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Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 22 — Nov. 15, 2006
  • pp: 3372–3374

On resolving the refractive index and the wave vector

Johannes Skaar  »View Author Affiliations

Optics Letters, Vol. 31, Issue 22, pp. 3372-3374 (2006)

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The identification of the refractive index and the wave vector for general (possibly active) linear, isotropic, homogeneous, and nonspatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions ε = ε ( ω ) and μ = μ ( ω ) . On the other hand, a necessary and sufficient condition for left handedness can be identified at a single frequency ( Re ε ε + Re μ μ < 0 ) . At oblique incidence to semi-infinite, active media, it is explained that the wave vector generally loses its usual interpretation for real frequencies.

© 2006 Optical Society of America

OCIS Codes
(000.2690) General : General physics
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Other Areas of Optics

Original Manuscript: July 11, 2006
Revised Manuscript: September 8, 2006
Manuscript Accepted: September 9, 2006
Published: October 26, 2006

Johannes Skaar, "On resolving the refractive index and the wave vector," Opt. Lett. 31, 3372-3374 (2006)

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  1. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). [CrossRef] [PubMed]
  2. S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101(R) (2003). [CrossRef]
  3. S. A. Ramakrishna, Opt. Lett. 30, 2626 (2005). [CrossRef] [PubMed]
  4. S. A. Ramakrishna, Rep. Prog. Phys. 68, 449 (2005). [CrossRef]
  5. T. G. Mackay and A. Lakhtakia, Phys. Rev. Lett. 96, 159701 (2006). [CrossRef] [PubMed]
  6. Y.-F. Chen, P. Fischer, and F. W. Wise, Phys. Rev. Lett. 95, 067402 (2005). [CrossRef] [PubMed]
  7. Y.-F. Chen, P. Fischer, and F. W. Wise, J. Opt. Soc. Am. B 23, 45 (2006). [CrossRef]
  8. J. Skaar, Phys. Rev. E 73, 026605 (2006). [CrossRef]
  9. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960), Chap. 9.
  10. Writing epsi(omega)=1+int inf 0 x(t) exp(iwt)dt [and similarly for µ(omega)], we restrict ourselves to stable media in the sense that the response function x(t) is bounded.
  11. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  12. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972), Chap. 1.
  13. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968). [CrossRef]
  14. M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, Eur. J. Phys. 22, 353 (2002). [CrossRef]
  15. R. A. Depine and A. Lakhtakia, Microwave Opt. Technol. Lett. 41, 315 (2004). [CrossRef]
  16. For passive media, Im [n(omega)omega-omega]>0 for real frequencies. As the function Im [n(omega)omega-omega] is harmonic, Poisson's integral formula ensures that Im [n(omega)omega-omega]>0 remains valid in the upper halfplane. It follows that n(omega)omega cannot be real there.
  17. If the function kz(omega,kx)=sqrt n2 (omega) omega2/c2-kx2 was discontinuous in kx, we could find a (omega,kx) and a tiny delta>0 such that kz(omega,kx+delta)ap -kz(omega,kx). This leads to a contradiction, since kz(omega,kx) is continuous in omega, and kz(omega,kx+delta)-->kz(omega,kx) as Re omega-->inf.

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