Abstract

We demonstrate active beam steering of terahertz radiation using a photo-excited thin layer of gallium arsenide. A constant gradient of phase discontinuity along the interface is introduced by an spatially inhomogeneous density of free charge carriers that are photo-generated in the GaAs with an optical pump. The optical pump has been spatially modulated to form the shape of a planar blazed grating. The phase gradient leads to an asymmetry between the +1 and −1 transmission diffracted orders of more than a factor two. Optimization of the grating structure can lead to an asymmetry of more than one order of magnitude. Similar to metasurfaces made of plasmonic antennas, the photo-generated grating is a planar structure that can achieve large beam steering efficiency. Moreover, the photo-generation of such structures provides a platform for active THz beam steering.

© 2014 Optical Society of America

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References

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2014 (3)

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, ”Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

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[Crossref] [PubMed]

N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “All-photoinduced terahertz optical activity,” Opt. Lett. 39, 3274 (2014).
[Crossref] [PubMed]

2013 (13)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

J. Sun, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref] [PubMed]

M. F. Farahani and H. Mosallaei, “Birrefringent reflectarray metasurface for beam enginnering in infrared,” Opt. Lett. 38, 462 (2013).
[Crossref]

N. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304 (2013).
[Crossref] [PubMed]

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21, 27438 (2013).
[Crossref] [PubMed]

X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mat. 25, 4567 (2013).
[Crossref]

Z. Wei, Y. Cao, X. Su, Z. Gong, Y. Long, and H. Li, “Highly efficient beam steering with a transparent metasurface,” Opt. Express 21, 10739 (2013).
[Crossref] [PubMed]

T. Roy, A. E. Nikolaenko, and E. T. F. Rogers, “A meta-diffraction-grating for visible light,” J. Opt. 15, 085101 (2013).
[Crossref]

M. D. Goldflam, T. Driscoll, D. Barnas, O. Khatib, M. Royal, N. M. Jokerst, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, and D. N. Basov, “Two-dimensional reconfigurable gradient index memory metasurface,” Appl. Phys. Lett. 102, 224103 (2013).
[Crossref]

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mat. 1, 186 (2013).
[Crossref]

Z. Xie, X. Wang, J. Ye, S. Feng, W. Sun, T. Akalin, and Y. Zhang, “Spatial terahertz modulator,” Sci. Rep. 3, 3347 (2013).
[Crossref]

I. Chatzakis, P. Tassin, L. Luo, N. Shen, L. Zhang, J. Wang, T. Koschny, and C. M. Soukoulis, “One- and two-dimensional photo-imprinted diffraction gratings for manipulating terahertz waves,” Appl. Phys. Lett. 103, 043101 (2013).
[Crossref]

L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21, 1344 (2013).
[Crossref] [PubMed]

2012 (6)

D. Paget, F. Cadiz, A. C. H. Rowe, F. Moreau, S. Arscott, and E. Peytavit, “Imaging ambipolar diffusion of photocarriers in GaAs thin films,” J. Appl. Phys. 111, 123720 (2012).
[Crossref]

S. Busch, B. Scherger, M. Scheller, and M. Koch, “Optically controlled terahertz beam steering and imaging,” Opt. Lett. 37, 1391 (2012).
[Crossref] [PubMed]

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702 (2012).
[Crossref] [PubMed]

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E. B. Kley, F. Lederer, A. Tnnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mat. 24, 6300 (2012).
[Crossref]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient metasurfaces,” Nano Lett. 12, 6223 (2012).
[Crossref] [PubMed]

2011 (2)

T. Okada and K. Tanaka, “Photo-designed terahertz devices,” Sci. Rep. 1, 121 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333 (2011).
[Crossref] [PubMed]

2010 (1)

2000 (2)

M. Schall and P. Jepsen, “Photoexcited GaAs surfaces studied by transient terahertz time-domain spectroscopy,” Opt. Lett. 25, 13 (2000).
[Crossref]

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382 (2000).
[Crossref]

1996 (1)

S. C. Howells and L. A. Schlie, “Transient terahertz reflection spectroscopy of undoped InSb from 0.1 to 1.1 THz,” Appl. Phys. Lett. 69, 550 (1996).
[Crossref]

1982 (1)

N. D. Arora, J. R. Hauser, and D. J. Roulston, “Electron and hole mobilities in silicon as a function of concentration and temperature,” IEEE Trans. Electron Dev. 29, 292 (1982).
[Crossref]

1974 (1)

C. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electron. Lett. 10, 259 (1974).
[Crossref]

1972 (1)

K. K. Chen and J. K. Furdyna, “Temperature dependence of intrinsic carrier concentration in InSb: direct determination by helicon interferometry,” J. Appl. Phys. 43, 1825 (1972).
[Crossref]

Adachi, S.

S. Adachi, Handbook on Physical Properties of Semiconductors (Kluwer, 2004).

Aieta, F.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333 (2011).
[Crossref] [PubMed]

Akalin, T.

Z. Xie, X. Wang, J. Ye, S. Feng, W. Sun, T. Akalin, and Y. Zhang, “Spatial terahertz modulator,” Sci. Rep. 3, 3347 (2013).
[Crossref]

Andrews, S. R.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382 (2000).
[Crossref]

Arora, N. D.

N. D. Arora, J. R. Hauser, and D. J. Roulston, “Electron and hole mobilities in silicon as a function of concentration and temperature,” IEEE Trans. Electron Dev. 29, 292 (1982).
[Crossref]

Arscott, S.

D. Paget, F. Cadiz, A. C. H. Rowe, F. Moreau, S. Arscott, and E. Peytavit, “Imaging ambipolar diffusion of photocarriers in GaAs thin films,” J. Appl. Phys. 111, 123720 (2012).
[Crossref]

Azad, A. K.

N. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304 (2013).
[Crossref] [PubMed]

Barnas, D.

M. D. Goldflam, T. Driscoll, D. Barnas, O. Khatib, M. Royal, N. M. Jokerst, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, and D. N. Basov, “Two-dimensional reconfigurable gradient index memory metasurface,” Appl. Phys. Lett. 102, 224103 (2013).
[Crossref]

Basov, D. N.

M. D. Goldflam, T. Driscoll, D. Barnas, O. Khatib, M. Royal, N. M. Jokerst, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, and D. N. Basov, “Two-dimensional reconfigurable gradient index memory metasurface,” Appl. Phys. Lett. 102, 224103 (2013).
[Crossref]

Bauhuis, G. J.

G. Georgiou, H. K. Tyagi, P. Mulder, G. J. Bauhuis, J. J. Schermer, and J. Gómez Rivas, “Photo-generated THz antennas,” Sci. Rep. 4, 3584 (2014).
[Crossref] [PubMed]

Bhaskaran, M.

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

Boyraz, O.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, ”Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Bozhevolnyi, S. I.

Busch, S.

Cadiz, F.

D. Paget, F. Cadiz, A. C. H. Rowe, F. Moreau, S. Arscott, and E. Peytavit, “Imaging ambipolar diffusion of photocarriers in GaAs thin films,” J. Appl. Phys. 111, 123720 (2012).
[Crossref]

Cao, Y.

Capasso, F.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333 (2011).
[Crossref] [PubMed]

Capolino, F.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, ”Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Chatzakis, I.

I. Chatzakis, P. Tassin, L. Luo, N. Shen, L. Zhang, J. Wang, T. Koschny, and C. M. Soukoulis, “One- and two-dimensional photo-imprinted diffraction gratings for manipulating terahertz waves,” Appl. Phys. Lett. 103, 043101 (2013).
[Crossref]

Chen, H. T.

N. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304 (2013).
[Crossref] [PubMed]

Chen, K. K.

K. K. Chen and J. K. Furdyna, “Temperature dependence of intrinsic carrier concentration in InSb: direct determination by helicon interferometry,” J. Appl. Phys. 43, 1825 (1972).
[Crossref]

Chen, W. T.

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient metasurfaces,” Nano Lett. 12, 6223 (2012).
[Crossref] [PubMed]

Chowdhury, D. R.

N. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304 (2013).
[Crossref] [PubMed]

Cluff, J. A.

P. G. Huggard, J. A. Cluff, G. P. Moore, C. J. Shaw, S. R. Andrews, S. R. Keiding, E. H. Linfield, and D. A. Ritchie, “Drude conductivity of highly doped GaAs at terahertz frequencies,” J. Appl. Phys. 87, 2382 (2000).
[Crossref]

Dalvit, D. A. R.

N. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340, 1304 (2013).
[Crossref] [PubMed]

Driscoll, T.

M. D. Goldflam, T. Driscoll, D. Barnas, O. Khatib, M. Royal, N. M. Jokerst, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, and D. N. Basov, “Two-dimensional reconfigurable gradient index memory metasurface,” Appl. Phys. Lett. 102, 224103 (2013).
[Crossref]

Eilenberger, F.

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E. B. Kley, F. Lederer, A. Tnnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mat. 24, 6300 (2012).
[Crossref]

Farahani, M. F.

Feng, S.

D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mat. 1, 186 (2013).
[Crossref]

Z. Xie, X. Wang, J. Ye, S. Feng, W. Sun, T. Akalin, and Y. Zhang, “Spatial terahertz modulator,” Sci. Rep. 3, 3347 (2013).
[Crossref]

Fumeaux, C.

Furdyna, J. K.

K. K. Chen and J. K. Furdyna, “Temperature dependence of intrinsic carrier concentration in InSb: direct determination by helicon interferometry,” J. Appl. Phys. 43, 1825 (1972).
[Crossref]

Gaburro, Z.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333 (2011).
[Crossref] [PubMed]

Genevet, P.

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333 (2011).
[Crossref] [PubMed]

Georgiou, G.

G. Georgiou, H. K. Tyagi, P. Mulder, G. J. Bauhuis, J. J. Schermer, and J. Gómez Rivas, “Photo-generated THz antennas,” Sci. Rep. 4, 3584 (2014).
[Crossref] [PubMed]

Goldflam, M. D.

M. D. Goldflam, T. Driscoll, D. Barnas, O. Khatib, M. Royal, N. M. Jokerst, D. R. Smith, B. J. Kim, G. Seo, H. T. Kim, and D. N. Basov, “Two-dimensional reconfigurable gradient index memory metasurface,” Appl. Phys. Lett. 102, 224103 (2013).
[Crossref]

Gómez Rivas, J.

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Figures (7)

Fig. 1
Fig. 1 (a) Real (solid) and imaginary (dotted) components of the refractive index of GaAs at ν = 1 THz as a function of the carrier density, N, calculated using the Drude model. The inset shows the complex permittivity as a function of N. (b) Transmission amplitude at ν = 1 THz through a GaAs layer with a 1μm thickness calculated as a function of the carrier density and normalized to the transmission through an intrinsic GaAs layer (red circles and curve). The cyan circles and curve correspond to the phase shift difference between the transmission through the GaAs layer with carrier density N and the transmission through the intrinsic GaAs layer.
Fig. 2
Fig. 2 (a) Blazed grating with 4 grating periods and a grating constant Γ = 600 μm. One grating period consists of the 8 carrier densities indicated by the circles in Fig. 1(b), N decreases from right to left in each period. (b) Calculated far-field intensity pattern at ν = 1 THz of the blazed grating with a decreasing carrier density from right to left (blue) and from left to right (green) in each period. The intensity is normalized by the transmission through a fully transparent window with the dimension of 4 grating periods and zero transmission outside. The vertical dashed lines indicate the angular range of interest for the experiment.
Fig. 3
Fig. 3 (a) CCD camera images of the 800 nm pump beam at the sample position. The pump beam is spatially modulated by the SLM in the shape of a blazed grating with Γ = 600 μm with a carrier tail to the left (top) and to the right (bottom). The central panel shows cuts through both gratings along the horizontal dotted lines. (b) Output of the pyroelectric detector at a position of θ = −30° with respect to the normal to the surface of the sample. The green curve corresponds to the signal measured when the blazed grating has a decreasing carrier density from left to right; The blue curve corresponds to a blazed grating with a carrier density decreasing from right to left. (c) The same as in (b) but at a detector angle of θ = 30° with respect to the normal to the surface of the sample.
Fig. 4
Fig. 4 Intensity spectrum of the THz probe pulse. The maximum intensity is normalized to 1.
Fig. 5
Fig. 5 Ratio between the diffracted THz intensities by the left and the right steering blazed gratings measured at θ = −30° for 19 different grating constants. The blue squares are measurements and the black curve are calculations using diffraction theory.
Fig. 6
Fig. 6 (a) Phase shift difference (colorscale) between a transmitted wave of frequency ν = 1 THz through a 1 μm thick layer with complex index of refraction given by the axis and a transmitted wave through a layer of air of equal thickness. The (n,κ)-curves for GaAs, InSb and Si are calculated using the Drude model and plotted with the solid curves. Different carrier concentration ranges are indicated with different colors as described by the legend. (b) Phase shift with respect to a layer of air as a function of the carrier concentration through a 1 μm layer of GaAs (blue), InSb (green) and Si (red) at ν = 1 THz. (c) Normalized transmission amplitude with respect to air as a function of the carrier concentration through a 1 μm layer of GaAs (blue), InSb (green) and Si (red) at ν = 1 THz.
Fig. 7
Fig. 7 (a) Calculated normalized transmission (red) and phase shift (cyan) with respect to a layer of intrinsic InSb at ν = 3 THz as a function of N. (b) Blazed grating with 12 grating periods and a grating constant Γ = 200 μm. One grating period consists of the carrier densities indicated by the circles in (a). (c) Calculated far-field intensity pattern at ν = 3 THz of the left (blue) and right (green) steering blazed gratings. The transmission is normalized by the transmission through a transparent window with the dimensions of the grating and zero transmission outside.

Equations (10)

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ε ¯ = ε ω p 2 ω + 1 / τ 2 ( 1 i ω τ + 1 ) ,
n ¯ = n + i κ = ε ¯ .
Δ ϕ = 2 π ν c Δ l ,
E 2 = t ¯ 1 , 2 E 1 = t ¯ 1 , 2 A 1 exp ( i k 1 x i ω 1 t ) ,
t ¯ 1 , 2 = | t 1 , 2 | exp ( ϕ 1 , 2 ) = n 1 n 1 + ( n 2 + i κ 2 ) .
Δ ϕ 1 , 2 = tan 1 ( κ 2 n 1 + n 2 ) ,
Δ ϕ 1 , 3 = Δ ϕ 1 , 2 + Δ ϕ 2 , 3 = tan 1 ( ( n 2 n 1 + κ 2 2 ) κ 2 ( n 1 + n 2 ) ( n 2 2 + n 1 n 2 + κ 2 2 ) + n 1 κ 2 2 ) .
I ( θ ) = 𝔉 [ T ¯ ( x ) ] 2 = 𝔉 [ T ( x ) exp ( i ϕ ( x ) ) ] 2 .
μ m , Si = 1 1000 [ 52.2 + 1364.8 1 + ( N / ( 1.295 × 10 17 ) ) 0.891 43.4 1 + ( 3.43 × 10 20 / N ) 2 ] m 2 V 1 s 1 ,
μ m , InSb = 18.03 1 + ( N / ( 3 × 10 17 ) 0.68 ) m 2 V 1 s 1 .

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