Abstract

It is shown experimentally that a Gaussian beam focused from within a finite wedge onto its edge at an angle of total reflection excites a leaky waveguide mode propagating along the edge. This newly described phenomenon is interpreted in terms of waveguide modes of a tapered dielectric slab of a mode index, which is known to decrease with slab thickness. This decrease in the refractive index leads to a gradual refraction of the incident beam parallel to the edge. A numerical simulation of a focused Gaussian beam incident on a finite dielectric wedge gives a full account of this phenomenon.

© 2009 Optical Society of America

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2008 (1)

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

2005 (2)

2003 (1)

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

1998 (1)

B. Polat, E. Topuz, and L. Sevgi, AEU, Int. J. Electron. Commun. 52, 105 (1998).

1994 (1)

U. C. Fischer, J. Koglin, and H. Fuchs, J. Microsc. 176, 231 (1994).
[CrossRef]

1992 (1)

P. Zwamborn and P. M. van den Berg, IEEE Trans. Microwave Theory Tech. 40, 1757 (1992).
[CrossRef]

1990 (1)

L. Kang and R. E. Dessy, Crit. Rev. Anal. Chem. 21, 377 (1990).
[CrossRef]

1989 (1)

1971 (1)

Burr, G. W.

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

Dessy, R. E.

L. Kang and R. E. Dessy, Crit. Rev. Anal. Chem. 21, 377 (1990).
[CrossRef]

Fischer, U. C.

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

U. C. Fischer, J. Koglin, and H. Fuchs, J. Microsc. 176, 231 (1994).
[CrossRef]

Fuchs, H.

U. C. Fischer, J. Koglin, and H. Fuchs, J. Microsc. 176, 231 (1994).
[CrossRef]

Gnaegi, H.

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev, J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

Grosjean, T.

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

Hashimoto, T.

Horowitz, B. R.

Kang, L.

L. Kang and R. E. Dessy, Crit. Rev. Anal. Chem. 21, 377 (1990).
[CrossRef]

Koglin, J.

U. C. Fischer, J. Koglin, and H. Fuchs, J. Microsc. 176, 231 (1994).
[CrossRef]

Maletzky, T.

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

Matzelle, T. R.

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

Polat, B.

B. Polat, E. Topuz, and L. Sevgi, AEU, Int. J. Electron. Commun. 52, 105 (1998).

Reichelt, R.

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

Ricker, A.

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

Sevgi, L.

B. Polat, E. Topuz, and L. Sevgi, AEU, Int. J. Electron. Commun. 52, 105 (1998).

Sugiyama, T.

Tamir, T.

Tanaka, K.

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

K. Tanaka, M. Tanaka, and T. Sugiyama, Opt. Express 13, 256 (2005).
[CrossRef] [PubMed]

Tanaka, M.

Topuz, E.

B. Polat, E. Topuz, and L. Sevgi, AEU, Int. J. Electron. Commun. 52, 105 (1998).

van den Berg, P. M.

P. Zwamborn and P. M. van den Berg, IEEE Trans. Microwave Theory Tech. 40, 1757 (1992).
[CrossRef]

Yoshino, T.

Zwamborn, P.

P. Zwamborn and P. M. van den Berg, IEEE Trans. Microwave Theory Tech. 40, 1757 (1992).
[CrossRef]

AEU, Int. J. Electron. Commun. (1)

B. Polat, E. Topuz, and L. Sevgi, AEU, Int. J. Electron. Commun. 52, 105 (1998).

Appl. Phys. B (1)

K. Tanaka, G.W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, Appl. Phys. B 93, 257 (2008).
[CrossRef]

Crit. Rev. Anal. Chem. (1)

L. Kang and R. E. Dessy, Crit. Rev. Anal. Chem. 21, 377 (1990).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. Zwamborn and P. M. van den Berg, IEEE Trans. Microwave Theory Tech. 40, 1757 (1992).
[CrossRef]

J. Appl. Phys. (1)

D. K. Gramotnev, J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

J. Microsc. (2)

T. R. Matzelle, H. Gnaegi, A. Ricker, and R. Reichelt, J. Microsc. 209, 113 (2003).
[CrossRef] [PubMed]

U. C. Fischer, J. Koglin, and H. Fuchs, J. Microsc. 176, 231 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Opt. Lett. (1)

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Figures (5)

Fig. 1
Fig. 1

Schematic view of a beam of light incident at an angle ε of total reflection onto the edge of a finite wedge, which ends at a tip.

Fig. 2
Fig. 2

Experimental configuration for the observation of a leaky waveguide mode in a wedge structure. A triangular glass fragment serves as a wedge structure. It is attached to a prism such that a focused beam of light can be injected into the edge of the wedge by using a microscope. The beam reflected from the edge is observed by a CCD1 camera. The CCD2 camera attached to a second microscope is used to detect light, which is emitted from the tip of the wedge.

Fig. 3
Fig. 3

Experimental observations. The white bars correspond to a 10 μ m (a) image of the reflected beam as recorded by CCD1 (see Fig. 2). To localize the focused spot in the tip structure, the tip was additionally illuminated by a weak nonlocal background illumination. (b) Image of the edge slightly displaced from the tip as recorded with CCD camera 2 (Fig. 2) showing light emission from the edge, which was illuminated by a high NA by adjusting iris diaphragm 2 (Fig. 2). (c) The same as (b) but with the tip in focus such that a blurred image of light emission from the edge and a weak emission from the tip is observed. (d) Image of the tip as in (b) but with a small NA of the illuminating beam such that no emission from the edge occurs. Only the emission from the tip is seen. The same NA of the exciting beam was chosen for image (a) of the reflected beam. (e) The same as (d) but with additional background illumination. (e) Schematic view of the orientation of the tip in the images.

Fig. 4
Fig. 4

Dispersion relations as a function of the thickness of a dielectric slab for different symmetric and antisymmetric transverse electric (TE) and transverse magnetic (TM) modes for a vacuum wavelength of 630 nm showing a decrease in the wave vector k z with decreasing thickness of the slab in all cases.

Fig. 5
Fig. 5

Numerical results of the intensity of the electric field E 2 in a dielectric tip of ε / ε 0 = 2.25 surrounded by vacuum with permittivity ε 0 and of dimensions B x = 6.1 λ and B y = 8.15 λ , where λ is the vacuum wavelength. The spot size is 0.8 λ , the intensity is unity at z = 0 , and the beam axis is in the x z plane parallel to the z axis but displaced from it by a distance d = 1.42 λ . The field intensity is shown for a section at y = 0 .

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