Abstract

Classical masking aperture methods are found to be mostly inaccurate to determine the terahertz beam size in terahertz time-domain spectroscopy (TDS) experiments, owing to complex diffraction effects. Here, we present a simple and reliable method for measuring beam waists in terahertz TDS. It is based on the successive diffraction by an opaque disk followed by a small circular aperture.

© 2010 Optical Society of America

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References

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2008 (1)

2006 (2)

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

J.-B. Masson and G. Gallot, Phys. Rev. B 73, 121401(R) (2006).
[CrossRef]

2005 (1)

2003 (1)

D. Mittleman, Sensing with Terahertz Radiation, Optical Sciences (Springer, 2003).

2001 (2)

2000 (3)

1990 (2)

D. Grischkowsky, S. R. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
[CrossRef]

J. C. G. Lesurf, Millimeter-wave Optics, Devices, and Systems (Adam Hilger, 1990).

1986 (1)

A. E. Siegman, Lasers (University Science Books, 1986).

1971 (1)

Arnaud, J. A.

Averitt, R. D.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Bakker, H. J.

Bartels, L.

Bonn, M.

Chen, Q.

de la Claviere, B. D.

Fattinger, C.

Franke, E. A.

Franke, J. M.

Gallot, G.

Grischkowsky, D.

Heinz, T. F.

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Hubbard, W. M.

Jamison, S. P.

Jiang, Z.

Johnson, J. L.

Keiding, S. R.

Knoesel, E.

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Lesurf, J. C. G.

J. C. G. Lesurf, Millimeter-wave Optics, Devices, and Systems (Adam Hilger, 1990).

Mandevil, G. D.

Masson, J.-B.

J.-B. Masson and G. Gallot, Phys. Rev. B 73, 121401(R) (2006).
[CrossRef]

McGowan, R. W.

Mittleman, D.

D. Mittleman, Sensing with Terahertz Radiation, Optical Sciences (Springer, 2003).

Mittleman, D. M.

Nahata, A.

Nienhuys, H. K.

Padilla, W. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Planken, P. C. M.

Podzorov, A.

Reider, G. A.

Rudd, J. V.

Shan, J.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Tani, M.

Taylor, A. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

van der Marel, W. A. M.

van der Valk, N. C. J.

van Exter, M.

Welling, A. S.

Wenckebach, T.

Zhang, X. C.

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Figures (4)

Fig. 1
Fig. 1

Half-maximum radius versus frequency for classical aperture/aperture strategy with a large second aperture: R 2 = 32 mm , d = 200 mm , and w = 3 mm . The horizontal line stands for theoretical value without diffraction: R ( 1 2 ) 1.108 w . Inset, experimental setup for both aperture/aperture and disk/aperture strategies.

Fig. 2
Fig. 2

R ( 1 2 ) versus θ max for aperture/aperture strategy (black solid line) and for disk/aperture strategy [gray (red online) lines] (dotted line: large aperture, R 2 = 32 mm ; dashed line: small aperture, R 2 = 2 mm ). In both cases, d = 200 mm , w 0 = 3 mm , and ν = 0.236 THz .

Fig. 3
Fig. 3

R ( 1 2 ) versus beam waist w, for circular aperture (black lines) and opaque disk [gray (red online) lines], at 1.1 THz (solid lines), 0.45 THz (dashed), and 0.2 THz (dotted). In both cases, d = 500 mm , R 2 = 2 mm , and θ max = 0.001 rad .

Fig. 4
Fig. 4

Experimental R ( 1 2 ) measurements (black solid lines) and calculated waist (dots) for 2 f 2 f (a) and f (b) geometries. The focal length f = 120 mm , and the distance between the two paraboloid mirrors in the f geometry is 1000 mm .

Equations (2)

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R ( 1 2 ) = ln [ 2 ( 2 1 ) ] w 1.108 w .
E ( r ) = i 2 π λ d exp ( i π r 2 λ d ) 0 a ρ E 0 ( ρ ) exp ( i π ρ 2 λ d ) J 0 ( 2 π ρ r λ d ) d ρ ,

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