Abstract

Engaging both theory and experiment, we investigate resonant photonic lattices in which the duty cycle tends to zero. Corresponding dielectric nanowire grids are mostly empty space if operated as membranes in vacuum or air. These grids are shown to be effective wideband reflectors with impressive polarizing properties. We provide computed results predicting nearly complete reflection and attendant polarization extinction in multiple spectral regions. Experimental results with Si nanowire arrays with 10% duty cycle show ~200-nm-wide band of high reflection for one polarization state and free transmission for the orthogonal state. These results agree quantitatively with theoretical predictions. It is fundamentally extremely significant that the wideband spectral expressions presented can be generated in these minimal systems.

© 2015 Optical Society of America

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References

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2014 (4)

2013 (1)

2012 (2)

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).
[Crossref]

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

2011 (3)

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

M. A. Ahmed, M. Haefner, M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, “High-power radially polarized Yb:YAG thin-disk laser with high efficiency,” Opt. Express 19(6), 5093–5104 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (1)

2006 (1)

2004 (3)

2003 (1)

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

2001 (1)

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

1999 (1)

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

1997 (2)

1995 (1)

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

1989 (1)

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

1985 (1)

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55(6), 377–380 (1985).
[Crossref]

1979 (1)

P. Vincent and M. Neviere, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Ahmed, M. A.

Ajayi, L.

Avrutsky, I. A.

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

Baehr-Jones, T.

Baets, R.

Biss, D. P.

Bolivar, P. H.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Brown, T. G.

Brucherseifer, M.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[Crossref] [PubMed]

Chen, C.-C.

Cher, R. T. P.

Choi, M.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Chou, H.-P.

Curzan, J.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

de Maagt, P.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Delbeke, D.

Ding, Y.

Ederra, I.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Fainman, Y.

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Gao, J.

Gaylord, T. K.

Giese, J.

Gonzalo, R.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Graf, T.

Grann, E. B.

Haefner, M.

He, S.

He, Y.

Hochberg, M.

Holker, M.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Homes, C. C.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

Hu, Y.

Johnson, E.

Kämpfe, T.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Kang, K.-Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kang, S. B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Karagodsky, V.

Kawakami, S.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

Kawashima, T.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

Kim, Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kwak, M. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Lagrange, A.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Lee, K. J.

Lee, S. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Lee, Y.-H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Levy, U.

Li, B.

Lim, A. E.-J.

Liu, S.

Lo, P. G.-Q.

Magnusson, R.

Mashev, L.

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55(6), 377–380 (1985).
[Crossref]

Min, B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Moharam, M. G.

Muys, P.

Neviere, M.

P. Vincent and M. Neviere, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

Novack, A.

Ohtera, Y.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

Osten, W.

Pang, L.

Park, N.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Parriaux, O.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Perrin, F.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Pommet, D. A.

Popov, E.

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55(6), 377–380 (1985).
[Crossref]

Pruss, C.

Ramirez, A. P.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

Renaud, D.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Reynolds, A. L.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Rivas, J. G.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microw. Theory Tech. 51(4), 1062–1066 (2003).
[Crossref]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salvekar, A. A.

Sato, T.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

Scherer, A.

Sedgwick, F. G.

Shapiro, S. M.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Shi, R.

Shin, J.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Shokooh-Saremi, M.

K. J. Lee, J. Curzan, M. Shokooh-Saremi, and R. Magnusson, “Resonant wideband polarizer with single silicon layer,” Appl. Phys. Lett. 98(21), 211112 (2011).
[Crossref]

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[Crossref] [PubMed]

Sixt, P.

T. Kämpfe, P. Sixt, D. Renaud, A. Lagrange, F. Perrin, and O. Parriaux, “Segmented subwavelength silicon gratings manufactured by high productivity microelectronic technologies for linear to radial/azimuthal polarization conversion,” Opt. Eng. 53(10), 107105 (2014).
[Crossref]

Streshinsky, M.

Sun, P.-C.

Sychugov, V. A.

I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[Crossref]

Tamamura, T.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35(15), 1271–1272 (1999).
[Crossref]

Tsai, C. H.

Tuan, R.-C.

Vincent, P.

P. Vincent and M. Neviere, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

Vogel, M.

Vogt, T.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

Voss, A.

Wakimoto, S.

C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, “Optical response of high-dielectric-constant perovskite-related oxide,” Science 293(5530), 673–676 (2001).
[Crossref] [PubMed]

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

Wang, W.

Wang, Y.

Xu, F.

Yang, W.

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

Yang, X.

Youngworth, K. S.

Zhao, H.

Zhao, J.

Adv. Opt. Photonics (1)

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

Appl. Opt. (3)

Appl. Phys. (Berl.) (1)

P. Vincent and M. Neviere, “Corrugated dielectric waveguides: a numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

Appl. Phys. Lett. (2)

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of an ultra-sparse TE reflector with concurrent TM invisibility.

Fig. 2
Fig. 2

Theoretical performance of ultra-sparse dielectric nanowire grid polarizers. (a) Zero-order TE and TM reflectance, R0(TE) and R0(TM), spectra under normal incidence for three different parameter sets (ε1, F, h/Λ) = (100, 0.01, 0.315), (50, 0.02, 0.317), and (10, 0.1, 0.342). Angle-dependent R0(TE) spectra for (b) (ε1, F, h/Λ) = (100, 0.01, 0.315) and (c) (ε1, F, h/Λ) = (10, 0.1, 0.342).

Fig. 3
Fig. 3

(a) Field distributions under TE (left panel) and TM (right panel) polarized light incidence for the parameter set (ε1, F, h/Λ) = (100, 0.01, 0.315) at wavelength λ = 1.343Λ. (b) Field distributions under TE (left panel) and TM (right panel) polarized light incidence for the parameter set (ε1, F, h/Λ) = (10, 0.1, 0.342) at wavelength λ = 1.224Λ. The indicated fields are electric field for TE and magnetic field for TM. Their values are normalized by the incident field amplitude in both (a) and (b).

Fig. 4
Fig. 4

Device fabrication and characterization. (a) A photograph of nine ultra-sparse Si nanowire grids with different Si-wire fill factors on a 1 × 1 inch2 glass substrate. Cross-sectional (b) and top-view (c and d) SEM images of the device.

Fig. 5
Fig. 5

Experimental performance of an ultra-sparse Si nanowire array reflector/polarizer. (a) Measured angle-dependent extinction (1–T0) spectra under TE- and TM-polarized light incidence. (b) Calculated angle-dependent TE and TM extinction spectra for comparison. (c) Measured spectra of the TE reflectance R0(TE), TM reflectance R0(TM), and TE extinction (1–T0). (d) Calculated spectra of the TE reflectance R0(TE), TM reflectance R0(TM), and TE extinction (1–T0) for comparison.

Equations (3)

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V TE ( q ) = ( ε 1 ε 0 )Fsinc(Fq) ε 1 Fsinc(Fq),
V TM ( q ) = ( ε 1 1 ε 0 1 )Fsinc(Fq) ε 0 1 Fsinc(Fq),
R 0 (TE)/ R 0 (TM)4 F 2 4 ε 1 2 ,

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