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Project Index for An Optical Method of Sorting Nanoparticles by Size

Title: OptSortSph: Optical Sorting in a Standing Wave Field Calculated with Effective Velocities and Diffusion Constants

Authors: Zachary Levine and John Curry

Software Description Article: Levine ZH & Curry JJ (2016) OptSortSph: Optical Sorting in a Standing Wave Field Calculated with Effective Velocities and Diffusion Constants. J Res Natl Inst Stan 121:420-421.

Main Research Article: Curry JJ & Levine ZH (2016) Continuous-feed optical sorting of aerosol particles. Opt Express 24(13):14100-14123. 

Software Version: 1.0

Key words: optical sorting; dielectric spheres; Mie scattering; gradient force; standing-wave laser field.


NIST scientists have devised and modeled a unique optical method of sorting microscopic and nanoscopic particles by size, with a resolution as fine as 1 nanometer (nm) for particles of similar composition (see:…).

As part of the work published in Optics Express the authors devised a method for calculating the effective velocities and effective diffusion constants for a particle in a standing-wave laser interference field.  A brief description of the software is given in the Journal of Research of NIST software description article.

In the course of doing the work, the authors used computer algebra to derive the scattering and gradient forces on a dielectric sphere in an optical field from the Maxwell stress tensor and the Mie scattering coefficients.  The work will be published here: Levine ZH & Curry JJ (2016) Scattering and Gradient Forces from the Electromagnetic Stress Tensor Acting on a Dielectric Sphere. The Mathematica Journal, in press.

The software is presented as a Mathematica ( 10 notebook, including a full description, executable software, and integrated graphical output.

Software Specifications


Fokker-Planck equation with extraction and use of effective velocity and diffusion constants

Targeted Users

Researchers interested in designing continuous optical sorting systems

Operating System(s)

Cross-platform, where Mathematica is installed

Programming Language

Mathematica 10.0


I/O is described in the Mathematica notebook.


The Mathematica notebook is self-documenting.


N/A small-scale research tool


Software Download

The Mathematica notebook can be downloaded here:

Because Mathematica requires a license, a document which may be viewed statically with the free CDF Player (available here: )

An ASCII version of the code (without documentation) is found here:


Created August 31, 2016, Updated June 2, 2021