Electrodynamics of TEM radiation normally incident upon a semi-infinite two-layered metal in the good-conductor approximation

Physica B: Condensed Matter

Volumn 240, Issue 4, 1997, Pages 298-310

  Beeli, Pieder ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Bimetal; Electromagnetic power dissipation; Good conductor approximation

Indexed keywords

APPROXIMATION THEORY; BIMETALS; CONDUCTIVE MATERIALS; ELECTRIC CONDUCTIVITY OF SOLIDS; ELECTRIC IMPEDANCE; ELECTROMAGNETIC WAVES; TRANSMISSION LINE THEORY;

ELECTROMAGNETIC POWER DISSIPATION; POYNTING'S THEOREM;

ELECTRODYNAMICS;

EID: 0031245270     PISSN: 09214526     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0921-4526(97)00446-8     Document Type: Article

References (26)

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2. I.K. Schuller, Solid State Comm. 92 (1994) 141-147 and references therein.
3. E. Budevski, G. Staikov, W. Lorenz, Electrochemical Phase Formation and Growth, VCH; Weinheim, Germany, 1996.
4. F.E. Ejeckam et al., Appl. Phys. Lett. 70 (1997) 1685.
5. j, is verisimiltudinous at all points and directions in our bimetallic structure.
6. J. Boettger, S. Trickey, J. Phys.: Condens. Matter 1 (1989) 4323 and references therein.
7. S. Little, A. Zangwill, Phys. Rev. B 49 (1994) 16 659.
8. J. Stratton, Electromagnetic Theory, McGraw Hill, New York, 1941 Section 9.9.
9. E.g. R. Matick, Transmission Lines for Digital and Communication Networks, IEEE Press, New York, 1994, Section 4.11.
10. D. Cheng, Field and Wave Electromagnetics, Addison-Wesley, London, 1983 Section 8-8.1.
11. D. Cheng, in: Field and Wave Electromagnetics, Addison-Wesley, London, 1993, p. 327.
12. sw (Eq. (2)), Eq. (8-37) for γ (Eq. (5)), Eq. (8-25) with Eq. (7-92) for η (Eq. (3)).
13. Provided that we remain self-consistent and do not accept conductivities so large or thicknesses so small that we violate our continuum assumption. See the relevant discussion in endnote [25].
14. D. Cheng, Field and Wave Electromagnetics, Addison-Wesley, London, 1983 Section 8-4.1.
15. E.g. J. Wait, Electromagnetic Waves in Stratified Media, Pergamon, New York, 1962, p. 11-12.
16. S. Ramo, J. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics, Wiley, New York, 1965 Section 6.08.
17. S. Schelkunoff, Bell Sys. Tech. J. 17 (1938) 17.
18. D. Cheng, Field and Wave Electromagnetics, Addison-Wesley, London, 1983 Sections 8-3.2 and 7-7.3.
19. S. Ramo, J. Whinnery, T. Van Duzer, Field and Wave Electromagnetics, Addison-Wesley, London, 1983, Section 5.15. Unlike the more general conditions qualifying Eq. (10), this referenced method used to relate H and K forbids interleaving layers which do not satisfy the good-conductor approximation. This reference denotes the surface current by the symbol J (which we reserve for the areal current density) while we use the more conventional symbol K to denote the surface current.
20. S. Ramo, J. Whinnery, T. Van Duger, Field and Wave Electromagnetics, Addison-Wesley, London, 1983 (Section 5.15. Eq. 5.14(3)).
21. P. Beeli, to be published. Derives a different expression for the surface impedance which uses an alternate basis for the solution of the Helmholtz equation, than that used in Eq. (16). The advantage of this alternate formulation is that is possesses more obvious limiting forms in k and ξ.
22. J. Jackson, Classical Electrodynamics, Wiley, New York, 1975, p. 242.
23. 2 and d » 3 Å). Thus these five lines of constant thickness serve to give boundaries of the validity of our continuum approximation. The boundaries also give the experimentalist, who wishes to probe the classical/quantum metallic boundary, relevant structures to consider. (The d = 3 μm and 3 mm structure lines serve as a reference.) The above discussion assumes that δ is a meaningful quantity. When the mean free path approaches and exceeds the computed δ (or when quantum mechanical effects destroy the assumed linearity in material parameters), δ ceases to retain its meaningfulness and our development cannot be expected to be verisimiltudinous. The relative permittivity and permeability is taken to be unity in all three regions, and f = 10.0 GHz.
24. 12 ℧/m for Al at 10 K are reported (p. 100).
25. 14 ℧/m for f = 10 GHz.
26. The first and the third requirement emerge from the conditions related to our application of Poynting's Theorem and the second requirement is to satisfy the requirements of Eq. (11).