Rabi oscillations of azimuthons in weakly
nonlinear waveguides
Kaichao Jin,
a,b
Yongdong Li,
a
Feng Li,
a
Milivoj R. Beli´c,
c
Yanpeng Zhang,
a
and Yiqi Zhang
a,b,
*
a
Xi’an Jiaotong University, Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an, China
b
Guangdong Xi’an Jiaotong University Academy, Foshan, China
c
Texas A&M University at Qatar, Science Program, Doha, Qatar
Abstract. Rabi oscillation, an interband oscillation, describes periodic motion between two states that belong
to different energy levels, in the presence of an oscillatory driving field. In photonics, Rabi oscillations can be
mimicked by applying a weak longitudinal periodic modulation to the refractive index. However, the Rabi
oscillations of nonlinear states have yet to be introduced. We report the Rabi oscillations of azimuthons—
spatially modulated vortex solitons—in weakly nonlinear waveguid es with different symmetries. The period
of the Rabi oscillations can be determined by applying the coupled mode theory, which largely depends
on the modulation strength. Whether the Rabi oscillations between two states can be obtained or not is
determined by the spatial symmetry of the azimuthons and the modulating potential. Our results not only
deepen the understand ing of the Rabi oscillation phenomena, but also provide a new avenue in the study
of pattern formation and spatial field manipulation in nonlinear optical systems.
Keywords: Rabi oscillations; azimuthons; weak nonlinearity; longitudinally periodic modulation.
Received May 29, 2020; revised manuscript received Jun. 21, 2020; accepted for publication Jul. 6, 2020; published online
Aug. 5, 2020.
© The Authors. Published by SPIE and CLP under a Creative Commons Attribution 4.0 Unpor ted License. Distribution or
reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
[DOI: 10.1117/1.AP.2.4.046002]
1 Introduction
Rabi oscillations were introduced in quantum mechanics,
1
but
by now are widely investigated in a variety of optical and pho-
tonic systems that include fibers,
2,3
multimode waveguides,
4–6
coupled waveguides,
7
waveguide arrays,
8–10
and two-dimensional
modal structures.
11,12
Recently, Rabi oscillations of topological
edge states
13,14
and modes in the fractional Schrödinger equation
15
were also reported. Rabi oscillations are interband oscillations
that require an AC field to be applied as an external periodic
potential. In optics, the longitudinal periodic modulation of
the refractive index plays the role of an AC field in temporal
quantum systems, and Rabi oscillations are indicated by the
resonant mode conversion. As far as we know, the investigation
of optical Rabi oscillations thus far has been limited to the linear
regime only, and the Rabi oscillation in nonlinear systems is
still an open problem that needs to be explored.
The aim of this work is to investigate Rabi oscillations of
azimuthons in weakly nonlinear waveguides that is accomplished
by applying a weak longitudinally modulated perio dic potential.
Azimuthons are a special type of spatial soliton; they are azi-
muthally modulated vortex beams that exhibit steady rotation
upon propagation.
16
Generally, azimuthons, especially the ones
with higher-order angular momentum structures, a re unstable
in media with local Kerr or saturable nonlinearities. To over-
come the instability drawback, a nonlocal nonlinearity is intro-
duced, and recently published reports demonstrate that the stable
propagation of azimuthons can indeed be obtained.
17–19
In addi-
tion, it was also reported that the spin-orbit-coupled Bose–
Einstein condensates can support stable azimuthons as well.
20
However, the treatment of nonlocal nonlinearity and spin-orbit-
coupled Bose–Einstein condensates is challenging in both theo-
retical modeling and experimental demonstration. Nevertheless, it
has been confirmed that weakly nonlinear waveguides
21
represent
an ideal platform for the investigation of stable azimuthons,
22,23
even with higher-order modal structures.
Following this path of inquiry, we first investigate Rabi
oscillations of azimuthons in a circular waveguide and then in
a square waveguide. Since in this nonlinear three-dimensional
wave propagation problem no analytical solutions are known,
*Address all correspondence to Yiqi Zhang, E-mail: zhangyiqi@mail.xjtu.edu.cn
Research Article
Advanced Photonics 046002-1 Jul∕Aug 2020
•
Vol. 2(4)