Abstract

We investigate triangular surface-relief gratings for reducing reflection at a planar silicon surface for light in the terahertz frequency region of 0.33.0THz. Structural parameters of the one- and two- dimensional (1D 2D) subwavelength gratings required for the antireflection (AR) layer were obtained numerically. Experimental results for the AR effects agreed well with those obtained numerically, except for gratings fabricated with laser ablation, which causes structural fluctuations of the grating. In the 1D grating, a high transmittance exceeding 90% for the TM wave was obtained. 2D gratings comprised of arrayed micropyramids were experimentally confirmed to be polarization insensitive.

© 2010 Optical Society of America

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2009

Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009).
[CrossRef]

2008

2006

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

2002

2001

2000

1998

1996

1995

1994

K. Shiraishi and K. Matsumura, “Fabrication of spatial walk-off polarizing films by oblique deposition,” Quantum Electron. 30, 2417–2420 (1994).
[CrossRef]

1991

K. Shiraishi, T. Sato, and S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett., 58, 211–212 (1991).
[CrossRef]

1953

W. L. Bragg and A. B. Pippard, “The form birefringence of macromolecules,” Acta Cryst. 6, 865–867 (1953).
[CrossRef]

Bengtsson, J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 705–708.

Bragg, W. L.

W. L. Bragg and A. B. Pippard, “The form birefringence of macromolecules,” Acta Cryst. 6, 865–867 (1953).
[CrossRef]

Brundrett, D. L.

Chen, Y. W.

Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009).
[CrossRef]

Craighead, H. G.

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

Habraken, S.

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Han, P. Y.

Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009).
[CrossRef]

Hard, S.

Heine, Claus

Ho, B. J.

Jiang, B.

Jiang, P.

Johansson, M.

Kawakami, S.

K. Shiraishi, T. Sato, and S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett., 58, 211–212 (1991).
[CrossRef]

Kuroo, S.

S. Kuroo, K. Shiraishi, and H. Sashou, “Optical components,” Japanese patent application 2008-061993 (12 March 2008).

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

Lenaerts, C.

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Lofving, B.

Loicq, J.

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Lopez, A. G.

Matsumura, K.

K. Shiraishi and K. Matsumura, “Fabrication of spatial walk-off polarizing films by oblique deposition,” Quantum Electron. 30, 2417–2420 (1994).
[CrossRef]

Mawet, D.

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Mittleman, D. M.

Moharam, M. G.

Muro, K.

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

Nikolajeff, F.

Pippard, A. B.

W. L. Bragg and A. B. Pippard, “The form birefringence of macromolecules,” Acta Cryst. 6, 865–867 (1953).
[CrossRef]

Pommet, D. A.

Rudd, J. Van

Sasho, H.

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

Sashou, H.

S. Kuroo, K. Shiraishi, and H. Sashou, “Optical components,” Japanese patent application 2008-061993 (12 March 2008).

Sato, T.

K. Shiraishi, T. Sato, and S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett., 58, 211–212 (1991).
[CrossRef]

Shiraishi, K.

K. Shiraishi and K. Matsumura, “Fabrication of spatial walk-off polarizing films by oblique deposition,” Quantum Electron. 30, 2417–2420 (1994).
[CrossRef]

K. Shiraishi, T. Sato, and S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett., 58, 211–212 (1991).
[CrossRef]

S. Kuroo, K. Shiraishi, and H. Sashou, “Optical components,” Japanese patent application 2008-061993 (12 March 2008).

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

Smith, R. E.

Sun, C-H.

Vandormeal, D.

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Vawter, G. A.

Warren, M. E.

Wendt, J. R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 705–708.

Yoda, H.

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

Zhang, X.-C.

Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009).
[CrossRef]

Acta Cryst.

W. L. Bragg and A. B. Pippard, “The form birefringence of macromolecules,” Acta Cryst. 6, 865–867 (1953).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009).
[CrossRef]

Appl. Phys. Lett.,

K. Shiraishi, T. Sato, and S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett., 58, 211–212 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Proc. SPIE

D. Vandormeal, S. Habraken, J. Loicq, C. Lenaerts, and D. Mawet. “Antireflective subwavelength patterning of IR optics,” Proc. SPIE 6395, 63950L (2006).

Quantum Electron.

K. Shiraishi and K. Matsumura, “Fabrication of spatial walk-off polarizing films by oblique deposition,” Quantum Electron. 30, 2417–2420 (1994).
[CrossRef]

Other

S. Kuroo, K. Shiraishi, H. Sasho, H. Yoda, and K. Muro, “Triangular surface-relief grating for reduction of reflection from silicon surface in the 0.1–3 terahertz region,” in Proceedings of the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, 2008 (IEEE, 2008), pp. 1–2.

S. Kuroo, K. Shiraishi, and H. Sashou, “Optical components,” Japanese patent application 2008-061993 (12 March 2008).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 705–708.

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Figures (17)

Fig. 1
Fig. 1

Structure of the 1D grating.

Fig. 2
Fig. 2

Structure of the 2D grating.

Fig. 3
Fig. 3

Effective refractive indices as a function of the normalized position Z / L .

Fig. 4
Fig. 4

Calculated transmittance and reflectance as a function of the frequency.

Fig. 5
Fig. 5

Calculated contour diagram of transmittance for the TE wave in the 1D grating.

Fig. 6
Fig. 6

Calculated contour diagram of transmittance for the TM wave in the 1D grating.

Fig. 7
Fig. 7

Calculated contour diagram of transmittance in the 2D grating.

Fig. 8
Fig. 8

Scanning-electron photomicrograph of the grating fabricated with the dicing blade.

Fig. 9
Fig. 9

Measured and calculated optical properties for the TE wave in the 1D grating fabricated with a dicing blade.

Fig. 10
Fig. 10

Measured and calculated optical properties for the TM wave in the 1D grating fabricated with a dicing blade.

Fig. 11
Fig. 11

Scanning-electron photomicrograph of the 1D grating fabricated with laser ablation.

Fig. 12
Fig. 12

Measured and calculated optical properties for the TE wave in the 1D grating fabricated with laser ablation.

Fig. 13
Fig. 13

Measured and calculated optical properties for the TM wave in the 1D grating fabricated with laser ablation.

Fig. 14
Fig. 14

Scanning-electron photomicrograph of the 2D grating fabricated with the dicing blade.

Fig. 15
Fig. 15

Measured and calculated optical properties of the 2D grating fabricated with the dicing blade for light polarized at 0 ° and 45 ° .

Fig. 16
Fig. 16

Scanning-electron photomicrograph of the 2D grating fabricated with laser ablation.

Fig. 17
Fig. 17

Measured and calculated optical properties of the 2D grating fabricated with laser ablation for light polarized at 0 ° and 45 ° .

Equations (4)

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n ( z ) 2 = q ( z ) ( n Si 1 ) 1 + ( 1 q ( z ) ) ( n Si 2 1 ) l + 1 ,
n TE = 1 q ( z ) + q ( z ) n Si 2 = 1 z L ( n Si 2 1 ) ,
n TM = n Si q ( z ) + ( 1 q ( z ) ) n Si = n Si z L ( 1 n Si ) + 1 ,
n TEM = n Si 2 ( 1 q ( z ) ) + 2 q ( z ) n Si q ( z ) + 1 n Si 2 ( 1 q ( z ) ) + q ( z ) + 1 = z L ( n Si 2 + 2 n Si 1 ) + n Si + 1 z L ( 1 n Si 2 ) + n Si 2 + 1 .

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