A single-beam gradient trap could potentially be used to hold a stylus for scanning force microscopy. With a view to development of this technique, we modeled the optical trap as a harmonic oscillator and therefore characterized it by its force constant. We measured force constants and resonant frequencies for 1–4-μm-diameter polystyrene spheres in a single-beam gradient trap using measurements of backscattered light. Force constants were determined with both Gaussian and doughnut laser modes, with powers of 3 and 1 mW, respectively. Typical values for spring constants were measured to be between 10⁻⁶ and 4 × 10⁻⁶ N/m. The resonant frequencies of trapped particles were measured to be between 1 and 10 kHz, and the rms amplitudes of oscillations were estimated to be around 40 nm. Our results confirm that the use of the doughnut mode for single-beam trapping is more efficient in the axial direction.

© 1996 Optical Society of America

[Optical Society of America ]

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