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Light-Matter InteractionPhysics and Engineering at the Nanoscale$
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John Weiner and Frederico Nunes

Print publication date: 2012

Print ISBN-13: 9780198567653

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198567653.001.0001

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Transmission Lines, Waveguides, and Equivalent Circuits

Transmission Lines, Waveguides, and Equivalent Circuits

Chapter:
(p.117) 4 Transmission Lines, Waveguides, and Equivalent Circuits
Source:
Light-Matter Interaction
Author(s):

Weiner John

Frederico Nunes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567653.003.0007

This chapter starts with a discussion of the two Kirchhoff rules, one for voltage and the other for current, that serve as the basis for lumped-element circuit theory. The quasistatic approximation is presented to establish the criteria for ‘subwavelength’ interaction. At the nanoscale, ‘subwavelength’ means structures (and lumped RLC components) of the order of tens of nanometers. Next, the generalisation of the localised lumped-circuit idea to an infinitely repeating group of such structures to form a transmission line is introduced. After the consideration of special termination cases (matched load, shorted line, open line, etc.) the concept of waveguides in one and two dimensions is explained. Two principal geometries — rectangular and cylindrical — are discussed at length. Finally, the combination of several transmission lines or waveguides into a network and the realisation of such networks at the nanoscale are discussed. The analysis of these two-port networks in terms of ‘equivalent circuits’ provides the capstone to this chapter. The correspondence between plane waves and transmission lines is presented.

Keywords:   Kirchhoff rules, quasistatic approximation, transmission lines, waveguide, equivalent circuits, nanometers

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