Investigation of super-resolution in microsphere-assisted microscopy with the Poynting vector of the dipole model

In this paper, the Fourier spectrum of an image in microsphere-assisted microscopy (MAM) and the wavenumber decomposition of the Poynting vector of the dipole model are compared for the first time to study the super-resolution performance within several wavelengths in MAM. Firstly, an experiment using microsphere-assisted microscopy is performed, and the fast Fourier transformation (FFT) spectra of the images along the distance are studied. Then the Poynting vector in the point dipole field is theoretically investigated based on the spectral decomposition of dyadic Green's function. Our study finds that the result of decomposition of the Poynting vector corresponds with the propagation results of components with different transverse wavenumbers k_ρ in an experiment. Even when k_ρ reaches 1.7k₀, the waves can still arrive outside one wavelength. Our work is the first effort (to our knowledge) to associate the Fourier spectrum and the decomposition of the Poynting vector together, and it may contribute to the quantitative exploration of super-resolution performance in MAM in the future.