TRAPPING FORCE IN OPTICAL TWEEZERS

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NUMERICAL APERTURE

BEAD REFRACTIVE INDEX

This web app illustrates the mechanism by which a restoring trapping force arises from the redistribution of light's momentum produced by the reflection and refraction of light rays on a dielectric sphere. Light rays are s-polarized (linearly polarized in the direction orthogonal to the screen). That is used for computing reflection and transmission coefficients. Each ray is propagated up to order O(r) (r is the reflectivity) meaning that we completely neglect reflection accompanying the third refraction. Each incident ray is split into three components emerging from the sphere respectively after the 1st reflection, the 2nd and the 3rd refraction. Blue arrows represent changes in light linear momentum corresponding to each of the three components. Gray dashed lines indicate the direction of incident rays. Red arrow is the resulting force on the particle calculated as the negative total change in light momentum flux (vectorial sum of blue arrows). Drag the bead around and play with different numerical aperture and refractive index values (the refractive index of the surrounding medium is 1.33). Observe that stable axial trapping is only achieved for large NA.

References:

Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime

A. Ashkin
Biophys J., 61, 569, (1992)