Enhancement of phase conjugation degenerate
four-wave mixing using a Bessel beam
QIAN ZHANG,
1,†
XUEMEI CHENG,
1,
*
,†
HAOWEI CHEN,
1,3
BO HE,
1
ZHAOYU REN,
1
YING ZHANG,
2
AND JINTAO BAI
1
1
State Key Laboratory Incubation Base of Photoelectric Technology and Functional Materials, National Photoelectric Technology
and Functional Materials and Application of Science and Technology International Cooperation Center,
Institute of Photonics & Photon-Technology, Northwest University, Xi’an 710069, China
2
School of Science, Engineering University of PAP, Xi’an 710086, China
3
e-mail: chenhaowei2005@126.com
*Corresponding author: xmcheng@nwu.edu.cn
Received 26 October 2017; revised 7 December 2017; accepted 22 December 2017; posted 3 January 2018 (Doc. ID 310019);
published 12 February 2018
We report on the enhancement of phase conjugation degenerate four-wave mixing (DFWM) in hot atomic Rb
vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation
based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the
Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the ex-
tended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable
intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the self-
healing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be
of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that
a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering
media.
© 2018 Chinese Laser Press
OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (350.6830) Thermal lensing; (060.5060) Phase modulation.
https://doi.org/10.1364/PRJ.6.000162
1. INTRODUCTION
Bessel beams are radiations of which the amplitudes can be
described by Bessel functions, which are sets of solutions to
the Helmholtz equation in free space [1]. As they exhibit the
propagation-invariant feature (non-diffraction) [2–5], people
can achieve an extended depth of field with a small focal spot
using Bessel beams. Moreover, they have the ability to reestab-
lish their transverse intensity profiles after passing through an
obstacle (self-healing, self-reconstructing). For those attractive
properties, Bessel beams have been applied in numerous areas,
such as atom optics [6,7], optical micromanipulation [2],
microscopy [8–10], and optical tweezers [11]. Bessel bea ms
are also of particular significance in nonlinear optics [12–14].
On one hand, nonlinear optical processes can be enhanced
(especially in thick and complex media) , thanks to the “non-
diffraction” and “self-reconstructing” properties of the Bessel
beam. On the other hand, more information of the nonlinear
medium can be retrieved because of the unique phase-matching
characteristics across the focal region.
Four-wave mixing (FWM) is a kind of third-order nonlinear
process in which three beams interact with the nonlinear
medium and a fourth beam (FW M signal) is generated when
the phase-matching condition is satisfied. FWM has a variety of
applications, such as squeezed states of light [15], wavelength
conversion [16], isotope selective analysis and determinat ion
[17,18], and image reconstruction [19,20]. In particular, de-
generate FWM (DFWM) is a superb method to generate a
phase-conjugate beam, in which a probe beam intersects two
counter-propagating pump beams, and the DFWM signal is
generated in the opposite direction of the probe beam.
Because the DFWM signal is the phase-conjugate beam of
the input probe beam, it can be used to eliminate the distortion
as the probe beam passes through an inhomogeneous phase-
distorting medium [21,22]. So far, DFWM has been widely used
in adaptive optics, laser communication, and so on. However,
the DFWM signal decreases or even disappears due to phase-
mismatching and loss of energy in a strongly scattering thick
medium, limiting its application in harsh environments.
In this work, we use a Bessel beam as the probe beam and
study the enhancement of DFWM in hot atomic Rb vapor.
The Bessel beam is generated by focusing the hollow beam
generated using cross-phase modulation based on the thermal
nonlinear optical effect [23]. Compared with commonly used
hollow beam generation methods (including axicon lenses [24]
162
Vol. 6, No. 3 / March 2018 / Photonics Research
Research Article
2327-9125/18/030162-06 Journal © 2018 Chinese Laser Press