Hollow Gaussian beam generated by beam shaping with phase-only liquid
crystal spatial light modulator
Yongming Nie
a,
n
, Xiujian Li
a
, Junli Qi
a
, Haotong Ma
b
, Jiali Liao
a
, Jiankun Yang
a
, Wenhua Hu
a
a
Tech-Physica1 Research Center, Science College, National University of Defense Technology, Changsha, Hunan 410073, China
b
College of Photon–Electron Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
article info
Article history:
Received 11 April 2011
Received in revised form
21 July 2011
Accepted 25 July 2011
Available online 12 August 2011
Keywords:
Beam shaping
Hollow Gaussian beam
Phase modulation
abstract
Based on the refractive beam shaping system, the transformation of a quasi-Gaussian beam into a dark
hollow Gaussian beam by a phase-only liquid crystal spatial light modulator (LC-SLM) is proposed.
According to the energy conservation and constant optical path principle, the phase distribution of the
aspheric lens and the phase-only LC-SLM can modulate the wave-front properly to generate the hollow
beam. The numerical simulation results indicate that, the dark hollow intensity distribution of the
output shaped beam can be maintained well for a certain propagation distance during which the dark
region will not decrease whereas the ideal hollow Gaussian beam will do. By designing the phase
modulation profile, which loaded into the LC-SLM carefully, the experimental results indicate that the
dark hollow intensity distribution of the output shaped beam can be maintained well even at a distance
much more than 550 mm from the LC-SLM, which agree with the numerical simulation results.
& 2011 Elsevier Ltd. All rights reserved.
1. Introduction
The dark hollow laser beam is needed for many practical
applications such as optical atom trapping [1,2], cold atom guiding
[3,4], multi-photon ionization of xenon [5], and harmonic generation
[6,7]. The beam with dark hollow intensity distribution may be
TEM
01
model profile, high-order Bessel profile, and hollow Gaussian
beam profile [8]. The dark hollow beams can be generated by
various methods such as the transverse mode selection method [9],
the geometrical optical method [10], the optical holographic method
[11,12], the binary spatial light modulator method [13],andthe
photonic crystal fiber method [14].
Usually, the low energy conversion efficiency is the main
problem to generate the dark hollow beams. In order to improve
the energy conversion efficiency, Kreuzer [15] proposed a refrac-
tive beam shaping systems with two aspheric lenses as the key
components, in which the first aspheric lens redistributes the
intensity profile of the input beam and the second aspheric lens
re-collimates the output beam. Based on the refractive beam
shaping system, Hoffnagle and Jefferson reported the generation
of flattop laser beam by two aspheric lenses [16], Hossain et al.
investigated the generation of Bessel beam from annular Gaussian
beam theoretically [17]. However, as the fabricated aspheric
lenses cannot be programmed, the system can only work well
for the specific single input to generate single output beam profile
[18]. In order to achieve beam shaping from various inputs,
Ma and his coworkers have succeeded in generating near-diffrac-
tion-limited flattop beams with the phase-only liquid crystal spatial
light modulator (LC-SLM) instead of the aspheric lens [19–21], in
which the LC-SLM is programmable and of high spatial resolution.
We replace the first aspheric lens by a phase-only LC-SLM to
generate dark hollow Gaussian beam. Ref. [2] has proposed a
theoretical method to generate a hollow Gaussian beam with LC-
SLM. However, it should be noticed that the method of Ref. [2] is
based on spatial filtering in the Fourier domain and is implemen-
ted with a typical 4-f optical system and a Michelson interferom-
eter type system. In this paper, we directly impose different phase
modulations on various areas of the wave-front of the input
beam, which is more compact and robust than the method
proposed in Ref. [2]. As re-collimation is needless for some near
field applications such as nonlinear optics and atom optics,
we concentrate on the intensity redistribution by one phase-only
LC-SLM rather than re-collimate the output beam.
This paper is organized as follows. In the second section, the
design principle will be introduced, and the propagation proper-
ties of the shaped beam and the ideal hollow Gaussian beam will
be analyzed in detail. In the third section, the experimental
generation of hollow Gaussian beam will be reported and dis-
cussed. In the fourth section, the conclusions are given.
2. Design principle and numerical analysis
According to the basic principle, the refractive shaping system can
be classified into two categories, i.e. the Galilean shaping system and
the Keplerian shaping system, which are shown in Fig. 1(a) and (b),
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Optics & Laser Techn ology
0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.optlastec.2011.07.021
n
Corresponding author. Tel.: þ86 73184573278.
E-mail address: xjli@nudt.edu.cn (Y. Nie).
Optics & Laser Technology 44 (2012) 384–389