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Objective To solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent threedimensional spatial resolution have important applications in optical microscopy and metal particle capture.In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions.To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.Methods We present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by defocusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.Results and Discussions Firstly, the number of generated spatial spherical focused spots is related to odd or even
Objective To solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent threedimensional spatial resolution have important applications in optical microscopy and metal particle capture.In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions.To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.Methods We present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by defocusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.Results and Discussions Firstly, the number of generated spatial spherical focused spots is related to odd or even
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