Abstract

We introduce and demonstrate a new interferometric method called longitudinal-differential (LD) interferometry, which measures the spatially resolved phase difference of the scattered field by an object relative to the illumination. This method is combined with a high-resolution interference microscope that allows recording three-dimensional field distributions in amplitude and phase. The method is applied to study the axial phase behavior of Arago spots, an effect observable in low-Fresnel-number systems behind objects with a size comparable to the wavelength. We directly observe the initial phase delay in the Arago spot and prove that the local phase velocity exceeds the speed of light in air. Such LD phase studies are applicable not only to the Arago spot but also to other kinds of light interactions with wavelength-scale objects, e.g., photonic nanojets.

© 2012 Optical Society of America

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References

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2011 (3)

X. Pang, T. D. Visser, and E. Wolf, Opt. Commun. 284, 5517 (2011).
[CrossRef]

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Appl. Phys. Lett. 98, 191114 (2011).
[CrossRef]

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Opt. Express 19, 10206 (2011).
[CrossRef]

2010 (2)

2007 (1)

2005 (1)

2002 (1)

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

2000 (1)

D. Mignai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef]

1995 (1)

1987 (1)

1984 (1)

J. E. Harvey and J. L. Forgham, Am. J. Phys. 52, 243 (1984).
[CrossRef]

1983 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

1890 (1)

L. G. Gouy and C. R. Hebd, Seances Acad. Sci. 110, 1251 (1890).

Brunel, M.

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

Burow, R.

Chauvat, D.

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

Eiju, T.

Elssner, K.-E.

Emile, O.

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

Floch, A. L.

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

Foley, J. T.

Forgham, J. L.

J. E. Harvey and J. L. Forgham, Am. J. Phys. 52, 243 (1984).
[CrossRef]

Gouy, L. G.

L. G. Gouy and C. R. Hebd, Seances Acad. Sci. 110, 1251 (1890).

Grzanna, J.

Hariharan, P.

Harvey, J. E.

J. E. Harvey and J. L. Forgham, Am. J. Phys. 52, 243 (1984).
[CrossRef]

Hebd, C. R.

L. G. Gouy and C. R. Hebd, Seances Acad. Sci. 110, 1251 (1890).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1987), 2nd ed., Chap. 10.

Herzig, H. P.

Khoroshun, A.

Kim, M.-S.

Merkel, K.

Mignai, D.

D. Mignai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef]

Mühlig, S.

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Appl. Phys. Lett. 98, 191114 (2011).
[CrossRef]

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Opt. Express 19, 10206 (2011).
[CrossRef]

Oreb, B. F.

Pang, X.

X. Pang, T. D. Visser, and E. Wolf, Opt. Commun. 284, 5517 (2011).
[CrossRef]

Pas’ko, V.

Ranfagni, A.

D. Mignai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Rockstuhl, C.

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Opt. Express 19, 10206 (2011).
[CrossRef]

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Appl. Phys. Lett. 98, 191114 (2011).
[CrossRef]

Ruggeri, R.

D. Mignai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef]

Scharf, T.

Schwider, J.

Slyusar, V.

Soskin, M.

Spolaczyk, R.

Subbarao, D.

Vasnetsov, M.

Visser, T. D.

X. Pang, T. D. Visser, and E. Wolf, Opt. Commun. 284, 5517 (2011).
[CrossRef]

T. D. Visser and E. Wolf, Opt. Commun. 283, 3371 (2010).
[CrossRef]

Wolf, E.

X. Pang, T. D. Visser, and E. Wolf, Opt. Commun. 284, 5517 (2011).
[CrossRef]

T. D. Visser and E. Wolf, Opt. Commun. 283, 3371 (2010).
[CrossRef]

J. T. Foley and E. Wolf, Opt. Lett. 30, 1312 (2005).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Am. J. Phys. (1)

J. E. Harvey and J. L. Forgham, Am. J. Phys. 52, 243 (1984).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, Appl. Phys. Lett. 98, 191114 (2011).
[CrossRef]

Opt. Commun. (2)

T. D. Visser and E. Wolf, Opt. Commun. 283, 3371 (2010).
[CrossRef]

X. Pang, T. D. Visser, and E. Wolf, Opt. Commun. 284, 5517 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Lett. A (1)

D. Chauvat, O. Emile, M. Brunel, and A. L. Floch, Phys. Lett. A 295, 78 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

D. Mignai, A. Ranfagni, and R. Ruggeri, Phys. Rev. Lett. 84, 4830 (2000).
[CrossRef]

Proc. R. Soc. London (1)

B. Richards and E. Wolf, Proc. R. Soc. London 253, 358 (1959).
[CrossRef]

Seances Acad. Sci. (1)

L. G. Gouy and C. R. Hebd, Seances Acad. Sci. 110, 1251 (1890).

Other (1)

E. Hecht, Optics (Addison-Wesley, 1987), 2nd ed., Chap. 10.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of the HRIM system and (b) close-up near the sample, which shows the scanning situation.

Fig. 2.
Fig. 2.

Measured longitudinal (xz) field distributions of the spot of Arago created by a 4 µm metallic disk: (a) intensity, (b) LD phase, and (c) retrieved propagating phase. The intensity is normalized. The metallic disk is placed at z=0μm.

Fig. 3.
Fig. 3.

(a) On-axis LD and (b) phase velocity excess of the spot of Arago generated by different disk sizes: the solid curve for the 4 µm disk, the dotted curve for the 10 µm disk, the dashed curve for the 15 µm disk, and the dashed–dotted curve for the 20 µm disk. Open circles and asterisks represent the experimental data for 4 and 10 µm disks. Close-up plots for the dashed square in (a) and (b) are (c) and (d), respectively. The FDTD results for the 4 µm disk are plotted with the plus signs in (c) and (d).

Equations (4)

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ΔOPL=(nuppernlower)·l,
OPD plane wave - diffracted wave=z2+r2z.
Δv=c(1+r2z21),
z2+r2zz=1+r2z21.

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