g1 solid line, g2 squares) and υ (g1
dashed line, g2 triangles), normalized to one (the cross sections are in
υ = 0 and ξ = 0.5, respectively). Results for g1 and g2 perfectly overlap.
Excitation waists are ω = 0.03 (a,b,c) and ω = 0.1 (d,e,f), respectively. . 53
x