Forces due to pulsed beams in optical tweezers: linear effects.

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.