![](https://csdnimg.cn/release/download_crawler_static/18272036/bg3.jpg)
46. J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by
focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
47. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener,
“Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
48. J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven
helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
1. Introduction
Recently, the multifocal spots array (MSA) under tight focusing condition in a high NA
objective has attracted great attention due to its intrinsic advantage of high processing
efficiency. This MSA has been widely used in a range of applications, including multiphoton
multifocal microscopic imaging [1–3], optical trapping and manipulation [4–6], real-time
molecular imaging [7], and laser micro/nano fabrication [8–10]. There are diverse ways to
produce MSAs in the focal region of a high NA objective. These approaches can be
summarized in the following two categories. One is obtained by applying optical elements,
such as beam splitters [11,12], etalon [13], microlens arrays [7,14,15], and diffractive optical
elements (DOEs) [16–19], to divide the incident beam into multiple beams. The other is
obtained by modulating the amplitude, phase or polarization of some special vector beams,
such as composite vector beams [20–24], vector-vortex Bessel-Gauss beams [25,26],
Laguerre-Gauss beams [27]. In order to achieve a high-quality MSA for practical
applications, the high uniformity, high diffraction efficiency and superresolved focal spots are
necessary. However, such high-quality MSA is difficult to accomplish by the methods
previously mentioned. For example, the quality of multi foci reduces with increasing
resolution due to interference effects. Hence, it is necessary to use an ultrashort-pulsed laser
to eliminate the interference among the split beams caused by splitters or etalon. Furthermore,
it is difficult to create two dimensional (2D) spot array by using that beam splitters. Using
microlens arrays or DOEs, a 2D focal spot array can be produced, but the manufacturing
process of that optical element is usually very complicated, and the structure parameters of a
microlens array or a diffractive optical element cannot be changed once the process is
completed. Therefore, it is not convenient to produce the MSA with tunable period and
spacing (the distance between two adjacent focal spots), and the method of using microlens
arrays or DOEs to produce the MSA lacks flexibility. By using the special vector beams, a
multifocal spots with high quality can be created. However, the number of the focal spots is
limited to small value (typically <10) in the focal region of the high NA objective. Hence, it is
hard to produce a 2D MSA with a large number of spots by using the vector beams.
Phase-only modulation implemented by a spatial light modulator (SLM) is a preferable
method for producing MSAs, owing to its programmable capability to dynamically update the
intensity distributions in the focal plane by varying the incident phase patterns. Based on the
method of using SLMs, not only a large number of focal spots with high quality can be
obtained, but also the shape of each spot can be engineered. Many approaches have been
reported for the purpose in recent years [1,9,20,28–33]. These previous investigations have
verified that the MSA can be achieved by spatial phase modulation at the back aperture of the
objective. A key issue in creation of a high-quality MSA is to retrieve accurate phase patterns
at the back aperture of the objective. Many approaches have been explored and developed for
this purpose, such as computer-generated hologram (CGH) [30–32], Gerchberg–Saxton
method (GS) [33], weighted Gerchberg-Saxton algorithm (GSW) [1,9,34,35], and other
modified Fourier transform methods [36,37]. The most commonly used methods are perhaps
those based on the iterative Fourier transform algorithms. These iterative methods usually
require a large number of iterations and may not lead to a unique solution. Therefore, based
on the noniterative method, how to retrieve accurate phase patterns to produce MSA in the
focal region of a high NA objective has been an attractive and important task for practical
applications.
As is well known, the fractional Talbot effect can generate spot arrays with high
uniformity and high compression ratio [38]. Zhou et al. have given a complete set of phase
equations for Talbot array illuminators with any compressed ratio [39,40]. And in our
Received 22 Jan 2014; revised 27 Mar 2014; accepted 28 Mar 2014; published 16 Apr 2014
21 April 2014 | Vol. 22, No. 8 | DOI:10.1364/OE.22.009798 | OPTICS EXPRESS 9800