Abstract

We accurately measure the profiles of a reflected divergent beam under a very common surface plasmon resonance configuration in both the near- and far-field regions. Through analysis of the normalized beam shapes, significant propagation-dependent distortion is experimentally revealed. The results are in very good agreement with the theoretical estimations, considering the nonlinear phase distribution within the angular range covered by the focused beam. The corresponding minimal positions of the angular reflectance spectrum measured at different locations could shift as much as a few tens of millidegrees. The propagation-dependent Goos–Hänchen shifts are also accurately obtained, and they significantly deviate from the estimates based on the traditional linear phase response but match very well with the simulation results from our model. This verifies our previous theoretical predictions of the propagation-dependent beam distortion, and it could have further implications for various sensing and device applications.

© 2011 Optical Society of America

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References

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  1. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010

H. Wang, Z. Zhou, and H. Tian, “Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film,” Appl. Phys. B 99, 513–517(2010).
[CrossRef]

Q. F. Dai, S. Lan, and H. Z. Wang, “Symmetric and adjustable phase of higher-order reflected light from two-dimensional photonic crystal,” J. Opt. Soc. Am. B 27, 358–362 (2010).
[CrossRef]

V. V. Moskalenko, I. V. Soboleva, and A. A. Fedyanin, “Surface wave-induced enhancement of the Goos–Hänchen effect in one-dimensional photonic crystals,” JETP Lett. 91, 382–386 (2010).
[CrossRef]

2009

2008

2007

2006

X. Yin and L. Hesselink, “Goos–Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

2004

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

2003

D. Felbacq, A. Moreau, and R. Smaâli, “Goos–Hänchen effect in the gaps of photonic crystals,” Opt. Lett. 28, 1633–1635 (2003).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

2002

1948

K. Artmann, “Berechnung der Seitenversetzung des Totalreflektieren Strahles (Calculation of the Lateral Shift of Totally Reflected Beams),” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Aiello, A.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des Totalreflektieren Strahles (Calculation of the Lateral Shift of Totally Reflected Beams),” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Boardman, A.

K. Tsakmakidis, A. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[CrossRef] [PubMed]

Cao, Z. Q.

Chan, S. W.

Chen, C. W.

Chen, L.

Chiang, H. P.

Cook, A. K.

Dai, Q. F.

Edward, G. G.

G. G. Edward, D. Palik, and E. J. Prucha, Handbook of Optical Constants of Solids (Academic, 1985).

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Fedyanin, A. A.

V. V. Moskalenko, I. V. Soboleva, and A. A. Fedyanin, “Surface wave-induced enhancement of the Goos–Hänchen effect in one-dimensional photonic crystals,” JETP Lett. 91, 382–386 (2010).
[CrossRef]

Felbacq, D.

Foster, D. H.

Hess, O.

K. Tsakmakidis, A. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[CrossRef] [PubMed]

Hesselink, L.

X. Yin and L. Hesselink, “Goos–Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Lai, H. M.

Lan, S.

Leung, P. T.

Li, H. G.

Liao, L. S.

Lin, W. C.

Lin, Z. H.

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Moreau, A.

Moskalenko, V. V.

V. V. Moskalenko, I. V. Soboleva, and A. A. Fedyanin, “Surface wave-induced enhancement of the Goos–Hänchen effect in one-dimensional photonic crystals,” JETP Lett. 91, 382–386 (2010).
[CrossRef]

Nockel, J. U.

Ou, F.

Palik, D.

G. G. Edward, D. Palik, and E. J. Prucha, Handbook of Optical Constants of Solids (Academic, 1985).

Prucha, E. J.

G. G. Edward, D. Palik, and E. J. Prucha, Handbook of Optical Constants of Solids (Academic, 1985).

Qiao, H. C.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Shen, Q. S.

Sijercic, E.

Smaâli, R.

Soboleva, I. V.

V. V. Moskalenko, I. V. Soboleva, and A. A. Fedyanin, “Surface wave-induced enhancement of the Goos–Hänchen effect in one-dimensional photonic crystals,” JETP Lett. 91, 382–386 (2010).
[CrossRef]

Tian, H.

H. Wang, Z. Zhou, and H. Tian, “Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film,” Appl. Phys. B 99, 513–517(2010).
[CrossRef]

Tsakmakidis, K.

K. Tsakmakidis, A. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[CrossRef] [PubMed]

Tse, W. S.

Wan, Y.

Wang, H.

H. Wang, Z. Zhou, and H. Tian, “Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film,” Appl. Phys. B 99, 513–517(2010).
[CrossRef]

Wang, H. Z.

Weber, M. J.

M. J. Weber, ed., Handbook of Optical Materials (CRC, 2003).

Woerdman, J.

Yin, X.

X. Yin and L. Hesselink, “Goos–Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Zheng, Z.

Zhou, Z.

H. Wang, Z. Zhou, and H. Tian, “Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film,” Appl. Phys. B 99, 513–517(2010).
[CrossRef]

Zhu, J.

Ann. Phys.

K. Artmann, “Berechnung der Seitenversetzung des Totalreflektieren Strahles (Calculation of the Lateral Shift of Totally Reflected Beams),” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Appl. Opt.

Appl. Phys. B

H. Wang, Z. Zhou, and H. Tian, “Large negative and positive lateral shift on reflection from a left-handed prism coated with a weakly absorbing dielectric film,” Appl. Phys. B 99, 513–517(2010).
[CrossRef]

Appl. Phys. Lett.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos–Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[CrossRef]

X. Yin and L. Hesselink, “Goos–Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

V. V. Moskalenko, I. V. Soboleva, and A. A. Fedyanin, “Surface wave-induced enhancement of the Goos–Hänchen effect in one-dimensional photonic crystals,” JETP Lett. 91, 382–386 (2010).
[CrossRef]

Nature

K. Tsakmakidis, A. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Other

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

M. J. Weber, ed., Handbook of Optical Materials (CRC, 2003).

G. G. Edward, D. Palik, and E. J. Prucha, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Measured reference beam profiles at dif ferent distances: dashed curve, experimental results and solid curve, Gaussian fit.

Fig. 3
Fig. 3

Normalized measured beam profiles under the SPR condition at different distances.

Fig. 4
Fig. 4

Experimental measured beam profile ratio at 0.456 z F and the theoretical fit.

Fig. 5
Fig. 5

Simulated beam profiles under the SPR condition at different distances.

Fig. 6
Fig. 6

Measured beam profile ratios at different distances.

Fig. 7
Fig. 7

Comparison of centroid GH shifts between the experimental data, simulation results based on our analysis [14], and the classic model derived in [13].

Equations (1)

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E ( x ) = C 0 2 π + r ( σ ) exp [ ( k σ w 0 2 ) 2 ] exp ( i k z 2 σ 2 ) exp ( i k x σ ) d σ ,

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