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.
Highlights
Since Ashkin’s pioneering paper [1], Optical Tweezers (OT) have opened up the possibility to perform micro- and nanoscale non–contact mechanical manipulation and measurements on particles in the nano-micron scale
The high refractive index appears at the absorption band edge, except for quantum dots (QD), for which the optical gap is larger than the bulk band gap
QD are typically smaller than 10 nm sizes, one could consider highly QD–doped microparticles with optical properties that are dominated by the QD refractive index
Summary
Since Ashkin’s pioneering paper [1], Optical Tweezers (OT) have opened up the possibility to perform micro- and nanoscale non–contact mechanical manipulation and measurements on particles in the nano-micron scale. The further development of fiber–based optical chromatography techniques requires a better understanding of the optical forces exerted on the particles by the waveguide modes, whose description strongly depends on particles size. On the other hand, particle resonances and their coupling to the waveguide modes must be taken into account to obtain expressions for the size–dependent optical forces This requires an integrated scattering theory that combines a Mie description of the particles with analytical waveguide modes, which has not been demonstrated to date. We will develop analytical equations for optical forces, including the scattering forces, on particles within waveguides and will discuss their implications to sorting of particles based on particle size, refraction index, absorption, and mass density. We will summarize illustrative results for special cases, applications, and experimental implementation
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