Note on the physics of negative e.
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Negative n from simultaneously negative e and m:
Negative Index Media made so far consist of arrays of wires and split-ring resonators. These systems have overlapping, narrow resonances in effective m and e as shown. In a narrow frequency region above the two resonances, both m and e can have negative real parts and small imaginary parts (low-loss "transparency range" with negative phase index).
The physics of the e resonance can be readily described by conventional discrete transmission line analysis. Arrays of small diameter wires have sufficiently large inductance to obtain resonance with the shunt capacitance of the unit cell in the GHz range. This mechanism has been well understood for decades [e.g., see W. Rotman, IRE Trans. Ant. Prop., AP10, 82 (1962)].

However, a paper by Pendry et. al. in Physical Review Letters (PRL, V.76, 25, 4773 June 1996) claimed that the real physics behind the e resonance is the lowering of the (quantum) plasmon mode in metal wires to extremely low frequencies because the self magnetic field of electrons in a thin (less than 10 microns) wire makes them as heavy as nitrogen atoms.

Walser, Valanju and Valanju's comment in PRL, V.87, No. 11, 119701-1 10 Sept. 2001 proved this "extermely low frequency plasmon" concept to be completely wrong since it neglected the dominant collisions and violated gauge invariance. It was shown that there are no "low frequency plasmons (classical or quantum)" and no "electrons as heavy as nitrogen atoms" in these wires, and none are needed to explain the observed electromagnetic responses.

Pendry et. al. reply to our PRL comment was not accepted or published by Physical Review Letters (PRL).


Some of the papers that cite the "Low Frequency Wire Plasmon" as a valid concept
  1. Comment on ``Extremely Low Frequency Plasmons in Metallic Mesostructures'' S. A. Mikhailov, Phys. Rev. Lett. 78, 4135 (1997).
  2. Far-infrared propagation in metal wire microstructures T. E. Huber et al., Appl. Phys. Lett. 70, 2502 (1997).
  3. Modal analysis of guiding structures patterned in a metallic photonic crystal, J. Danglot et al., Appl. Phys. Lett. 73, 2712 (1998).
  4. Two-dimensional metallodielectric photonic crystal with a large band gap, Chongjun Jin et al., Appl. Phys. Lett. 75, 1201 (1999).
  5. Loop-wire medium for investigating plasmons at microwave frequencies, D. R. Smith et al., Appl. Phys. Lett. 75, 1425 (1999).
  6. Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths, A. de Lustrac et al., Appl. Phys. Lett. 75, 1625 (1999).
  7. Low-loss one-dimensional metallodielectric photonic crystals fabricated by metallic insertions in a multilayer dielectric structure Yong-Hong Ye et al., Appl. Phys. Lett. 77, 235 (2000). 7.
  8. High-transmission defect modes in two-dimensional metallic photonic crystals F. Gadot et al., J. Appl. Phys. 85, 8499 (1999).
  9. A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions Min Qiu et al., J. Appl. Phys. 87, 8268 (2000).
  10. Mean-field theory of two-dimensional metallic photonic crystals G. Guida et al., J. Opt. Soc. Am. B 15, 2308 (1998).
  11. Giant gaps in photonic band structures L. Dobrzynski et al., Phys. Rev. B 57, R9388 (1998).
  12. Impurity bands in photonic insulators N. Stefanou et al., Phys. Rev. B 57, 12127 (1998).
  13. Plasma modes in periodic two-dimensional superconducting-wire networks F. Parage et al., Phys. Rev. B 58, R8921 (1998).
  14. Order-N photonic band structures for metals and other dispersive materials J. Arriaga et al., Phys. Rev. B 59, 1874 (1999).
  15. Electromagnetic wave propagation through a wire array composite Tito E. Huber et al., Phys. Rev. B 59, 7446 (1999).
  16. Pendry et al. Reply J. B. Pendry et al., Phys. Rev. Lett. 78, 4136 (1997).
  17. 3D Metallo-Dielectric Photonic Crystals with Strong Capacitive Coupling between Metallic Islands D. F. Sievenpiper et al., Phys. Rev. Lett. 80, 2829 (1998).
  18. Three-Dimensional Complete Photonic-Band-gap Structures in the Visible, Alexander Moroz, Phys. Rev. Lett. 83, 5274 (1999).
  19. Composite Medium with Simultaneously Negative Permeability and Permittivity D. R. Smith et al., Phys. Rev. Lett. 84, 4184 (2000).
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