X. H. Hu, Z. H. Hang, J. Li, J. Zi, and C. T. Chan, Phys. Rev. E 73, 015602 (2006).

[Crossref]

C. Y. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, Phys. Rev. Lett. 96, 043903 (2006).

[Crossref]
[PubMed]

X. Q. Huang, L. Zhou, and C. T. Chan, Phys. Rev. B 74, 045123 (2006).

[Crossref]

A. B. Kozyrev and D. W. von der Weide, Phys. Rev. Lett. 94, 203902 (2005).

[Crossref]
[PubMed]

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).

[Crossref]

Y. Zhang, T. M. Grzegorzyk, and J. A. Kong, Electromagn. Waves 35, 271 (2002).

[Crossref]

R. Ruppin, J. Phys. Condens. Matter 13, 1811 (2001).

[Crossref]

M. Einat and E. Jerby, Phys. Rev. E 56, 5996 (1997).

[Crossref]

We note that such states had been observed experimentally, see R. B. Pettit, J. Silcox, and R. Vincent, Phys. Rev. B 11, 3116 (1975).

[Crossref]

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).

[Crossref]

Y. Zhang, T. M. Grzegorzyk, and J. A. Kong, Electromagn. Waves 35, 271 (2002).

[Crossref]

R. Ruppin, J. Phys. Condens. Matter 13, 1811 (2001).

[Crossref]

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).

[Crossref]

X. Q. Huang, L. Zhou, and C. T. Chan, Phys. Rev. B 74, 045123 (2006).

[Crossref]

We note that such states had been observed experimentally, see R. B. Pettit, J. Silcox, and R. Vincent, Phys. Rev. B 11, 3116 (1975).

[Crossref]

X. H. Hu, Z. H. Hang, J. Li, J. Zi, and C. T. Chan, Phys. Rev. E 73, 015602 (2006).

[Crossref]

M. Einat and E. Jerby, Phys. Rev. E 56, 5996 (1997).

[Crossref]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, Phys. Rev. Lett. 91, 133901 (2003).

[Crossref]
[PubMed]

C. Y. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, Phys. Rev. Lett. 96, 043903 (2006).

[Crossref]
[PubMed]

A. B. Kozyrev and D. W. von der Weide, Phys. Rev. Lett. 94, 203902 (2005).

[Crossref]
[PubMed]

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).

[Crossref]

J. A. Kong, Electromagnetic Wave Theory (Higher Education, 2002).

Qualitative conclusions reported here are not affected by the specific forms of ϵr(ω), μr(ω), and the parameters are chosen only for easy illustration. Given the velocity adopted in this paper, we find that calculations based on a Galilean transformation do not lead to a significantly different result.

The spectrum is reduced to ω̃=ω0 when vr=0.

Another cross point is automatically excluded in the calculations by the causality requirement.

R̃TE(ω̃,k̃x) is obtained by applying a Lorentz transformation to RTE(ω,kx), the reflection coefficient calculated in the static-slab frame following .

In the static-slab frame, D⃗(r⃗,t) is determined by E⃗(r⃗,t′), as the response is spatially local. However, after the Lorentz transformation in a moving frame, the point {r⃗,t} is spatially different from the point {r⃗,t′} as long as t≠t′, so that the response appears spatially nonlocal.

We get ω̃r=ω0(1+βs)/(1−βs) when vr=0 and ω̃r=ω0(1−βr)/(1+βr) when vs=0. The frequency shift is zero (ω̃r=ω0) when βs=βr.