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Optics Letters

Optics Letters


  • Editor: Alan E. Willner
  • Vol. 33, Iss. 4 — Feb. 15, 2008
  • pp: 369–371

Doppler effects of a light source on a metamaterial slab: a rigorous Green’s function approach

Weihua Wang, Xueqin Huang, Lei Zhou, and C. T. Chan  »View Author Affiliations

Optics Letters, Vol. 33, Issue 4, pp. 369-371 (2008)

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We apply a (rigorous) Green’s function theory to study the Doppler effects of a light source placed on top of a metamaterial slab. When the receiver is in motion with the source and the slab, we find that, in addition to a conventional Doppler mode, there are several other frequency components that do not obey the standard frequency-shift rule. We show that such new effects are caused by the coupling between the radiated electromagnetic waves and the surface modes of the metamaterial slab, whose dispersion relation varies as a function of velocity in the moving reference frame.

© 2008 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

Original Manuscript: October 12, 2007
Revised Manuscript: January 10, 2008
Manuscript Accepted: January 14, 2008
Published: February 14, 2008

Weihua Wang, Xueqin Huang, Lei Zhou, and C. T. Chan, "Doppler effects of a light source on a metamaterial slab: a rigorous Green's function approach," Opt. Lett. 33, 369-371 (2008)

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  9. 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.
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  12. R̃TE(ω̃,k̃x) is obtained by applying a Lorentz transformation to RTE(ω,kx), the reflection coefficient calculated in the static-slab frame following .
  13. 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.
  14. 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.
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  17. 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]
  18. The spectrum is reduced to ω̃=ω0 when vr=0.
  19. Another cross point is automatically excluded in the calculations by the causality requirement.

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