Diffraction and shaping analysis of excimer laser
through an ultrasonic grating
Lixia Liu, Jinyun Zhou
n
, Yafei Deng, Haiyong Liu, Liang Lei, Bo Wang
School of Physics and Optoelectronic Engineering, Guangdong University of Technology, WaiHuan Xi Road, No. 100, Guangzhou 510006, PR China
article info
Article history:
Received 9 September 2013
Received in revised form
20 October 2013
Accepted 4 November 2013
Keywords:
Excimer laser
Beam shaping
Ultrasonic grating diffraction
abstract
A novel numerical simulation method for the shaping of an excimer laser beam by an acoustic grating is
proposed. Partially coherent theory and extended Huygens–Fresnel principle are used to analyze the
light intensity diffraction pattern. Fast Fourier transform function FFT in the Matlab is used to calculate
the numerical integral, which makes the integral operation simple and efficient. It is shown by a
numerical simulation that the output intensity distribution is closely related to the coherence width,
Raman–Nath comprehensive parameter, diffraction distance and ultrasonic wave frequency. The
simulation results show that a flat top beam can be obtained by controlling these parameters. On the
other hand, the results are used as an effective analytic tool for the determination of the design
parameters of acousto-optic modulator.
Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
1. Introduction
Excimer lasers are widely used for lithography because of their
high conversion efficiency, high average power and high pulse
energies at UV wavelengths [1]. However, the intensity distribu-
tion of output beam produced by most excimer lasers which is a
partially coherent Gaussian beam is not uniform [2]. They cannot
meet the requirements for the lithography applications such as the
manufactures of FPD and HD-PCB [3]. Over the years, some
techniques to improve the homogeneity of excimer laser beams
have been proposed [4–11]. In particular, diffraction optical ele-
ments stand out by their merits of flexibility, high diffraction
efficiency and good performances [12,13]. Compared with micro-
lens arrays, the acousto-optic modulator has a lower-cost produc-
tion. The numerical simulation method using Collins integral and
ABCD matrix formalism to shape a Gaussian beam into a flat top
beam has been reported [11]. According to different ultrasonic
wave frequencies and different acousto-optic interaction lengths,
there are two basic regimes of acousto-optic interaction: Bragg
and Raman–Nath diffraction [14,15]. The parameter Q ¼ 2
πλL=λ
2
s
n
0
is used to predict the two types of diffraction [16].
In this paper, we propose a simple numerical simulation
method by building up a new theoretical model for the shaping
of an excimer laser beam. Due to the partial coherence of excimer
laser, it can be studied using Gaussian Schell-model. The output
intensity profile in free space at different propagation distances is
analyzed by utilizing the extended Huygens–Fresnel principle. All
calculations are done in the near-field. When calculating the
integral, the Fourier transform is used to take the place of integral,
which can avoid the complicated operation in the analytical
calculation. We show the influence of different parameters on
the uniformity of intensity distribution. Our work is focused on
obtaining a flat top beam by controlling the parameters, which has
a wide application value and guiding significance for the beam-
shaping experiments.
2. Theoretical model
As an ultrasonic wave propagates in an acousto-optic medium,
the acousto-optic medium in the ultrasonic field will be com-
pressed. Variations of density cause the refractive index to vary
periodically, which forms an ultrasonic grating. The laser beam
will be diffracted and suffers a phase modulation when passing
through the acousto-optic interaction medium. Here, we consider
only the Raman–Nath diffraction regimes. Based on the Raman–
Nath multiple-order diffraction, each position where the laser
beam is diffracted will produce a group of discrete diffraction
light. Then, the different diffraction orders of each group will
overlap and there are no interference effects. As a result, a good
approximation of a flat top distribution is obtained. The complex
amplitude transmittance of the medium is written as
tðxÞ¼TðxÞexpðjk ∇nðxÞLÞð1Þ
where TxðÞis the amplitude transmittance, k stands for the light
wave vector and L represents the acousto-optic interaction
length. In addition, k∇nðxÞL is defined as the relative phase
delay after light passes through the acousto-optic crystal with
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journal homepage: www.elsevier.com/locate/optlastec
Optics & Laser Technology
0030-3992/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.optlastec.2013.11.002
n
Corresponding author. Tel: þ86 13610256271.
E-mail address: zhjy@gdut.edu.cn (J. Zhou).
Optics & Laser Technology 58 (2014) 71–75