Abstract

We present novel designs for aspheric lenses used in terahertz (THz) imaging. As different surfaces result in different beam shaping properties and in different losses from reflection and absorption, the resultant imaging resolution (i.e. the focal spot size) depends critically on the design approach. We evaluate the different lens designs using Kirchhoff’s scalar diffraction theory, and test the predictions experimentally. We also show that our lenses can achieve sub-wavelength resolution. While our lens designs are tested with THz radiation, the design considerations are applicable also to other regions of the electro-magnetic spectrum.

© 2008 Optical Society of America

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  1. T. Yasui, K. I. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, "Real-time terahertz color scanner for moving objects," Opt. Express 16, 1208-1221 (2008).
    [CrossRef] [PubMed]
  2. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, "Non-destructive terahertz imaging of illicit drugs using spectral fingerprints," Opt. Express 11, 2549-2554 (2003).
    [CrossRef] [PubMed]
  3. R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
    [CrossRef] [PubMed]
  4. G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
    [CrossRef]
  5. C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
    [CrossRef]
  6. T. Kampfrath, J. Notzold, and M. Wolf, "Sampling of broadband terahertz pulses with thick electro-optic crystals," Appl. Phys. Lett. 90, 231,113/1-3 (2007).
    [CrossRef]
  7. S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
    [CrossRef]
  8. R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman lectures on physics (Addison-Wesley, 1963).
  9. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  10. T. H. Blakesley, "Single-piece lenses," Proc. Phys. Soc. 18, 591-595 (1903). UK.
    [CrossRef]
  11. M. Born and E. Wolf, Principles of optics : electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford; New York, 1980).
    [PubMed]

2008

2007

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

2003

2002

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

1998

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

1903

T. H. Blakesley, "Single-piece lenses," Proc. Phys. Soc. 18, 591-595 (1903). UK.
[CrossRef]

Abraham, E.

Araki, T.

Arnone, D. D.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Blakesley, T. H.

T. H. Blakesley, "Single-piece lenses," Proc. Phys. Soc. 18, 591-595 (1903). UK.
[CrossRef]

Brener, I.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Cole, B. E.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Faist, J.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Fischer, M.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Hashimoto, M.

Hoyler, N.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Ihara, A.

Inoue, H.

Kawase, K.

Koch, M.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Linfield, E. H.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Nuss, M. C.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Ogawa, Y.

Pepper, M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Planken, P. C. M.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Pye, R. J.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Sawanaka, K. I.

Scalari, G.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Schouten, R. N.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Terazzi, R.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

van der Valk, N.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Wallace, V. P.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Walther, C.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Watanabe, Y.

Wenckebach, W. T.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Woodward, R. M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Yasui, T.

Zhao, G.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Appl. Phys. Lett.

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, "Quantum cascade lasers operating from 1.2 to 1.6 THz," Appl. Phys. Lett. 91, 1-3 (2007).
[CrossRef]

Opt. Commun.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, "THz near-field imaging," Opt. Commun. 150, 22-26 (1998).
[CrossRef]

Opt. Express

Phys. Med. Biol.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, "Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue," Phys. Med. Biol. 47, 3853-3863 (2002).
[CrossRef] [PubMed]

Proc. Phys. Soc.

T. H. Blakesley, "Single-piece lenses," Proc. Phys. Soc. 18, 591-595 (1903). UK.
[CrossRef]

Rev. Sci. Instrum.

G. Zhao, R. N. Schouten, N. van der Valk,W. T. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002).
[CrossRef]

Other

T. Kampfrath, J. Notzold, and M. Wolf, "Sampling of broadband terahertz pulses with thick electro-optic crystals," Appl. Phys. Lett. 90, 231,113/1-3 (2007).
[CrossRef]

M. Born and E. Wolf, Principles of optics : electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford; New York, 1980).
[PubMed]

R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman lectures on physics (Addison-Wesley, 1963).

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

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Figures (6)

Fig. 1.
Fig. 1.

The three lenses we designed: (a) planar-hyperbolic lens; (b) elliptical-aspheric lens; (c) symmetric-pass lens.

Fig. 2.
Fig. 2.

(a) Three different lens characteristics: 1) Reflection losses, r 1 and r 2; 2) Absorption losses, α(r); 3) Beam shaping, δ(r). (b) The δ(r) curve, showing the relation between the cone angle and the radial distance from the optics axis of the incident beam.

Fig. 3.
Fig. 3.

Intensity profiles of the focal spots from the different lenses, determined by Kirchhoff’s scalar diffraction theory and using a frequency of 0.7 THz.

Fig. 4.
Fig. 4.

Experimental setup for measuring focal spot sizes.

Fig. 5.
Fig. 5.

Half-plane scan results for the different lenses, at 0.7 THz: (a) Result for p-h lens; (b) Result for e-a lens; (c) Result for s-p lens.

Fig. 6.
Fig. 6.

(a) Double pinhole used as the imaging sample; (b) Result for p-h lens; (c) Result for e-a lens; (d) Result for s-p lens.

Tables (1)

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Table 1. Focal spot sizes determined from Kirchhoff’s scalar diffraction theory.

Equations (1)

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E P = S K ( θ ) ε A r cos ( k r w t π 2 ) d S

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