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Spotlight on Optics


  • September 2010

Optics InfoBase > Spotlight on Optics > Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction

Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction

Published in JOSA A, Vol. 27 Issue 10, pp.2293-2303 (2010)
by Vincent L. Y. Loke and M. Pinar Mengüç

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Spotlight summary: The diffraction-induced lower bounds on optical resolution (quantified by Abbe in 1873) are a major obstacle in technological and scientific endeavors as varied as bioimaging, astronomy, semiconductor manufacture, and data storage. However, as early as 1928 it was recognized (by Synge in a letter to Einstein) that Abbe's law does not apply in the near field of a subwavelength aperture, leading to the possibility of imaging with resolution below the diffraction limit. Despite this early understanding, the difficult practical issues associated with positioning an object in an optical near field delayed the successful implementation of Synge's ideas until 1984. Since then a number of near field optical techniques have been demonstrated, with nanoscale applications in fluorescence bioimaging, Raman spectroscopy, laser ablation, and others. While progress has been substantial, there is still a clear need for robust quantitative tools for designing and analyzing near-field optical systems. It is this need that is addressed by Loke and Mengüç in the current article.

Because of the exponential decay of evanescent fields, many near-field optical systems are designed to operate in proximity to a well-defined planar substrate. Such systems are difficult to model analytically, as arbitrary objects and the nontrivial geometry of probing tips/apertures preclude general closed-form solutions. Standard numerical techniques (e.g., finite-difference time-domain solutions) are difficult to implement because, in part, of the large range of scales present in the three-dimensional problem—the optical fields vary significantly over small fractions of a wavelength while the substrate extends for many wavelengths. Consequently, accurate discrete representations of the system often require a prohibitively large number of discrete elements. Loke and Mengüç overcome many of these difficulties by developing a discrete dipole approximation (DDA) that includes the effects of the substrate analytically. The near field probe and nanoscale object are discretely approximated by a collection of dipoles as in the standard DDA. By rigorously including the reflection image of each dipole when solving for the dipole moments, the substrate is implicitly included in the model. The resulting method is tractable, intuitive, and formulated so that standard highly optimized solvers of linear systems of equations can carry the bulk of the computational load.

With the burgeoning application of nanotechnology and nano-optics, near-field analytical tools will continue to increase in importance. For example, the authors discuss the potential of their method to aid in the improvement of nanofabrication methods. I look forward to seeing the development of techniques and methods aided by the insights afforded by this new tool.

--Brynmor Davis

Technical Division: Light–Matter Interactions
ToC Category: Optics at Surfaces
OCIS Codes: (240.0240) Optics at surfaces : Optics at surfaces
(050.1755) Diffraction and gratings : Computational electromagnetic methods

Posted on September 24, 2010

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