Lineshape study of optical force spectra on resonant structures

Understanding the frequency spectrum of the optical force is important for controlling and manipulating micro- and nano-scale objects using light. Spectral resonances of these objects can significantly influence the optical force spectrum. In this paper, we develop a theoretical formalism based on the temporal coupled-mode theory that analytically describes the lineshapes of force spectra and their dependencies on resonant scatterers for arbitrary incident wavefronts. We obtain closed-form formulae and discuss the conditions for achieving symmetric as well as asymmetric lineshapes, pertaining, respectively, to a Lorentzian and Fano resonance. The relevance of formalism as a design tool is exemplified for a conceptual scheme of the size-sorting mechanism of small particles, which plays a role in biomedical diagnosis.