Toward Waveguide-Based Optical Chromatography

Abstract

We report analytical expressions for optical forces acting on particles inside waveguides. The analysis builds on our previously reported Fourier Transform method to obtain Beam Shape Coefficients for any beam. Here we develop analytical expressions for the Beam Shape Coefficients in cylindrical and rectangular metallic waveguides. The theory is valid for particle radius a ranging from the Rayleigh regime to large microparticles, such as aerosols like virus loaded droplets. The theory is used to investigate how optical forces within hollow waveguides can be used to sort particles in “optical chromatography” experiments in which particles are optically propelled along a hollow-core waveguide. For Rayleigh particles, the axial force is found to scale with a6, while the radial force, which prevents particles from crashing into the waveguide walls, scales with a3. For microparticles, narrow Mie resonances create a strong wavelength dependence of the optical force, enabling more selective sorting. Several beam parameters, such as power, wavelength, polarization state and waveguide modes can be tuned to optimize the sorting performance. The analysis focuses on cylindrical waveguides, where meter-long liquid waveguides in the form of hollow-core photonic crystal fibers are readily available. The modes of such fibers are well-approximated by the cylindrical waveguide modes considered in the theory.