Focus splitting induced by a pure phase-shifting apodizer

doi:10.1016/j.optcom.2004.05.029

Optics Communications

Volume 239, Issues 1–3, 1 September 2004, Pages 55-59

https://doi.org/10.1016/j.optcom.2004.05.029 Get rights and content

Abstract

Effect of a pure phase-shifting apodizer on the three-dimensional light intensity distribution in focal region is theoretically investigated in this paper. The results show that the proposed apodizer may induce focus splitting and local minimization of light intensity. By adjusting the geometrical parameters of the phase-shifting apodizer, the focus can split into two or three peaks. And one or two local minimums of light intensity may occur between two intensity peaks. Under the condition of two-peak focus, the distance between the peaks is tunable by the apodizer.

Introduction

Since Ashkin developed optical tweezers system [1], optical tweezers technique has accelerated many major advances in numerous areas of science [2], [3]. A number of approaches have been proposed to constructing optical trap, such as generalized phase-contrast technique [4], [5], holographic optical tweezers arrays [6], [7], and single fiber probe with an annular light distribution [8]. An interferometer pattern between two annular laser beams was also used to construct three-dimensional optical trapping structures [2]. Because the local minimum of light intensity has application in optical trap, local minimization of light intensity becomes very attractive. The superposition of two Laguerre–Gaussian modes is employed to form an optical beam with a localized intensity null at its focus [9]. For high-Fresnel-number focusing systems illuminated by certain classes of partially coherent light, it is also possible to produce a local minimum of light intensity [10]. Recently, as a novel technique, a liquid–crystal cell was proposed to produce a doughnut laser beam with local minimum of light intensity [11]. In this paper, effect of a pure phase-shifting apodizer on the light intensity distribution in focal region is theoretically investigated. The simulations show that the proposed apodizer may induce focus splitting and local minimization of light intensity, though the pure phase-shifting apodizer has been introduced in focusing optical system to extend the focal depth [12], [13]. And the gradient force is also simulated to show that this kind of pure phase-shifting apodizer may be very useful for constructing optical trap.

Section snippets

Principle of the system

In the apodized focusing system we investigated, the incident light passes through a pure phase-shifting apodizer and objective lens, then converges. The three-portion phase-shifting apodizer with the phase shift 0, π, 0 for its inner, middle and outer concentric portions, respectively, is used in our study. The motive for choosing this kind of apodizer is that the apodizer may be easy to produce and duplicate for mass production [13], and the analysis method of the proposed apodizer can be

Results and discussion

Basing on the Eq. (1), the three-dimensional distribution of light intensity in focal region is simulated under the condition of the relative waist width w = 0.8 and a = 0.5. Fig. 1 shows the evolution of the light intensity distribution. From the simulation, it can be seen that the three-dimensional distribution of light intensity for b = 0.4 is similar to the distribution of original system (which has not any apodization at all). However, when the inner radius b decreases from 0.4 to 0.3, the focus

Conclusions

Effect of a pure phase-shifting apodizer on the three-dimensional light intensity distribution in focal region is theoretically investigated in this paper. The results show that the proposed apodizer may induce focus splitting. By adjusting the geometrical parameters of the phase-shifting apodizer, the focus can split into two or three peaks. And one or two local minimization of light intensity may, but not always, occur between two intensity peaks. Under the condition of two-peak focus, the

Acknowledgement

This work was supported by the Science and Technology Committee of Shanghai (022261045, 03QG14057), National Natural Science Foundation of China (60207005) and National 863 Project of China (2002AA313030). All the program codes and equation derivation are obtainable conveniently by sending e-mail to [email protected].

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Focus splitting induced by a pure phase-shifting apodizer

Abstract

Introduction

Section snippets

Principle of the system

Results and discussion

Conclusions

Acknowledgement

Opt. Lett.

Science

Nature

Opt. Commun.

Opt. Lett.

Rev. Sci. Instrum.