# Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size

## Abstract

A closed-form expression of the force on an infinite lossless dielectric cylinder illuminated by a TM incidence (electric field parallel to the cylinder's axis) is derived. The formula, expressed as a simple sum, is straightforward to compute and is shown to be faster converging than the direct application of the Maxwell stress tensor and the expansion of the fields in the cylindrical coordinate system. A generalization of the formula to multiple incidences is provided and is illustrated by studying the force due to a Gaussian beam on cylinders of various parameters. We show in this way that the effects of the gradient of the intensity profile on the transverse and longitudinal confinements are decoupled, due to the permittivity contrast and to the size of the particle. Since the formula we derive is exact and is therefore not limited to the Rayleigh or ray optics regime, we expect it to be important for the modeling of optical forces on elongated particles of arbitrary sizes.

- Authors:

- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 20929629

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of the Optical Society of America. Part B, Optical Physics; Journal Volume: 24; Journal Issue: 3; Other Information: DOI: 10.1364/JOSAB.24.000644; (c) 2007 Optical Society of America; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFINEMENT; COORDINATES; CYLINDERS; DIELECTRIC MATERIALS; ELECTRIC FIELDS; ELECTROMAGNETIC RADIATION; EXPANSION; LASERS; OPTICS; PARTICLES; PERMITTIVITY; RADIATION PRESSURE; RAYLEIGH SCATTERING; SIMULATION; STRESSES; TENSORS; WAVE PROPAGATION

### Citation Formats

```
Grzegorczyk, Tomasz M., and Kong, Jin Au.
```*Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size*. United States: N. p., 2007.
Web. doi:10.1364/JOSAB.24.000644.

```
Grzegorczyk, Tomasz M., & Kong, Jin Au.
```*Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size*. United States. doi:10.1364/JOSAB.24.000644.

```
Grzegorczyk, Tomasz M., and Kong, Jin Au. Thu .
"Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size". United States.
doi:10.1364/JOSAB.24.000644.
```

```
@article{osti_20929629,
```

title = {Analytical expression of the force due to multiple TM plane-wave incidences on an infinite lossless dielectric circular cylinder of arbitrary size},

author = {Grzegorczyk, Tomasz M. and Kong, Jin Au},

abstractNote = {A closed-form expression of the force on an infinite lossless dielectric cylinder illuminated by a TM incidence (electric field parallel to the cylinder's axis) is derived. The formula, expressed as a simple sum, is straightforward to compute and is shown to be faster converging than the direct application of the Maxwell stress tensor and the expansion of the fields in the cylindrical coordinate system. A generalization of the formula to multiple incidences is provided and is illustrated by studying the force due to a Gaussian beam on cylinders of various parameters. We show in this way that the effects of the gradient of the intensity profile on the transverse and longitudinal confinements are decoupled, due to the permittivity contrast and to the size of the particle. Since the formula we derive is exact and is therefore not limited to the Rayleigh or ray optics regime, we expect it to be important for the modeling of optical forces on elongated particles of arbitrary sizes.},

doi = {10.1364/JOSAB.24.000644},

journal = {Journal of the Optical Society of America. Part B, Optical Physics},

number = 3,

volume = 24,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}