Abstract
The conventional multifocal optical elements cannot precisely control the focal number, spot size, as well as the energy distribution in between. Here, the binary amplitude-type super-oscillatory lens (SOL) is utilized, and a robust and universal optimization method based on the vectorial angular spectrum (VAS) theory and the genetic algorithm (GA) is proposed, aiming to achieve the required focusing performance with arbitrary number of foci in preset energy distribution. Several typical designs of multifocal SOLs are demonstrated. Verified by the finite-difference time-domain (FDTD) numerical simulation, the designed multifocal SOLs agree well with the specific requirements. Moreover, the full-width at half-maximum (FWHM) of the achieved focal spots is close to λ/3 for all the cases (λ being the operating wavelength), which successfully breaks the diffraction limit. In addition, the designed SOLs are partially insensitive to the incident polarization state, functioning very well for both the linear polarization and circular polarization. The optimization method presented provides a useful design strategy for realizing a multiple sub-diffraction-limit foci field of SOLs. This research can find its potentials in such fields as parallel particle trapping and high-resolution microscopy imaging.
Highlights
Multifocal optical elements are important for such applications as parallel particle trapping and three-dimensional imaging system[1,2,3,4]
According to the available publications, the design theories for a far-field superfocusing super-oscillatory lens (SOL) have been based on the scalar angular spectrum theory[10, 17], vectorial angular spectrum (VAS) theory[13, 14, 18], or vectorial Rayleigh-Sommerfeld diffraction integral[15]
Assuming the linearly polarized beam (LPB) illuminates normally on the SOL and propagates along the +Z direction, as shown in Fig. 1, according to the VAS theory under the cylindrical coordinate system, the electric field components of an arbitrary point P(r, φ, z) on the observation plane (Z > 0) can be expressed as[14, 19, 20]
Summary
Multifocal optical elements are important for such applications as parallel particle trapping and three-dimensional imaging system[1,2,3,4]. The metalens with longitudinal multiple foci has been proposed[5, 6] These multifocal optical elements cannot precisely control the energy distribution among the realized focal spots, neither the relative positions nor the actual sizes. On the other hand, resolving power is restricted by the Rayleigh diffraction limit 0.61λ/NA (where NA is numerical aperture) for an ideal optical system[7] Overcoming this resolution barrier can improve the imaging quality, or greatly decrease the size of a single particle that can be manipulated. The optimizing procedure of the model is designed adopting the Matlab programming language based on the genetic algorithm (GA) and the fast Hankel transform algorithm It can flexibly control the intensity of electric field immediately behind the lens, making the number of foci arranged, as well as their relative positions and sizes. The design described mainly suits for the linearly polarized beam (LPB), it is applicable for the other polarized waves, like the circularly, radially, and azimuthally polarized beams
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