Sub-wavelength focusing of light by the two-mode interference from an optical microfiber

The ability to focus light at subwavelength scales is essential in modern photonics. Optical microfiber-based sub-wavelength focusing would allow a miniaturized, flexible and versatile tool to be superior for many applications such as biomedical imaging and optomechanics. When a single mode exits from the microfiber endface, it would experience significant diffraction into the free space. This situation could be altered by incorporating two-mode interference with its dependence on the distributions of E -field amplitude and phase. Here we report a novel approach to sub-wavelength focusing based on the two-mode interference from an optical microfiber. By utilizing unique distributions of electric field amplitude and phase of two interacting optical modes, interference field patterns with a single focus (via a two-mode set of HE₁₁ and HE₁₂) or multiple foci (via a two-mode set of HE₁₁ and HE₃₁) could be obtained. The constructed foci are then demonstrated to facilitate tunable and selective trapping of nanoparticles. Circular polarization of optical modes is utilized so as to improve the angular symmetry of sub-wavelength focusing patterns other than linear polarized optical modes. Our simulation results show the smallest focal spot could be produced from the EH₁₁ and HE₁₂ mode interference, with a full width at half-maximum (FWHM) of ~348 nm (0.65λ). Such a subwavelength focusing field is applied in optical trapping of an 85-nm-diameter polystyrene nanosphere. Further calculation reveals that stable trapping could be fulfilled with axial and transverse trap stiffness of 11.48 pN/(μm·W) and 64.98 pN/(μm·W) (via two-mode set of HE₁₁ and HE₁₂), as well as axial and transverse potential well of 101 k_BT/W and 641 k_BT/W via two-mode interference of HE₁₁ and HE₁₂. These values exhibit great improvement over conventional tapered fibers. Further investigations show that different foci (via a two-mode set of HE₁₁ and HE₃₁) exhibit distinct trap stiffnesses and potential wells, justifying the potential for nanoparticle size sorting. Based on the flexible, all-fiber device, this subwavelength focusing strategy by two-mode interference may find promising applications in optical manipulation, superresolution optical imaging, data storage and nanolithography.