Abstract

We theoretically investigate the terahertz (THz) dielectric response of a semiconductor slab hosting a tunable grating photogenerated by the interference of two tilted infrared (IR) plane waves. In the case where the grating period is much smaller than the THz wavelength, we numerically evaluate the ordinary and extraordinary component of the effective permittivity tensor by resorting to electromagnetic full-wave simulation coupled to the dynamics of charge carriers excited by IR radiation. We show that the photo-induced metamaterial optical response can be tailored by varying the grating and it ranges from birefringent to hyperbolic to anisotropic negative dielectric without resorting to microfabrication.

© 2013 Optical Society of America

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A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, Phys. Rev. B 86, 121108 (2012).
[CrossRef]

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, Adv. OptoElectron. 2012, 1 (2012).
[CrossRef]

C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, Opt. Lett. 37, 3345 (2012).
[CrossRef]

2011

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

2010

I. S. Nefedov, Phys. Rev. B 82, 155423 (2010).
[CrossRef]

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

T. Okada, K. Ooi, Y. Nakata, K. Fujita, K. Tanaka, and K. Tanaka, Opt. Lett. 35, 1719 (2010).
[CrossRef]

2007

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

2006

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. A. Sánchez-Gil and J. G. Rivas, Phys. Rev. B 73, 205410 (2006).
[CrossRef]

2005

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2000

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

1999

1982

J. S. Blakemore, J. Appl. Phys. 53, R123 (1982).
[CrossRef]

1967

Y. P. Varshni, Phys. Status Solidi 20, 9 (1967).
[CrossRef]

Alekseyev, L. V.

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, Adv. OptoElectron. 2012, 1 (2012).
[CrossRef]

Andryieuski, A.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, Phys. Rev. B 86, 121108 (2012).
[CrossRef]

Averitt, R. D.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Bäumgartner, S.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Beard, M. C.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

Belov, P. A.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” arXiv:1211.5117v1 (2012).

Blakemore, J. S.

J. S. Blakemore, J. Appl. Phys. 53, R123 (1982).
[CrossRef]

Bolivar, P. H.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

C. Janke, J. G. Rivas, P. H. Bolivar, and H. Kurz, Opt. Lett. 30, 2357 (2005).
[CrossRef]

Bonn, M.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

Brambilla, M.

Brantley, C.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Chang, Y. C.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Chen, H. T.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Chen, M. K.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Chigrin, D. N.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, Phys. Rev. B 86, 121108 (2012).
[CrossRef]

Ciattoni, A.

Columbo, L.

Dawson, P.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Edwards, E.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Feldmann, J.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Fujita, K.

Garmire, E.

E. Garmire and A. Kost, Nonlinear Optics in Semiconductors I (Academic, 1999).

Gokkavas, M.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Gómez Rivas, J.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

Gossard, A. C.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Guo, Y.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Hecker, N. E.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Hempel, M.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Hendry, E.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

Iorsh, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” arXiv:1211.5117v1 (2012).

Janke, C.

Kafesaki, M.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Kivshar, Y. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” arXiv:1211.5117v1 (2012).

Koch, M.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Koschny, T.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Kost, A.

E. Garmire and A. Kost, Nonlinear Optics in Semiconductors I (Academic, 1999).

Kuipers, L.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

Kurz, H.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

C. Janke, J. G. Rivas, P. H. Bolivar, and H. Kurz, Opt. Lett. 30, 2357 (2005).
[CrossRef]

Kuttge, M.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

Lavrinenko, A. V.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, Phys. Rev. B 86, 121108 (2012).
[CrossRef]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

Libon, I. H.

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

Lockyear, M. J.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

Lugiato, L. A.

Luo, C.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Maggipinto, T.

Manceau, J. M.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Massaouti, M.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Mazurowski, J.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Mukhin, I. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” arXiv:1211.5117v1 (2012).

Nakata, Y.

Narimanov, E. E.

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, Adv. OptoElectron. 2012, 1 (2012).
[CrossRef]

Nefedov, I. S.

I. S. Nefedov, Phys. Rev. B 82, 155423 (2010).
[CrossRef]

Okada, T.

Ooi, K.

Ozbay, E.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Padilla, W. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Perrini, I. M.

Podolskiy, V. A.

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, Adv. OptoElectron. 2012, 1 (2012).
[CrossRef]

Rivas, J. G.

J. A. Sánchez-Gil and J. G. Rivas, Phys. Rev. B 73, 205410 (2006).
[CrossRef]

C. Janke, J. G. Rivas, P. H. Bolivar, and H. Kurz, Opt. Lett. 30, 2357 (2005).
[CrossRef]

Rizza, C.

Ruffin, P.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Sánchez-Gil, J. A.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. A. Sánchez-Gil and J. G. Rivas, Phys. Rev. B 73, 205410 (2006).
[CrossRef]

Schmuttenmaer, C. A.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Shadrivov, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” arXiv:1211.5117v1 (2012).

Shen, N. H.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Spinelli, L.

Spinozzi, E.

Tanaka, K.

Taylor, A.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Taylor, A. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef]

Tissoni, G.

Turner, G. M.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

Tzortzakis, S.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, Phys. Rev. Lett. 106, 037403 (2011).
[CrossRef]

Varshni, Y. P.

Y. P. Varshni, Phys. Status Solidi 20, 9 (1967).
[CrossRef]

Yang, C. E.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Yin, S.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Zide, J. M. O.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Adv. OptoElectron.

L. V. Alekseyev, V. A. Podolskiy, and E. E. Narimanov, Adv. OptoElectron. 2012, 1 (2012).
[CrossRef]

Appl. Phys. Lett.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. H. Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

I. H. Libon, S. Bäumgartner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000).
[CrossRef]

J. Appl. Phys.

J. S. Blakemore, J. Appl. Phys. 53, R123 (1982).
[CrossRef]

J. Opt. Soc. Am. B

Microw. Opt. Technol. Lett.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, Microw. Opt. Technol. Lett. 52, 979 (2010).
[CrossRef]

Nature

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. Taylor, and R. D. Averitt, Nature 444, 597 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. B

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, Phys. Rev. B 75, 235305 (2007).
[CrossRef]

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, Phys. Rev. B 86, 121108 (2012).
[CrossRef]

J. A. Sánchez-Gil and J. G. Rivas, Phys. Rev. B 73, 205410 (2006).
[CrossRef]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Sketch of a tunable photo-induced THz dielectric metamaterial slab. The two IR plane waves (with incidence angles ±θ) induce a dielectric grating along the x axis affecting the THz radiation. The THz plane wave normally impinges on the semiconductor slab of thickness L.

Fig. 2.
Fig. 2.

(a) Transmissivity T (T) and reflectivity R (R||) of an ordinary (extraordinary) wave as a function of the incident IR intensity I. (b) Effective dielectric permittivity (ϵ,ϵ) retrieved by transmissivity and reflectivity of panel (a) as a function of the incident IR intensity I. (c) Magnification of the shadow region of panel (b) where the THz response is hyperbolic.

Tables (1)

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Table 1. Effective THz Dielectric Behavior of the Considered GaAs Slab at Different IR Intensity

Equations (2)

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D2NNτ(N)+ϵ02Im[ϵ(IR)(N)]|E(IR)|2=0,
ϵ(THz)=ϵb+iϵ0e2τ/m*Nω(THz)(1iω(THz)τ),

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