Research On Far-field Super-resolution Focusing Devices For Cylindrical Vector Fields

Cylindrical vector beams have unique optical properties which make them suitable for creating special focusing fields such as the hollow ring,hollow needle,and three-dimensional?3D?hollow spots.Such optical fields have great potential applications in optical tweezers,particle manipulation,and optical microscopy.However,the generation of such spots mainly relies on conventional focusing devices,suffering from the diffraction limit that seriously affects the development in the above optical areas.New methods to break the diffraction limit need to be developed.Optical super-oscillation utilizes the harmonic components with a lower spatial frequency to realize the rapid oscillation of local spatial frequency,making it capable of achieving far-field super-resolution focusing.It is of great research scientific significance and practical value to carry out the research on the far-field super-resolution focusing devices of cylindrical vector fields.To settle the problems of bulky size,difficult integration and diffraction limit of the conventional focusing devices,binary-phase modulation planar devices for creating hollow ring,hollow needle,and 3D hollow spot are proposed.For a working wavelength?=632.8 nm of azimuthally polarized beam?APB?,by using the vectorial angular spectrum method and a particle swarm algorithm,a hollow ring focusing device is designed with the radius of 500?,and the focal length of 600?.The full-width-at-half-maxima?FWHM?is 0.57?,and the sidelobe ratio is 5.1%.There is no sideband in the designing range of[-500?,500?].To realize the binary-phase modulation,Si₃N₄ dielectric concentric ring is utilized as the basic unit of the device.By using inductively coupled plasma enhanced chemical vapor deposition?ICPECVD?,electron beam lithography?EBL?and inductively coupled plasma?ICP?etching,the focusing device is fabricated.A far-field super-resolution optical field measurement system based on nano-fiber-probe is used to measure the hollow ring.Experimental results show:the FWHM is 0.61?,the sidelobe ratio is 11.4%,and there is no sideband in the measurement range of[-40?,120?].The proposed device realizes far-field super-resolution focusing of the APB,and the size of the hollow ring is smaller than the Abbe diffraction limit 0.78??0.5?/NA?.Such device settles the problems of bulky size,difficult integration,and diffraction limit of the conventional devices.For a working wavelength?=632.8 nm of APB,by using the same designing method and fabrication techniques,a hollow needle focusing device is designed and fabricated with the radius of 650?and the focal length of 300?.The designing results demonstrate:the depth of focus?DOF?is about 11.3?,the sidelobe ratio is lower than 38.4%,and the inner FWHM is 0.34?-0.40?.A super-resolution optical field measurement system based on high numerical aperture microscopy is built to measure the hollow needle spot.Experimental results show:the DOF is about 10?,the inner FWHM is 0.34?-0.42?which is smaller than the Abbe diffraction limit?0.5?/NA?,and the sidelobe ratio is lower than 40%.The focusing device overcomes the shortcoming of the short depth of focus of the existing hollow ring focusing spot.The present 3D hollow spots generation relies on complex optical system and requires precise optical path adjustment.For a working wavelength?=632.8 nm of cylindrical vector beam?CVB?,by using the same designing method and fabrication techniques,a 3D hollow spot focusing device is fabricated with radius of 650?,the focal length of 300?,and the NA of 0.908;The designing transverse and axial inner FWHMs are 0.567?and 1.621?respectively.The transverse and axial center-to-peak ratios are 7.1%and 0.7%respectively.The far-field super-resolution optical field measurement system based on nano-fiber-probe is utilized to measure the 3D hollow spot.Experimental results show:the transverse inner FWHM is 0.546?,which is smaller than the Abbe diffraction limit 0.551??0.5?/NA?,the axial FWHM is 1.585?,and the transverse and axial center-to-peak ratios are 3.5%and 3.7%,respectively.The proposed 3D hollow spot focusing device solves the problems of the complex optical path adjustment and diffraction limit of the transverse spot size.The coaxial alignment errors of the incident beam and focusing device seriously affect the focusing characteristics.To overcome the problem,a transmissive birefringent metasurfaces with phase and polarization modulation is proposed.An amorphous silicon??-Si?unit produces 180 degrees phase shift of orthogonal polarizations to realize a half-wave plate.By rotating the sub-wavelength half-wave plate 90 degrees,the binary-phase modulation can be achieved.Under the illumination of linear polarized beam,the polarization direction of the optical field can be continuously regulated by rotating the sub-wavelength half-wave plate.Combined with the binary-phase modulation,the polarization conversion and focusing can be integrated in a single device,and the multi-dimensional modulations?phase and polarization?problem of the optical field can be solved.For a working wavelength?=632.8 nm of linear polarized beam,by using the same designing method,a hollow ring focusing device is designed with the radius of 27?,the focal length of 14.5?,and the NA of 0.874.FDTD Solutions software is adopted to conduct the simulations.The simulation results show:the inner FWHM is 0.379?which is smaller than the super-oscillation criterion 0.435??0.38?/NA?,and the sidelobe ratio is 26.8%.The integration of azimuthal polarization conversion and super-oscillation focusing is realized,and the difficulty of alignment between the center of incident beam and the center of focusing device is solved.To solve the problem of non-uniform intensity of focusing field in transverse and axial directions of the present 3D hollow spot,a set of all-dielectric metasurfaces with independent binary-phase modulation of azimuthal and radial polarization components are proposed.By optimizing the geometric parameters of the sub-wavelength?-Si units,the independent binary-phase modulation in orthogonal directions is realized.For a working wavelength?=632.8 nm of cylindrical vector beam,by using the same designing method,a 3D hollow spot focusing device is designed with the radius and the focal length being 35?and 14.5?respectively,and the NA of 0.946.FDTD Solutions software is adopted to conduct the simulation.The simulation results show:the transverse inner FWHM is 0.33?,which is smaller than the super-oscillation criterion0.402??0.38?/NA?,and the axial FWHM is 1.33?.The device realizes independent optimization design of the transverse and axial focusing optical field,and solves the problem of non-uniformity of the transverse and axial intensity of the 3D hollow spot.