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 ≤ RIC ≤ 1.75 with the proper radius r of microsphere, the microsphere can generate a near-field focal spot with lateral resolution slightly beyond λ/2ns, which is also the lateral resolution limit of the dielectric microsphere. The r for each RIC can be obtained by optimizing r from 1.125λ/n o to 1.275λ/n o. Here λ, 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 π 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 9.53λ, 0.41λ, 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.
Graphene has been widely utilized in optoelectronic applications due to its high carrier mobility, and extremely fast optical response. Microcavity-integrated graphene waveguide structure is one basic module of integrated photonic devices which can greatly improve the light-matter interaction strength. The enhanced optical absorption in the undoped graphene layer results from the light trapping and the corresponding long light-graphene interaction length. Tuning the Fermi energy level of the graphene layer enables the electro-optical modulation. We report the realization of reconfigurable electro-optical attenuator and switch with unity-order modulation depth in light reflection and transmission at near-infrared frequency. The transformation from a lossy absorber to a quasi-perfect transparent condition of the monolayer graphene by tuning the Fermi level leads to the unity-order tunability of the electro-optical attenuator and switch. We investigate theoretically and numerically the absorption properties of the designed microcavity-integrated graphene with respect to different graphene Fermi levels. Electro-optical attenuator with attenuating coefficient from 10% to 98.29% is fulfilled. On-off electro-optical switching with a switching contrast larger than 21 dB is demonstrated. Our approach provides the possibilities of graphene photonics applied in communications, and sensing.
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.
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