By Josh Conway
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A local minimum in the right hand side of Equation (2-21) could easily be rejected by discarding any answers greater than 10-6. To rapidly arrive at the global minimum, various techniques were used to determine appropriate starting values for the components of k in Mathematica’s ‘FindMinimum’ routine. For instance, the imaginary component of εm tends to only be a small perturbation to the dispersion relation. It can, therefore, be discarded and the minimization routine is then run over only the real part of the wavevector.
As is the case for all optimized waveguides, the decay lengths are limited by dissipation in the metal. As the electrons collectively oscillate at these surface plasmon frequencies, they collide with the background lattice of positive ions, transferring energy which is dissipated as heat. This powerful loss mechanism strongly constrains the design of any plasmonic device. For surface plasmons to achieve even modest levels of efficiency careful selection of materials and operating frequencies is required.
17 Figure 1-6: Technique for Photoassisted STM A key physical process which contributes to the enhancement of the Photoassisted STM is the propagation of plasmons down a tapered metallic wire. Although analogous to the geometry described above, this tends to be treated separately in the literature and is known as the Negative Dielectric (ND) pin35. This design is characterized by a solid cylinder of negative dielectric surrounded by a positive dielectric medium which extends to infinity. This geometry has the advantageous feature of a monotonically increasing k-vector with decreasing pin radius36.