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.

我们报告了作用在波导内部粒子上的光学力的解析表达式。该分析基于我们先前报道的傅里叶变换方法来获得任何光束的光束形状系数。在这里，我们开发了圆柱和矩形金属波导中光束形状系数的解析表达式。该理论对粒子半径有效一个从瑞利（Rayleigh）政权到大型微粒，例如像病毒一样的液滴等气溶胶。该理论用于研究在“光学色谱”实验中空心波导内的光学力如何用于对颗粒进行分选，在“光学色谱”实验中，颗粒沿空心波导光学推进。对于瑞利粒子，发现轴向力与一个^{如图6所示}，防止颗粒撞入波导壁的径向力随着一个³。对于微粒而言，狭窄的Mie共振会产生强烈的波长与光学力的依存关系，从而实现更具选择性的分类。可以调整几个光束参数，例如功率，波长，偏振态和波导模式，以优化分选性能。该分析着重于圆柱形波导，其中容易获得中空光子晶体纤维形式的米长液体波导。这种光纤的模式与理论中考虑的圆柱形波导模式非常接近。