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.
You must log in to add comments.