Subwavelength Far-field Focusing Based On Discrete Coding Of Generalized Pupil Function

The diffraction limit limits the resolution of optical microscopic imaging and micro-nano processing.Although increasing the numerical aperture（NA）or decreasing the wavelengthλ0 can reduce the diffraction limit and obtain focal spots with smaller lateral sizes,the existing numerical apertures and wavelengths have approached their limits and are difficult to be respectively further increased and decreased.This is because of the limitations from the maximum convergence angle that an optical system can achieve and material properties.Therefore,in the context that the existing numerical apertures and wavelengths have approached their limits,it is an important scientific problem in the field of microscopic imaging and micro-nano processing to study how to obtain a focal spot smaller than the diffraction limit.Focusing on this scientific problem,this subject has carried out subwavelength focusing studies of optical far-field regions.From vector diffraction theories,the generalized pupil function was defined.Based on the discrete coding of the generalized pupil function,the realization of subwavelength spot focal fields,subwavelength optical needle focal fields,and subwavelength multifocal array focal fields are studied.Focusing devices to generate these three kinds of subwavelength focal fields were designed and the generated foccal light fields were analyzed.The research results of this subject can provide theoretical supports for the design of focusing devices in optical microscopies and micro-nano processing equipments,and will promote the developments of microscopic imaging,micro-nano processing,particle capturing and manipulating.The main research contents of this subject are as follows:（1）From vector diffraction theories,the transmission function of an aperture with the focusing function was defined as the generalized pupil function.Under the condition that the incident optical field has been determined,the generalized pupil function of the focusing device will determine the generated focal field.On this basis,the basic form of the generalized pupil function was given.The characteristics of the generalized pupil function were analyzed.To achieve subwavelength far-field focusing,this subject proposed the discrete coding of the generalized pupil function to design the focusing device.Then,the meaning of discrete coding of the generalized pupil function was clarified.And three kinds of basic discrete coding methods of the generalized pupil function were summarized.（2）Based on the discrete coding of the generalized pupil function,the research on subwavelength spot focusing was carried out.Firstly,the discrete coding principle of the generalized pupil function of a Fresnel zone plate（FZP）was studied.A FZP with a high NA and a long focal length was designed and fabricated.The focal fields generated by the FZP illuminated by an azimuthally polarized vortex（APV）beam and an azimuthally polarized（AP）beam were exprimentally measured.And a subwavelength spot smaller than the diffraction limit was experimentally generated.Then,a discrete generalized pupil function with vortex phase modulation and focusing functions is realized by a spiral band plate（SZP）.A method to focusing an AP beam into a subwavelength spot by a single device was proposed.A SZP with a high NA and a long focal length was designed to focus an AP beam.A subwavelength spot with a lateral full width at half maximum（FWHM）of 0.43λ0was generated,which was smaller than the diffraction limit.Meanwhile,a stable three-dimensional optical trap was generated.（3）To obtain the axial one-dimensional expansion result of a subwavelength spot,namely the subwavelength optical needle,based on the discrete coding of the generalized pupil function,the research on subwavelength optical needle focusing was carried out.Firstly,binary phase annulus filters were designed to focus APV beams to generate transversely polarized subwavelength optical needles.And the effects of the annulus number and radius errors of the filters were studied.Then,a new design method of a binary planar lens（BPL）with a long depth of focus was proposed.The method designed a long focal depth BPL composed of 102non-subwavelength annuli by only solving 5 focal lengths.After fabricating this long focal depth BPL,a subwavelength optical needle with a lateral FWHM smaller than the diffraction limit and an axial FWHM of about 14.7λ₀ was exprimentally generated by the fabracated BPL.Meawhile,a photoresist hole structure with a center-to-center distance of about 0.77λ₀ was also exprimentally generated by the fabracated BPL.（4）To obtain the spatial multi-dimensional expansion result of a subwavelength spot,namely the subwavelength mutilfocal array,based on the discrete coding of the generalized pupil function,the research on subwavelength multifocal array focusing was carried out.The design method of the dartboard segmentation phase filter was proposed.Different dartboard filters were designed.Axial one-dimensional,lateral two-dimensional and spatial three-dimensional subwavelength multifocal arrays with uniformities of not less than 92.5%were generated,and the position and polarization directon of each focal spot could be independently controlled.The effects of the filter design parameters were studied.The filter solves the problems that the existing pupil plane segmentation filters for generating polarization controllable multifocal arrays contain only one design degree of freedom,are not easy to obtain multifocal arrays with more focal spots,and only can increase cell zones to improve the uniformities of the generated multifocal arrays.