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In general, here they are depending on frequency, and in this way dispersion is fully taken into account (see also section 2.3). A thorough discussion on the different techniques with clarifying examples is also given in. A Good review and perspectives concerning the relationship between differential and integral equations (IE) modeling is recommended in a review paper by Miller. Recent work on the last developments in CEM concentrates on the two main approaches of differential and integral methods. A history and a comprehensive overview of the different numerical techniques and of their application in computational electromagnetics (CEM) may be found in. Most standard reference works on full-wave computational electromagnetics by consequence can be found within this community. Since this community traditionally is dealing with structures in the order of wavelengths, right from its beginning days, it had no choice than to try to rigorously solve Maxwell’s equations. The cradle of computational electromagnetics can be found in the microwave research community. Based on their theoretical specificities, the application of each method in the case of plasmonics is discussed.
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In this section the full wave modeling techniques are introduced and categorized on the basis of their solution method: Finite Elements (FE), Finite Differences in the Time Domain (FDTD), Finite Integration Technique (FIT), and Integral Equations (IE) solved by the Method of Moments (MoM). Basically, the coupling between an electromagnetic (light-) wave and a plasmonic scatterer is thus the same as it is at microwave frequencies, and can be studied in the same way. It means that the concept of a “scatterer”, a device able to be excited by electromagnetic waves rather than particles, still works. The fact that at this small scale, no quantum effects have to be taken into account is really a crucial observation. The underlying formulation of Maxwell’s equations can remain unaffected. As long as quantum effects do not have to be taken into account, which is still the case for the plasmonic applications considered, since the structures are not that small, there is no fundamental problem. Missing links will be pointed out and suggestions will be given for the future.įirst of all, it is essential to point out that the interaction between light and plasmonic structures in the frequency bands considered can still be analyzed with a high degree of accuracy using classical electromagnetic theory.Although the frequency is orders of magnitude higher in plasmonics compared to microwaves, Mawell’s laws are the same. This is done through an overview of benchmarks available in literature and by considering a few thoroughly analyzed structures. Instead, this chapter focuses on those aspects that come into the picture when the structure is plasmonic.Īfter the section on techniques and tools, this chapter will focus on the performance of these techniques and tools for plasmonic structures. These techniques will not be derived or explained here in full detail. This means that in this chapter the major numerical techniques can be overviewed in a general sense, referring to standard literature.
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By far most plasmonic topologies reported in literature have been analyzed / designed with the well-known numerical techniques implemented within in-house developed or commercial software packages. the microwave range, in most cases no special modeling techniques have to be used. Although this frequency range is totally different from the traditional range where computational tools have been developed, i.e. at near IR and optical frequencies, and beyond. The plasmonic structures targeted are structures in the order of magnitude of a wavelength at plasmonic frequencies, i.e. There are many challenges that still need to be faced and “missing links” that have to be solved. Plasmonics is a quite novel research field and the application of computational electromagnetics in plasmonics can be categorized as “very recent”.
The situation is quite different in plasmonics.
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Whereas 30 years ago, the design of an antenna was based on simple analytical models, or trial and error strategies, nowadays, simulations seem to be as crucial to the design as real measurements.
This has been especially true in the design of microwave and millimeter wave components and antennas. The rapidly growing computer capacity and calculation speeds make accurate solutions of very complex problems feasible. In electromagnetics, numerical techniques have been essential in the development of new technology in the last two decades.
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