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We present a method for the precise calculation of optical forces due to a tightly-focused pulsed laser beam using generalized Lorenz-Mie theory or the T-matrix method. This method can be used to obtain the fields as a function of position and time, allowing the approximate calculation of weak non-linear effects, and provides a reference calculation for validation of calculations including non-linear effects. We calculate forces for femtosecond pulses of various widths, and compare with forces due to a continuous wave (CW) beam. The forces are similar enough so that the continuous beam case provides a useful approximation for the pulsed case, with trap parameters such as the radial spring constant usually differing by less than 1% for pulses of 100 fs or longer. For large high-index (e.g., polystyrene, with n = 1.59) particles, the difference can be as large as 3% for 100 fs pulses, and up to 8% for 25 fs pulses. A weighted average of CW forces for individual spectral components of the pulsed beam provides a simple improved approximation, which we use to illustrate the physical principles responsible for the differences between pulsed and CW beams.

Theory and practice of simulation of optical tweezers, Journal of Quantitative Spectroscopy and Radiative Transfer, http://dx.doi.org/10.1016/j.jqsrt.2016.12.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractComputational modelling has made many useful contributions to the field of optical tweezers. One aspect in which it can be applied is the simulation of the dynamics of particles in optical tweezers. This can be useful for systems with many degrees of freedom, and for the simulation of experiments. While modelling of the optical force is a prerequisite for simulation of the motion of particles in optical traps, non-optical forces must also be included; the most important are usually Brownian motion and viscous drag. We discuss some applications and examples of such simulations. We review the theory and practical principles of simulation of optical tweezers, including the choice of method of calculation of optical force, numerical solution of the equations of motion of the particle, and finish with a discussion of a range of open problems.

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