Abstract

We present a promising coupling device, namely, a terahertz (THz) planar photonic crystal (PhC) lens based on the effective refractive-index contrast between the PhC and the surrounding unpatterned area. Three-dimensional finite-difference time-domain calculations show a 90% power transfer from a 100-μm silicon waveguide to a 10-μm waveguide, and 45% coupling efficiency is confirmed experimentally. These results demonstrate the utility of the PhC lens as an effective approach to coupling into PhC THz circuits.

© 2005 Optical Society of America

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References

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  1. P. H. Siegel, IEEE Trans. Microwave Theory Tech. 50, 910 (2002).
    [CrossRef]
  2. T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
    [CrossRef] [PubMed]
  3. T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
    [CrossRef] [PubMed]
  4. A. Mekis, J. Lightwave Technol. 19, 861 (2001).
    [CrossRef]
  5. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
    [CrossRef] [PubMed]
  6. T. Baba, IEEE J. Quantum Electron. 38, 909 (2002).
    [CrossRef]
  7. P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
    [CrossRef]
  8. P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
    [CrossRef]
  9. K. Iizuka, Elements of Photonics, B. E.A. Saleh, ed. (Wiley, New York, 2002), Vol. 1, pp. 292–295.
  10. A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
    [CrossRef]
  11. K. S. Chiang, J. Lightwave Technol. 17, 716 (1999).
    [CrossRef]

2004 (1)

2003 (2)

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
[CrossRef] [PubMed]

2002 (3)

A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
[CrossRef]

T. Baba, IEEE J. Quantum Electron. 38, 909 (2002).
[CrossRef]

P. H. Siegel, IEEE Trans. Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

2001 (1)

1999 (3)

K. S. Chiang, J. Lightwave Technol. 17, 716 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Arriaga, J.

A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
[CrossRef]

Baba, T.

T. Baba, IEEE J. Quantum Electron. 38, 909 (2002).
[CrossRef]

Baras, T.

T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
[CrossRef] [PubMed]

Bykhovskaia, M.

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

Chen, C.

Chiang, K. S.

Gelmont, B. L.

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

Globus, T. R.

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

Halevi, P.

A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Iizuka, K.

K. Iizuka, Elements of Photonics, B. E.A. Saleh, ed. (Wiley, New York, 2002), Vol. 1, pp. 292–295.

Khromova, T.

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

Kleine-Ostmann, T.

T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
[CrossRef] [PubMed]

Koch, M.

T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
[CrossRef] [PubMed]

Krokhin, A. A.

A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
[CrossRef]

Mekis, A.

Murakowski, J.

Prather, D. W.

Pustai, D. M.

Schneider, G. J.

Sharkawy, A.

Shi, S.

Siegel, P. H.

P. H. Siegel, IEEE Trans. Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

Venkataraman, S.

Woolard, D. L.

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

P. Halevi, A. A. Krokhin, and J. Arriaga, Appl. Phys. Lett. 75, 2725 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Baba, IEEE J. Quantum Electron. 38, 909 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. H. Siegel, IEEE Trans. Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

J. Biol. Phys. (2)

T. R. Globus, D. L. Woolard, T. Khromova, M. Bykhovskaia, and B. L. Gelmont, J. Biol. Phys. 29, 89 (2003).
[CrossRef] [PubMed]

T. Baras, T. Kleine-Ostmann, and M. Koch, J. Biol. Phys. 29, 187 (2003).
[CrossRef] [PubMed]

J. Lightwave Technol. (2)

Opt. Lett. (1)

Phys. Rev. B (1)

A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Other (1)

K. Iizuka, Elements of Photonics, B. E.A. Saleh, ed. (Wiley, New York, 2002), Vol. 1, pp. 292–295.

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Figures (4)

Fig. 1
Fig. 1

(a) EFCs of the designed PhC lens and the free space at 10.6 - μ m wavelength. The inner circle represents the EFC of the free space, whereas the outer circle represents the EFC of the PhC; both of them are in the normalized frequency of 0.13 ( ω a 2 π c ) , where a is the lattice constant. (b) Steady-state 3D FDTD simulation results of the H z component of the electromagnetic field for the PhC lens at 10.6 μ m .

Fig. 2
Fig. 2

(a) SEM images of a fabricated PhC lens on a SOI substrate with device silicon and SiO 2 layer thicknesses of 2.56 and 2 μ m , respectively. (b) SEM images of the PhC lens devices, in which the lens coupled the wave from a 100 - μ m -wide dielectric waveguide into a 10 - μ m -wide dielectric waveguide

Fig. 3
Fig. 3

Images from a thermal imager showing the PhC lens coupling a 10.6 - μ m wave from a 100 - μ m waveguide into a 10 - μ m -wide dielectric waveguide (left), and the top view of the reference structure (right), which is identical to the device but without the PhC lens. In comparison with the reference structure, one can see a bright output spot from the PhC lens device, indicating efficient coupling.

Fig. 4
Fig. 4

(a) Transmission spectrum of the PhC lens calculated by 3D FDTD methods. The bandwidth of the transmission is approximately 1 μ m ; the highest transmission is 90% at 10.6 μ m . (b) Measured transmission of the PhC lens from 10.1 to 10.7 μ m with a peak transmission of 45% at the 10.6 - μ m wavelength, and the transmission of the reference structure, which is approximately flat, peaking around 10%.

Equations (1)

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v g = k ω ( k ) ,

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