Abstract

The numerical results, Figs. 16 and 18, for the double negative (DNG) metatmaterial Goos-Hänchen examples were incorrect. Corrected numerical results show closer agreement to predictions.

© 2003 Optical Society of America

The numerical results represented by Figs. 16 and 18 in [1] were incorrect; they are corrected below. The author inadvertently over-rode the background material specifications for the slab. The movie in Fig. 16 of [1] actually depicts a Gaussian beam with a center frequency f 0=ω 0/2π=c0=30GHz and a λ0 waist incident at 40° from a DPS medium with ε r =9.0 and µ r =1.0 onto a slab with ε r (ω)=9.0+[1-ωp2 /ω(ω+iΓ)] and µ r (ω)=1-ωp2 /ω(ω+iΓ). Thus, the slab values at the center frequency were Re[ε r (ω 0)]≈+6.0 and Re[µ r (ω 0)]≈-3.0; hence, the slab was a lossy magnetic conductor rather than the intended DNG slab. This explains why, in contrast to the DPS case, there was no penetration of the beam into the slab and why a smaller than expected negative lateral shift was obtained. Figure 1 shows the corrected results for the beam incident on a DNG slab with ε r (ω)=1-ωp2 (ω+iΓ) and µ r (ω)=1-ωp2 (ω+iΓ) so that, as was originally intended, Re[ε r (ω 0)]≈-3.0 and Re[µ r (ω 0)]≈-1.0. The transverse lateral shift of the beam can be seen more clearly in the movie and, like the DPS case, there is penetration into the DNG slab. A time delay in the emergence of the reflected beam from the DNG slab is still apparent. Moreover, in contrast to the DPS case in which the penetration occurs with a positive angle of refraction, one can see that the penetration occurs with a negative angle of refraction. The corrected transverse sampling of the incident and reflected beams is given in Fig. 2. The initial beam center and the specularly reflected beam center are indicated by the vertical black lines. The predicted Goos-Hänchen-shifted beam center is indicated by the vertical green line. An analysis of the centroid of the reflected beams yielded approximately a lateral shift of -33cells, in excellent agreement with the predicted value of -32cells. These corrected DNG Goos-Hänchen results are now completely consistent with those reported in [1] for the DPS case.

 

Fig. 1. (1.17 MB movie) Electric field intensity distribution for the interaction of a CW Gaussian beam that is incident at 40° in a DPS medium with ε r =9.0 and µ r =+1, i.e., n=+3; to a DNG slab having ε r =-3.0 and µ r =-1, i.e., n=-√3. The negative Goos-Hachen shift of this beam is observed.

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Fig. 2. The electric field intensity distribution measured at t=6000Δt at two cells in front of the TF-SF plane for the total internal reflection DNG slab case. The positions of the incident beam center and the specularly-reflected beam center are indicated by the vertical black lines. The theoretical negative Goös-Hachen shift is indicated by the vertical green line.

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References and links

1. R. W. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11, 662–681 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-662. [CrossRef]   [PubMed]  

References

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  1. R. W. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11, 662-681 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-662.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-662</a>.
    [CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: GIF (764 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

(1.17 MB movie) Electric field intensity distribution for the interaction of a CW Gaussian beam that is incident at 40° in a DPS medium with ε r =9.0 and µ r =+1, i.e., n=+3; to a DNG slab having ε r =-3.0 and µ r =-1, i.e., n=-√3. The negative Goos-Hachen shift of this beam is observed.

Fig. 2.
Fig. 2.

The electric field intensity distribution measured at t=6000Δt at two cells in front of the TF-SF plane for the total internal reflection DNG slab case. The positions of the incident beam center and the specularly-reflected beam center are indicated by the vertical black lines. The theoretical negative Goös-Hachen shift is indicated by the vertical green line.

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