CHIN. PHYS. LETT. Vol. 36, No. 12 (2019) 124203
A V-Folded Digital Laser for On-Demand Vortex Beams by Astigmatic
Transformation of Hermite–Gaussian Modes
∗
Sen-Sen Liu(
刘
森森
), Xu-Dong Chen(
陈
旭
东
)
**
, Ji-Xiong Pu(
蒲
继
雄
),
Zhi-Li Lin(
林
志
立
), Zi-Yang Chen(
陈
子
阳
)
Fujian Key Laboratory of Light Propagation and Transformation, College of Information Science and Engineering,
Huaqiao University, Xiamen 361021
(Received 5 September 2019)
A V-folded digital laser using a spatial light modulator (SLM) for intra-cavity loss shaping is exploited to generate
Hermite–Gaussian modes with on-demand mode order. With a 𝜋/2 astigmatic mode converter, vortex beams
carrying on-demand orbital angular momentum (OAM) with a tunable range from −11~ to 12~ are obtained.
The mode order of the HG mode, hence the OAM of the vortex beam, is digitally switched by changing the
phase pattern imposed on the SLM without requiring any mechanic alignment of the cavity. This work has great
potential applications in various OAM-tunable vortex beams.
PACS: 42.50.Tx, 42.60.By, 42.60.Jf DOI: 10.1088/0256-307X/36/12/124203
Due to their unique phase and amplitude
structures, Hermite–Gaussian (HG) and Laguerre–
Gaussian (LG) beams have gained considerable at-
tention and found a lot of applications in frontier
technologies,
[1]
such as optical trapping and manipu-
lation of particles,
[2−4]
quantum information and opti-
cal telecommunication,
[5−7]
and so on. Several extra-
cavity generation methods for these modes have been
reported by utilizing diffraction optical elements,
[8]
spatial light modulators (SLMs)
[9]
or digital micromir-
ror devices (DMDs).
[10,11]
However, generally speak-
ing, the vortex beam quality generated by most sub-
sequent mode conversion methods is limited by poor
mode purity or low conversion efficiency.
[12]
Mean-
while, pure HG or LG modes can be directly generated
in a laser cavity. Annular pumping method is a well-
known method to directly generate vortex beams in
laser resonators.
[13,14]
However, it is difficult to ob-
tain high order LG modes from a laser cavity with an
annular pumping method. Fortunately, an astigmatic
mode converter can efficiently convert a diagonal HG
mode into an LG mode in a simple way.
[15−17]
In recent years, off-axis pumping has been
widely employed to produce high-order HG modes
in end-pumped lasers, which enables the genera-
tion of vortex beams with large OAM via mode
transformation.
[18−23]
The mode order is generally
limited by the laser crystal size. However, to contin-
uously tune the HG mode order, not only the off-axis
displacement of pump beam should be increased but
also the position of output coupler needs to be pre-
cisely adjusted. Consequently, this scheme is less prac-
tical for generation of a vortex beam with on-demand
OAM. Gain-shaping based methods have also been
proposed for selective HG mode excitation, by extra-
cavity shaping the pump beam of an end-pumped
laser.
[24−28]
With these methods, no adjustment of the
cavity itself was required for mode switching between
different HG modes. However, the excitable HG
𝑚,𝑛
modes were limited to relatively low mode numbers.
Recently, the application of a DMD in pump shaping
has exhibited a computer-controlled selective excita-
tion of high-order HG modes.
[29]
A digital laser, which utilizes an SLM as the back
cavity mirror, has shown its simplicity in intra-cavity
mode shaping.
[30−33]
By employing an SLM as an am-
plitude modulator for intracavity loss shaping, low or-
der HG modes have been generated.
[31,33]
The output
mode of digital laser is customized and switched by
controlling the SLM. During the on-demand mode se-
lection in the digital laser, neither new specially de-
signed optical elements nor additional alignment of
the laser cavity is required. However, a digital laser is
limited to the damage threshold of SLM, which is gen-
erally several to dozens of watts per square centime-
ter. To avoid the damage of the SLM, the transverse
mode size on the SLM should be as large as possible,
Meanwhile, to obtain high-order modes the limitation
of the crystal aperture should also be overcome; that
is, the transverse mode size on the crystal should be
as small as possible. To balance this contradiction, a
V-folded cavity can be employed. Compared to linear
geometry, V-folded laser cavity configuration allows
easy control of the transverse mode sizes at different
intracavity positions.
[34,35]
In this Letter, we demonstrated a V-folded digi-
tal laser for on-demand vortex beam generation. A
computer controlled SLM serves as a folding mirror,
while two spherical mirrors enclose the resonant cav-
ity. This specially designed cavity makes a small
∗
Supported by the National Natural Science Foundation of China under Grant Nos 61605049 and 61575070, and the Natural
Science Foundation of Fujian Province of China under Grant No 2018J01003, the Fundamental Research Funds for the Central
Universities under Grant No ZQN-707, and the Subsidized Project for Postgraduates’ Innovative Fund in Scientific Research of
Huaqiao University.
**
Corresponding author. Email: chenxd@hqu.edu.cn
© 2019 Chinese Physical Society and IOP Publishing Ltd
124203-1