Abstract

We report on a novel concept for transmissive optical elements based on resonant waveguide gratings (RWGs), which enables the realization of direction selective filters. Hereby, the broadband reflectivity of an RWG for nearly normal incidence angles is combined with high diffractive efficiency in transmission for a specific angle of incidence. Silicon is used as material with high refractive index and good compatibility with semiconductor fabrication. By adjusting the grating parameters different transmission angles and angular widths of the transmission range are feasible. First experimental results of the introduced filters provide a high transmission up to 63% at an incidence angle of 45° with a full width at half maximum of 20°.

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References

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  1. G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
    [CrossRef]
  2. S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
    [CrossRef]
  3. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  4. R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett. 34, 8106–8109 (1995).
  5. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications” Opt. Express 12, 5661–5674 (2004).
    [CrossRef] [PubMed]
  6. C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
    [CrossRef]
  7. F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
    [CrossRef] [PubMed]
  8. Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
    [CrossRef]
  9. S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26, 584–586 (2001).
    [CrossRef]
  10. Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
    [CrossRef]
  11. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
    [CrossRef]
  12. P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
    [CrossRef]
  13. V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
    [CrossRef] [PubMed]
  14. S. Kroker, F. Brückner, E.B. Kley, and A. Tünnermann, “Enhanced angular tolerance of resonant waveguide grating reflectors,” Opt. Lett. 36, 537–539 (2011).
    [CrossRef] [PubMed]
  15. S. Kroker, T. Kasebier, F. Brückner, F. Fuchs, E. B. Kley, and A. Tünnermann, “Reflective cavity couplers based on resonant waveguide gratings,” Opt. Express 19, 16466–16479 (2011).
    [CrossRef] [PubMed]
  16. M. G. Moharam and T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  17. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
    [CrossRef]

2011 (2)

2010 (2)

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

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

2006 (2)

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[CrossRef]

2004 (2)

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications” Opt. Express 12, 5661–5674 (2004).
[CrossRef] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

2001 (1)

1998 (1)

1996 (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

1995 (1)

R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett. 34, 8106–8109 (1995).

1992 (1)

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

1990 (1)

1985 (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

1981 (2)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

M. G. Moharam and T. K. Gaylord, “Rigorous Coupled-Wave Analysis of Planar-Grating Diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Andrewartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Bagby, J. S.

Botten, L. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Britzger, M.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Brückner, F.

Burmeister, O.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Chang-Hasnain, C. J.

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

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

Chavel, P.

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

Clausnitzer, T.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Danzmann, K.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Ding, Y.

Friedrich, D.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Fuchs, F.

Gaylord, T. K.

Golubenko, G. A.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Hane, K.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
[CrossRef]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

Hugonin, J. P.

Kanamori, Y.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
[CrossRef]

Karagodsky, V.

Kasebier, T.

Kley, E. B.

S. Kroker, T. Kasebier, F. Brückner, F. Fuchs, E. B. Kley, and A. Tünnermann, “Reflective cavity couplers based on resonant waveguide gratings,” Opt. Express 19, 16466–16479 (2011).
[CrossRef] [PubMed]

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Kley, E.B.

Kroker, S.

Lalanne, P.

P. Lalanne, J. P. Hugonin, and P. Chavel, “Optical properties of deep lamellar gratings: A coupled bloch-mode insight,” J. Lightwave Technol. 24, 2442–2449 (2006).
[CrossRef]

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Liu, Z. S.

Magnusson, R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

McPhedran, R. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Moharam, M. G.

Schnabel, R.

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Sedgwick, F. G.

Shimono, M.

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
[CrossRef]

Shin, D.

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

Svakhin, A. S.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Sychugov, V. A.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Tibuleac, S.

Tishchenko, A. V.

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

Tünnermann, A.

Wang, S. S.

R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett. 34, 8106–8109 (1995).

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

S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
[CrossRef]

Young, P. P.

Appl. Phys. Lett. (2)

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

R. Magnusson and S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Phys. Lett. 34, 8106–8109 (1995).

IEEE Phot. Tech. Lett. (2)

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Phot. Tech. Lett. 16, 1676–1678 (2004).
[CrossRef]

Y. Kanamori, M. Shimono, and K. Hane, “Fabrication of transmission color filters using silicon subwavelength gratings on quartz substrates,” IEEE Phot. Tech. Lett. 18, 2126–2128 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta. (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta. 28, 413–428 (1981).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

F. Brückner, D. Friedrich, T. Clausnitzer, M. Britzger, O. Burmeister, K. Danzmann, E. B. Kley, A. Tünnermann, and R. Schnabel, “Realization of a monolithic high-reflectivity cavity mirror from a single silicon crystal,” Phys. Rev. Lett. 104, 163903 (2010).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Sov. J. Quantum Electron. 15, 886–887 (1985).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic sketch of the considered angular bandpass filter and its working principle. The light is not transmitted for incident angles shown in (a) but transmitted for the angle in (b).

Fig. 2
Fig. 2

Incidence angle (relating to the perpendicular) dependent total transmission of the designed filter without (a) and with sub grating in the substrate (b) utilizing a duty cycle of 0.5.

Fig. 3
Fig. 3

Transmission of the zeroth (black and dashed line) and first orders (−1st, 1st) (red line) as a function of the incidence angle for the configurations shown in Fig. 2.

Fig. 4
Fig. 4

Changing the width of the total transmission range by varying the duty cycle of the fused silica grating, e.g. about 15° FWHM for f = 0.25 (black and dashed line); 20° for f = 0.5 (red); 26° for f = 0.75 (blue and dotted); 32° for f = 1 (green and dot-and-dashed). The center of the transmission is shifted slightly from 44° to 52°.

Fig. 5
Fig. 5

The center angle of the total transmission range can be shifted by varying the period of the resonant waveguide grating, e.g. from 35° for p=530 nm to 45° for p=550 nm.

Fig. 6
Fig. 6

SEM image of a fabricated angular bandpass grating. The period is 550 nm, the depths are 200 nm for the silicon grating and 300 nm for the fused silica grating. Platinum was deposited on the sample locally in order to protect the structure during milling.

Fig. 7
Fig. 7

Measured total transmission of the sample shown in Fig. 3 at 850 nm wavelength and TE- polarization in comparison with the simulation (red line). The maximum transmission is 63% in combination with a range of about 30° FWHM. For small angles of incidence the transmission is smaller than 20%.

Equations (4)

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p < λ n l .
λ n l + sin θ target < p < λ n l ,
464 nm < p < 586 nm .
h = λ n eff ( 0 ) ( θ = 0 ° ) - n eff ( 1 ) ( θ = 0 ° ) ,

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