Abstract

Rugate filters made of anisotropically nanostructured birefringent silicon have been fabricated and studied by polarization-resolved transmission measurements. Electrochemical etching of a (110) oriented Si wafer results in porous silicon layers which exhibit a strong in-plane birefringence. We demonstrate that a sinusoidal refractive index variation of birefringent porous silicon combined with index-matching layers and apodization results in a dichroic rugate filter having a stop-band dependent on the polarization direction of the incident light without higher-order harmonics and sidelobes. We also demonstrate that the combination of different dichroic rugate filters allow us to realize filters with more complex properties in a single preparation step.

© 2008 Optical Society of America

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References

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  1. F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
    [CrossRef]
  2. F. Xu, R. C. Tyan, P. C. Sun, Y. Fainman, C. C. Cheng, and A. Scherer, "Fabrication, modeling, and characterization of form-birefringent nanostructures," Opt. Lett. 20, 2457-2459 (1995).
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    [CrossRef]
  4. J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
    [CrossRef]
  5. J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
    [CrossRef]
  6. J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
    [CrossRef]
  11. N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
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    [CrossRef] [PubMed]

2007 (1)

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

2006 (1)

2005 (2)

E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, "Porous silicon-based rugate filters," Appl. Opt. 44, 5415-5421 (2005).
[CrossRef] [PubMed]

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

2004 (1)

2002 (1)

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

2001 (3)

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

1997 (2)

W. H. Southwell, "Extended-bandwidth reflector designs by using wavelets," Appl. Opt. 36, 314-318 (1997).
[CrossRef] [PubMed]

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

1995 (1)

1993 (2)

1989 (1)

1983 (1)

1978 (1)

Abu Alijarayesh, I. O.

Abu-Safia, H. A.

Al-Sharif, A. I.

Arens-Fischer, R.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Berger, M. G.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Billat, S.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Birner, A.

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Bovard, B. G.

Capuj, N. E.

Cheng, C. C.

Diener, J.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
[CrossRef] [PubMed]

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Dobrowolski, J. A.

Fainman, Y.

Fujii, M.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
[CrossRef] [PubMed]

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

Gaburro, Z.

Genereux, F.

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Ghulinyan, M.

Gösele, U.

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Gross, E.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
[CrossRef] [PubMed]

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Grosse, P.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Hilbrich, S.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Imenes, A. G.

Koch, F.

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Kovalev, D.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
[CrossRef] [PubMed]

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Krüger, M.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Künzner, N.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

J. Diener, N. Künzner, E. Gross, D. Kovalev, and M. Fujii, "Planar silicon-based light polarizers," Opt. Lett. 29, 195-197 (2004).
[CrossRef] [PubMed]

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Leonard, S.W.

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Lorenzo, E.

Lowe, D.

Lüth, H.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

McKenzie, D. R.

Navarro-Urrios, D.

Ogata, Y. H.

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

Oton, C. J.

Pavesi, L.

Polisski, G.

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

Sailor, M. J.

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

Sakka, T.

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

Salem, M. S.

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

Scherer, A.

Southwell, W. H.

Sun, P. C.

Theiß, W.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Thönissen, M.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Timoshenko, V. Yu.

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

N. Künzner, D. Kovalev, J. Diener, E. Gross, V. Yu. Timoshenko, G. Polisski, F. Koch, and M. Fujii, "Giant birefringence in anisotropically nanostructured silicon," Opt. Lett. 26, 1265-1267 (2001).
[CrossRef]

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

Tyan, R. C.

van Driel, H. M.

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

Xu, F.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

J. Diener, N. Künzner, D. Kovalev, E. Gross, V. Yu. Timoshenko, G. Polisski, and F. Koch, "Dichroic Bragg reflectors based on birefringent porous silicon," Appl. Phys. Lett. 78, 3887-3889 (2001).
[CrossRef]

J. Appl. Phys. (2)

J. Diener, N. Künzner, D. Kovalev, E. Gross, F. Koch, and M. Fujii, "Dichroic behavior of multilayer structures based on anisotropically nanostructured silicon," J. Appl. Phys. 91, 6704-6709 (2002).
[CrossRef]

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, "Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure," J. Appl. Phys. 101, 063503 (2007).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (2)

F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gösele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
[CrossRef]

N. Künzner, J. Diener, E. Gross, D. Kovalev, V. Yu. Timoshenko, and M. Fujii, "Form birefringence of anisotropically nanostructured silicon," Phys. Rev. B 71, 195304 (2005).
[CrossRef]

Thin Solid Films (1)

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich,W. Theiβ, and P. Grosse, "Dielectric filters made of PS: advanced performance by oxidation and new layer structures," Thin Solid Films 297, 237-240 (1997).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Etching rate of a (110) oriented p+ Si wafer as a function of current density. (b) Refractive indices and optical anisotropy (Δn) for single layers of (110) PSi estimated from the interference fringes for E ‖[001] and E‖ [1̄10] as a function of current density.

Fig. 2.
Fig. 2.

Cross-sectional TEM images of a rugate filter made from a (110) Si wafer observed from a [1̄12] direction (a). The magnification factors are (b)104, (c)5×104 and (d)4×105, respectively.

Fig. 3.
Fig. 3.

A dichroic rugate filter with 30 periods: (a) refractive index profiles versus physical depth, (b) calculated and (c) measured polarization-resolved transmittance spectra for E ‖[001] and E‖[1̄10]. The maximum optical density at the center of the stop-band is 2.7 for both polarization directions.

Fig. 4.
Fig. 4.

An apodized dichroic rugate filter with 30 periods and index-matching layers: (a) refractive index profiles versus physical depth, (b) calculated and (c) measured polarization-resolved transmittance spectra for E‖[001] and E‖[1̄10]. The optical density is 2.5 for E‖[001] and 2.2 for E‖[1̄10] at the center of the stop-band. Inset shows polarizationresolved transmittance spectra of the same structure in the spectral range from 1355 to 1450 nm.

Fig. 5.
Fig. 5.

Narrow bandwidth dichroic rugate filter with 70 periods: (a) refractive index profiles versus physical depth, (b) calculated and (c) measured polarization-resolved transmittance spectra for E parallel to the [1̄10] and [001] directions.

Fig. 6.
Fig. 6.

Double band dichroic rugate filter centered around 1500 nm and 1900 nm with 63 and 50 periods, respectively: (a) refractive index profiles versus physical depth, (b) calculated and (c) measured polarization-resolved transmittance spectra for E parallel to the [1̄10] and [001] directions.

Equations (3)

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n = 1 2 d ( 1 λ r 1 λ r + 1 ) 1
n ( x ) = exp [ ln n H + ln n L 2 + ln n H ln n L 2 sin ( 4 π x λ 0 + ϕ ) ]
n ( t ) = n 1 + ( n 2 n 1 ) ( 10 t 3 15 t 4 + 6 t 5 )

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