Parameter determination and transformation for the focusing of dielectric microspheres illuminated by optical needle

Tongnan Xia,Jinbing Hu,Songlin Zhuang,Hanming Guo

doi:10.1038/s41598-017-06146-7

Abstract

By eliminating the spherical aberrations of microsphere we derived a simple but useful formula on the focusing of dielectric microsphere. On basis of this formula, not only can researchers determine the parameters of an optical microsphere system with super-resolution, but they can also perform parameter transformation. In order to facilitate the application, the principle of parameter transformation was summarized into three kinds of case listed in Table 1, which were all demonstrated numerically with concrete examples by finite-difference time-domain method. This formula will be conducive to the development of applications based on microsphere, such as photonic nano-jet lithography, microsphere nano-scope.

Highlights

Microspheres have recently attracted numerous attentions in the field of super-resolution due to its sub-diffraction focusing size and magnification of objects ahead of it[1,2,3,4,5,6,7], and have been used in nano-scale imaging[8, 9], nano-scale lithography[10, 11] etc
Once spherical aberrations (SAs) are well eliminated the incident beam will be focused at the shadow side of microsphere, and the highest resolution is achieved for the microsphere system
As reported in ref. 16 that for nonconventional system, defined as with characteristic dimension λ < r < 10λ, the results obtained by ray tracing approach are in excellent agreement with electromagnetic theory, and the same thesis was obtained by ref. 18 in the experimental investigation of imaging of circular aperture with wavelength-scale radius

Summary

Introduction

Microspheres have recently attracted numerous attentions in the field of super-resolution due to its sub-diffraction focusing size and magnification of objects ahead of it[1,2,3,4,5,6,7], and have been used in nano-scale imaging[8, 9], nano-scale lithography[10, 11] etc. (ii) How to obtain the same resolution (normalized to the wavelength in surrounding medium) as before if one or more parameters are altered, i.e., performing parameter transformation without changing the resolution of microsphere system. As for these issues above, few literatures concern about them. The focusing property of microsphere with radius in the range from n1 * λ0 to 1.4 * n1 * λ0 (n1 and λ0 are the refractive index of surrounding medium and illumination wavelength in free space, respectively) mainly depend on SAs; NA only makes a small effect to the focusing property of microsphere, because NA is very small (

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Results

Conclusion