Metalens recently attracts enormous attention due to its microscale figure and versatile functionalities. With the combination of geometric phase and propagation phase, we first wrote the phase equation of bifocal metalens that can high efficiently focus incidence into one or two foci in tandem along longitudinal direction, depending on the polarization of incidence. More importantly, the relative intensity of the two foci can be modulated conveniently by changing the ellipticity of incidence, which is different from previous bifocal metalenses need to be repatterned for each kind of relative intensity [Opt. Express 23, 29855 (2015)]. Besides, the focusing efficiency of the proposed metalens is as high as 72%, and the separate distance between those two foci can be designed at will, which may find itself significant applications in optical tomography technique, optical data storage, and so on.

We focus on physically analyzing the origins of the numerical aperture ($NA$) and the spherical aberration of the microsphere with wavelength scale radius. We demonstrate that the microsphere naturally has negligible spherical aberration and high $NA$ when the refractive index contrast ($RIC$) between the microsphere and its surrounding medium is about from 1.5 to 1.75. The reason is due to the spherical aberration compensation arising from the positive spherical aberration caused by the surface shape of the microsphere and the $RIC$ and the negative spherical aberration caused by the focal shifts due to the wavelength scale dimension of the microsphere. We show that, only within the approximate region of $1.5\le RIC\le 1.75$ with the proper radius $r$ of microsphere, the microsphere can generate a near-field focal spot with lateral resolution slightly beyond $\lambda /2n_s$, which is also the lateral resolution limit of the dielectric microsphere. The $r$ for each $RIC$ can be obtained by optimizing $r$ from $1.125\lambda /n_o$ to $1.275\lambda /n_o$. Here $\lambda$, $n_s$, and $n_o$ are the wavelength in vacuum and the refractive indices of microsphere and its surrounding medium, respectively. For the case of the near-field focusing, we also develop a simple transform formula used to calculate the new radius from the known radius of microsphere corresponding to the original illumination wavelength when the illumination wavelength is changed.

When the pupil filters are used to improve the performance of the imaging system, the conversion efficiency is a critical characteristic for real applications. Here, in order to take full advantage of the subwavelength focusing property of the radially polarized higher-order Laguerre-Gaussian (LG) beam, we introduce the multi-zone binary phase pupil filters into the imaging system to deal with the problem that the focal spot is split along the $z$ axis for the small size parameter of the incident LG beam. We provide an easy-to-perform procedure for the design of multi-zone binary phase pupil filters, where the zone numbers of $\pi$ phase are uncertain when the optimizing procedure starts. Based on this optimizing procedure, we successfully find the set of optimum structures of a seventeen-belt binary phase pupil filters and generate the excellent focal spot, where the depth of focus, the focal spot transverse size, the Strehl ratio, and the sidelobe intensity are $9.53\lambda$, $0.41\lambda$, 41.75% and 16.35% in vacuum, respectively. Most importantly, even allowing the power loss of the incident LG beam truncated by the pupil of the imaging system, the conversion efficiency is still as high as 37.3%. Theoretical calculations show that we succeed to have sufficient conversion efficiency while utilizing the pupil filters to decrease the focal spot and extend the depth of focus.

A light beam propagating over an infinite anti-diffracting distance requires infinite power to preserve its shape. However, the fundamental barrier of finite power in free space has made the problem of diffraction insurmountable in recent decades. To overcome this limitation, we report an approach that employs the multiple energy oscillation mechanism, thereby permitting the creation of a light beam with an ultralong anti-diffracting distance in free space. A versatile optical pen is therefore developed to manipulate the number, amplitude, position and phase of energy oscillations for a focusing lens so that multiple energy oscillations can be realized. A light beam with a tunable number of energy oscillations is eventually generated in free space and propagates along a wavy trajectory. This work will enable the extension of non-diffractive light beams to an expanded realm and facilitate extensive developments in optics and other research fields, such as electronics and acoustics.

We investigate in detail the focusing properties of the composite vector beam (CVB) composed of two orthogonally linearly polarized beams with inhomogeneous polarization modulation. By optimizing the modulation factor, a multifocus with excellent quality is obtained, where the sizes of each focus are fairly smaller than that of the focusing spot of a radially polarized beam, the uniformity in the intensity of the focal spots is as high as 1, and the distributions of each focal spot have nearly circular symmetry. In order to decrease the power loss of the incident beam, the CVB formed by an annular beam is demonstrated as the substitute for the optimized CVB formed by a Gaussian beam. This work is important for high-resolution and high-speed imaging in biology and micro- nanofabrication.

Achromatic bifunctional metasurface is of great significance in optical path miniaturization among advanced integrated optical systems. However, the reported achromatic metalenses mostly utilize a phase compensate scheme, which uses geometric phase to realize the functionality and uses transmission phase to compensate the chromatic aberration. In the phase compensation scheme, all the modulation freedoms of a nanofin are driven at the same time. This makes most of the broadband achromatic metalenses restricted to realizing single function. Also, the phase compensate scheme is always addressed with circularly polarized (CP) incidence, leading to a limitation in efficiency and optical path miniaturization. Moreover, for a bifunctional or multifunctional achromatic metalens, not all the nanofins will work at the same time. Owing to this, achromatic metalenses using a phase compensate scheme are usually of low focusing efficiencies. To this end, based on the pure transmission phase in the x-/y- axis provided by the birefringent nanofins structure, we proposed an all-dielectric polarization-modulated broadband achromatic bifunctional metalens (BABM) in the visible light. Applying two independent phases on one metalens at the same time, the proposed BABM realizes achromatism in a bifunctional metasurface. Releasing the freedom of nanofin’s angular orientation, the proposed BABM breaks the dependence on CP incidence. As an achromatic bifunctional metalens, all the nanofins on the proposed BABM can work at the same time. Simulation results show that the designed BABM is capable of achromatically focusing the incident beam to a single focal spot and an optical vortex (OV) under the illumination of x- and y-polarization, respectively. In the designed waveband 500 nm (green) to 630 nm (red), the focal planes stay unchanged at the sampled wavelengths. Simulation results prove that the proposed metalens not only realized bifunctional achromatically, but also breaks the dependence of CP incidence. The proposed metalens has a numerical aperture of 0.34 and efficiencies of 33.6% and 34.6%. The proposed metalens has advantages of being flexible, single layer, convenient in manufacturing, and optical path miniaturization friendly, and will open a new page in advanced integrated optical systems.