Bouncing of vector solitons
ABSTRACT Summary form only given. We have shown how to control the collisions of vector solitons: from solitons going through, to solitons bouncing and developed a simple physical explanation based on gratings. We are currently investigating experimental implementations in saturable nonlinear media such as photorefractives.
Bouncing of Vector Solitons
Princeton University, Electrical Engineering, Princeton, NJ 08544
Phone 609-258 0430, email@example.com
Ken Steiglitz, Darrin Lewis
Princeton University, Computer Science, Princeton, NJ 08544
Technion, Physics Department, Haifa 32000, Israel and
Princeton University, Department of Electrical Engineering, Princeton, NJ 08544
J. A. Giordmaine
Princeton University, Electrical Engineering, Princeton, NJ 08544, and
NEC Research Institute, Princeton, NJ 08540
Abstract: We show how to control the collisions of vector solitons: from solitons going
through each other, to solitons bouncing off each other. In bouncing, a weak soliton
component switches most of the energy of the strong component.
OCIS codes: 190.0190, 190.3270
When two scalar solitons collide in an ideal Kerr type medium, they experience only a phase
shift while conserving their energies, linear momenta, and shapes . Manakov vector solitons however
consist of two  or more components and their interactions are much richer than those of scalar solitons
It is useful to think of generating vector solitons in the following manner: starting with two scalar
solitons A and B that belong to two independent optical fields (e.g., two orthogonal polarizations) take
some energy from each field and inject into the other. More specifically: split A into A1 and A2, and B into
B1 and B2 and then superimpose B1 on A1 to form vector soliton 1, VS1, and superimpose A2 on B2 to form
vector soliton 2, VS2. One would expect that, if the amount of energy split-off is small, then the vector
solitons should behave almost as scalar solitons: be unaffected by the collision. Here we show, through
numerical simulations and analytical calculations [4, 5], that as little as 10% intensity split-off (i.e., |B1/A1|2
= 0.1) can drastically change the collision outcome, making the solitons "bounce" off rather than go
through each other.
The setup of the numerical "experiments" is shown in Fig. 1. The input condition is shown in Fig.
1a, and the state transformation (based on the analytic formulation of Ref. ) is shown in Fig. 1b. The two
amplitude ratios at the input are ρ1 = A1/B1 = R and ρL = A2/B2 = ± 1/R where the ± accounts for in or
out of phase respectively. The final states are ρ2 and ρR and depend on the collision angle, on R, and on the
total intensity in each vector soliton. The final states can be calculated exactly from Ref. . Vector
Soliton 1 (so-called VS1) is launched from left to right and VS2 from right to left as shown in Fig. 1b.
Fig1. (a) The A-field (dotted line) and the B-field (solid line). (b) State transformations and the
geometry of the collision, ρ1 and ρL are the initial states and ρ2 and ρR are the final states after the
Bouncing occurs due to large energy exchanged between the components of each field and it
occurs for |ρ2|2 > 1. In that case, the peaks of each field remain on the same side as they begin, giving the
impression of bouncing off each other, as shown in Figs. 2a and 2b, where |ρ2| 2 = 2.75. The simulations in
Fig. 2 show the intensities for the A and the B fields and corresponds to an angle of 0.6o, R = 3, and to a
nonlinear index change of 6.3 x 10-4 in physical units for an intensity of 16. Figs. 2a and 2b show both A
and B fields to highlight the symmetry of the bouncing process. Intuitively we can think of this bouncing-
interaction being caused by diffraction off two gratings with the same periodicity: the grating written by A1
and A2 and the grating written by B1 and B2. The ratio R gives the modulation depth of the grating, and
together with the total intensity, they determine the strength of the grating. The angle gives the length of
Building upon the grating intuition we reduce the intensity by a factor of 8 so that the grating is
weaker and there is no bouncing as shown in Fig. 2c, where |ρ2| 2 = 0.53. The grating does switch some
energy (symmetrically) between the field components of the solitons (as in Ref. ) but is not strong
enough to switch most of the energy as in Figs. 2a, 2b. Up to now the two gratings were in-phase and they
add constructively. But, by making the B1 out of phase with B2 the two gratings can cancel each other and
therefore the two vector solitons are transparent to each other, as shown in Fig. 2d.
Fig.2. (a) ,(b). The bouncing case showing the A and the B fields respectively. The total intensity in each vector
soliton is 16 and |ρ2| 2 = 2.75. (c) The total intensity is reduced to 2, the gratings weaken, |ρ2|2 = 0.53 and there is
no bouncing. (d) Same as (a) but with the two gratings out of phase. This is the transparent case since the
collision has no effect on the field components.
In summary, have shown how to control the collisions of vector solitons: from solitons going
through, to solitons bouncing and developed a simple physical explanation based on gratings. We are
currently investigating experimental implementations in saturable nonlinear media such as photorefractives.
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