Interference model for back-focal-plane displacement detection in optical tweezers

Area of Science:

• Optical trapping
• Nanotechnology
• Microscopy

Background:

• Optical tweezers are crucial for manipulating microscopic objects.
• Precise monitoring of trapped particle position is essential for many applications.
• Existing methods may have limitations in accuracy or field-of-view independence.

Purpose of the Study:

• To model the mechanism of lateral position detection using quadrant photodiodes in optical trapping.
• To provide a simple, closed-form analytic solution for this detection method.
• To relate intensity shifts to the spring constant of the optical trap.

Main Methods:

• Utilizing a quadrant photodiode to measure intensity shifts in the back focal plane of a collimating lens.
• Developing a theoretical model based on far-field interference principles.
• Comparing model predictions with experimental results.

Main Results:

• Demonstrated nanometer-level precision in monitoring the lateral position of optically trapped objects.
• Identified intensity shifts as interference between the laser beam and scattered light, influenced by Gouy phase anomaly.
• Derived a relationship between interference patterns, momentum transfer, and the trap spring constant.

Conclusions:

• The developed model accurately describes optical trap detection via quadrant photodiodes.
• This method offers high precision and is largely independent of the trap's position within the field of view.
• The findings provide a fundamental understanding and practical tool for optical trapping applications.