0 1,000 2,000 3,000
Delay (ps) Delay (ns)
0 20 40 60 80 100
18. 5 19 19. 5 20 20. 5 21 21. 5 22 22. 5 23 23. 5
light makes for remarkable interaction
ranges. Using the first acoustic echo,
we observed interactions ranging up to
8,000 times the width of the solitons.
Our observations illustrate the robustness of solitons and further cement the
exceptional status of these objects.
The accompanying movie shows the
real-time evolution of two temporal
cavity solitons as recorded on an oscilloscope. Initially separated by 1. 7 ns,
they attract each other before reaching
a stable separation. The attraction is
initially very weak, but speeds up as
they get closer.
Solitons are self-localized wave pack- ets that do not spread. As the name
suggests, solitons behave like particles:
they conserve their individual characteristics when interacting. 1 In the last 20
years, this trait has triggered extensive
studies in the field of optics. 2
We report what is, by orders of magnitude, the weakest interaction observed
between two solitons. 3 In our optical
fiber experiment, two temporal solitons
traveling one behind the other change
their relative separation by as little as
1 Å for each 100 m of propagation—a
difference in scale of 12 orders of magnitude. Such a displacement represents
a 1/10,000 of the wavelength of the
underlying carrier wave and translates
into a change of only half an attosecond
for the temporal delay between the two
picosecond pulses. The interactions are
so weak that at the speed of light, they
require an effective propagation distance
on the order of an astronomical unit to
fully develop. We used temporal cavity
solitons that recirculate in a passive ring
resonator to make this happen. 4 Thanks
to a coherent continuous-wave driving
field balancing the losses, propagation
can persist indefinitely.
Interactions are mediated by sound.
The leading soliton excites transverse
acoustic waves through minute deformations of the fiber core. The sound
waves perturb the refractive index of
the medium which alters the velocity
of trailing solitons. 5 The mechanism
is not new but cavity solitons barely
react to it, their phase being locked
to the coherent driving field. Sound
echoing from the fiber edge combined
with the slowness of sound against
(a) Evolution of two temporal cavity solitons initially separated by 1,800 ps. (b) Acoustic
perturbation of the refractive index generated by the leading cavity soliton. Inset: Illustration of multiple echoes. (c) Juxtaposition of four measurements with initial separations
around 20 ns to probe the first acoustic echo [peak 2 in (b)]. Stable separations after 5 min
correspond to maxima of the acoustic response. Red curves are numerical simulations.
Jae K. Jang, Miro Erkintalo,
Stuart G. Murdoch
and Stéphane Coen
University of Auckland,
1. N.J. Zabusky and M.D. Krus-kal. Phys. Rev. Lett. 15, 240
2. G. I. Stegeman and M. Segev.
Science 286, 1518 (1999).
3. J.K. Jang et al. Nature Photon. 7, 657 (2013).
4. F. Leo et al. Nature Photon. 4,
5. E.M. Dianov et al. Appl. Phys.
B 54, 175 (1992).
Visit www.opnmagazine-digital.com to view
the video that accompanies this article.