Abstract

A transmissive, square-wave Ronchi phase grating has been fabricated from the dielectric polytetrafluoroethylene to diffract an ~0.7 THz beam quasi-optically. When illuminated by a coherent, cw terahertz (THz) source, the spot separation of the ±1 diffractive orders and the diffraction efficiency were measured as a function of THz frequency and rotation angle. The grating performance depends sensitively on the refractive index, whose value can be measured with an accuracy limited by the fabrication precision. The use of these gratings for polarization-insensitive quasi-optical imaging and phased arrays is discussed.

© 2010 Optical Society of America

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References

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  1. I. V. Minin and O. V. Minin, in Proceedings of the 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 371-372.
  2. H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
    [CrossRef]
  3. R. May, J. A. Murphy, and W. Lanigan, in Proceedings of 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 349-350.
  4. C. Chen, S. Shi, and D. W. Prather, Appl. Opt. 43, 2431(2004).
    [CrossRef] [PubMed]
  5. J. C. Wiltse, in Proceedings of 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 608-609.
  6. S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
    [CrossRef]
  7. E. D. Walsby, J. Alton, H. E. Beere, D. A. Ritchie, and D. R. S. Cumming, Opt. Lett. 32, 1141 (2007).
    [CrossRef] [PubMed]
  8. E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
    [CrossRef]
  9. J. W. Lamb, Int. J. Infrared Millim. Waves 17, 1997 (1996).
    [CrossRef]
  10. V. Ronchi, Appl. Opt. 3, 437 (1964).
    [CrossRef]
  11. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  12. To account for the angular sensitivity of the detector, the calculated η1 was empirically multiplied by 0.95.

2007 (1)

2004 (3)

C. Chen, S. Shi, and D. W. Prather, Appl. Opt. 43, 2431(2004).
[CrossRef] [PubMed]

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

2003 (1)

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

1996 (1)

J. W. Lamb, Int. J. Infrared Millim. Waves 17, 1997 (1996).
[CrossRef]

1964 (1)

Ala-Laurinaho, J.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Alton, J.

Beere, H. E.

Biber, S.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Blaikie, R. J.

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

Chen, C.

Collischon, M.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Cumming, D. R. S.

E. D. Walsby, J. Alton, H. E. Beere, D. A. Ritchie, and D. R. S. Cumming, Opt. Lett. 32, 1141 (2007).
[CrossRef] [PubMed]

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

Durbin, S. M.

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

Goodman, W.

W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Häkli, J.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Hoffmann, A.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Koskinen, T.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Lamb, J. W.

J. W. Lamb, Int. J. Infrared Millim. Waves 17, 1997 (1996).
[CrossRef]

Lanigan, W.

R. May, J. A. Murphy, and W. Lanigan, in Proceedings of 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 349-350.

Lönnqvist, A.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Mallat, J.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

May, R.

R. May, J. A. Murphy, and W. Lanigan, in Proceedings of 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 349-350.

Meltaus, H.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Minin, I. V.

I. V. Minin and O. V. Minin, in Proceedings of the 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 371-372.

Minin, O. V.

I. V. Minin and O. V. Minin, in Proceedings of the 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 371-372.

Murphy, J. A.

R. May, J. A. Murphy, and W. Lanigan, in Proceedings of 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 349-350.

Noponen, E.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Prather, D. W.

Räisänen, A. V.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Ritchie, D. A.

Ronchi, V.

Säily, J.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Salo, J.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Salomaa, M. M.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Schmidt, L. P.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Schulz, R.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Shi, S.

Viikari, V.

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

Walsby, E. D.

E. D. Walsby, J. Alton, H. E. Beere, D. A. Ritchie, and D. R. S. Cumming, Opt. Lett. 32, 1141 (2007).
[CrossRef] [PubMed]

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

Weinzierl, J.

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Wiltse, J. C.

J. C. Wiltse, in Proceedings of 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 608-609.

Appl. Opt. (2)

Curr. Appl. Phys. (1)

E. D. Walsby, S. M. Durbin, D. R. S. Cumming, and R. J. Blaikie, Curr. Appl. Phys. 4, 102 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

H. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, IEEE Trans. Microwave Theory Tech. 51, 1274 (2003).
[CrossRef]

S. Biber, A. Hoffmann, R. Schulz, M. Collischon, J. Weinzierl, and L. P. Schmidt, IEEE Trans. Microwave Theory Tech. 52, 2183 (2004).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

J. W. Lamb, Int. J. Infrared Millim. Waves 17, 1997 (1996).
[CrossRef]

Opt. Lett. (1)

Other (5)

W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

To account for the angular sensitivity of the detector, the calculated η1 was empirically multiplied by 0.95.

I. V. Minin and O. V. Minin, in Proceedings of the 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 371-372.

R. May, J. A. Murphy, and W. Lanigan, in Proceedings of 12th International Conference on Terahertz Electronics (IEEE, 2004), pp. 349-350.

J. C. Wiltse, in Proceedings of 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 608-609.

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Figures (3)

Fig. 1
Fig. 1

(a) Grating design, (b) photograph, and (c) optical configuration. The 10-mm-thick plano–convex lenses L1, L2 (effective focal length 143.5 mm ) are located 203.0 and 222.1 mm from the source, followed by the Ronchi grating 60 mm away (grating faces THz source).

Fig. 2
Fig. 2

(a) Measured THz spots showing the frequency- dependent evolution of the 1 , 0, and + 1 diffracted orders. (b) Measured first-order diffraction separation, overlaid by the ZEMAX design with 2 b = 9.96 mm (spot diameters are 5 mm ).

Fig. 3
Fig. 3

(a) Measured η 0 and η ± 1 , normalized to remove the frequency-dependent output variability of the source. The data are overlaid by a fit of η 0 for n using Eq. (7) and d = 0.578 mm , extrapolated to indicate frequencies of lowest and highest efficiency. (b) Ratio η 0 / η 1 measured as a function of ω (with ± 1 ° accuracy), overlaid by the predictions of Eqs. (3, 9).

Equations (10)

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t ( x ) = [ exp ( i φ 2 ) · rect ( x + b / 2 b ) + exp ( i φ 2 ) · rect ( x b / 2 b ) ] 1 2 b comb ( x 2 b ) ,
φ = 2 π · ( n 1 ) · d · ν / c ,
η N = | T ( f x ) | 2 = | sinc ( b f x ) cos ( φ 2 + π b f x ) · j = δ ( f x j 2 b ) | 2 = sinc 2 ( N 2 ) cos 2 ( φ 2 + π N 2 ) ,
η N = sinc 2 ( N 2 ) = ( 2 N π ) 2 N = odd , = 0 N = even ,
n 2 · 2 b · sin θ 2 n 1 · 2 b · sin θ 1 = N c / ν
θ 2 = sin 1 ( N c ν · 2 b ) .
η 0 = cos 2 ( π · ( n 1 ) · d · ν c ) ,
η ± 1 = 4 π 2 cos 2 ( π · ( n 1 ) · d · ν c + π 2 ) .
φ ( ω ) = d cos ( sin 1 ( sin ω n ) ) · ( n cos ( ω sin 1 ( sin ω n ) ) ) · 2 π · ν c ,
δ n · ν 0 n 1 + δ d · ν 0 d = δ ν .

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