Abstract

A Wollaston prism-like binary dielectric grating is presented and analyzed. It behaves like a transmission grating, differentially and symmetrically blazed for the two crossed polarization states, TE and TM. The phase profile is obtained by means of subwavelength structures etched in a high optical index isotropic dielectric medium (gallium arsenide, for instance). The performance of the device is illustrated by numerical examples and sketched in terms of spectral bandwidth and of extinction ratio. Some practical issues related to the fabrication are discussed.

© 2005 Optical Society of America

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References

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    [Crossref]
  22. W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
    [Crossref]
  23. M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
    [Crossref]
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2005 (1)

2004 (2)

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

U. Levy , C. H. Tsai , L. Pang , and Y. Fainman , “ Engineering space-variant inhomogeneous media for polarization contro,l ” Opt. Lett.   29 , 1718 – 1720 ( 2004 ).
[Crossref] [PubMed]

2002 (1)

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

2001 (1)

1999 (2)

G. Nordin and P. Deguzman , “ Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region ,” Opt. Express   5 , 163 – 168 ( 1999 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-8-163
[Crossref] [PubMed]

W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
[Crossref]

1998 (1)

1997 (2)

1996 (1)

Ph. Lalanne and D. Lemercier-Lalanne , “ On the effective medium theory of subwavelength periodic structures ,” J. of Mod. Opt.   43 , 2063 – 2086 ( 1996 ).
[Crossref]

1995 (1)

1994 (3)

1992 (2)

1991 (1)

1990 (1)

1985 (1)

S. Adachi , “ GaAs, AlAs, and AlxGa1-xAs Material parameters for use in research and device applications ,” J. Appl. Phys.   58 , R1 – R29 ( 1985 ).
[Crossref]

1982 (1)

J. M. Bell , G.H. Derrick , and R.C. McPhedran , “ Diffraction gratings in the quasi-static limit ,” Optica Acta   29 , 1475 ( 1982 ).
[Crossref]

1978 (1)

K. Knop , “ Reflection grating polarizer for the infrared ,” Opt. Commun.   26 , 281 – 283 ( 1978 )
[Crossref]

1956 (1)

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

Adachi, S.

S. Adachi , “ GaAs, AlAs, and AlxGa1-xAs Material parameters for use in research and device applications ,” J. Appl. Phys.   58 , R1 – R29 ( 1985 ).
[Crossref]

Astilean, S.

Bell, J. M.

J. M. Bell , G.H. Derrick , and R.C. McPhedran , “ Diffraction gratings in the quasi-static limit ,” Optica Acta   29 , 1475 ( 1982 ).
[Crossref]

Borghi, R.

Bouchitté, G.

G. Bouchitté and R. Petit , Electromagnetics , 5 , 17 – 36 ( 1985 ).

Brauer, R.

Brundrett, D. L.

Bryngdahl, A.

Cambril, E.

Cescato, L.H.

Chavel, P.

Daneau, R.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

Deguzman, P.

Derrick, G.H.

J. M. Bell , G.H. Derrick , and R.C. McPhedran , “ Diffraction gratings in the quasi-static limit ,” Optica Acta   29 , 1475 ( 1982 ).
[Crossref]

Fainman, Y.

Farn, W. M.

Frezza, F.

Gaylord, Th. K.

Gluch, E.

Glytsis, E. N.

Grann, E.B.

Haidner, H.

Iwata, K.

Kikuta, H.

Kipfer, P.

Knop, K.

K. Knop , “ Reflection grating polarizer for the infrared ,” Opt. Commun.   26 , 281 – 283 ( 1978 )
[Crossref]

Kotlyar, M. V.

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

Krauss, T. F.

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

Lajunen, H.

Lalanne, Ph.

Launois, H.

Lemercier-Lalanne, D.

Ph. Lalanne and D. Lemercier-Lalanne , “ Depth dependence of the effective properties of subwavelength gratings ,” J. Opt. Soc. Am. A   14 , 450 – 458 ( 1997 ).
[Crossref]

Ph. Lalanne and D. Lemercier-Lalanne , “ On the effective medium theory of subwavelength periodic structures ,” J. of Mod. Opt.   43 , 2063 – 2086 ( 1996 ).
[Crossref]

Levy, U.

Manin, L.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

McPhedran, R.C.

J. M. Bell , G.H. Derrick , and R.C. McPhedran , “ Diffraction gratings in the quasi-static limit ,” Optica Acta   29 , 1475 ( 1982 ).
[Crossref]

Mériadec, C.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

Michael Miller, J.

Moharam, M.G.

Moussa, H.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

Noponen, E.

Nordin, G.

O’Faolain, L.

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

Ohira, Y.

Pajewski, L.

Pang, L.

Petit, R.

G. Bouchitté and R. Petit , Electromagnetics , 5 , 17 – 36 ( 1985 ).

Pommet, D.A.

Raj, R.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

Richter, I.

Rytov, S. M.

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

Sagnes, I.

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

Santarsiero, M.

Schettini, G.

Stork, W.

Streibl, N.

Sun, P.C.

Taghizadeh, M. R.

Tervo, J.

Tsai, C. H.

Turunen, J.

Vasara, A.

Vawter, G. A.

W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
[Crossref]

Wendt, J. R.

W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
[Crossref]

Wilson, R.

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

Xu, F.

Zubrzycki, W. J.

W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
[Crossref]

Appl. Opt. (7)

J. Appl. Phys. (1)

S. Adachi , “ GaAs, AlAs, and AlxGa1-xAs Material parameters for use in research and device applications ,” J. Appl. Phys.   58 , R1 – R29 ( 1985 ).
[Crossref]

J. of Mod. Opt. (1)

Ph. Lalanne and D. Lemercier-Lalanne , “ On the effective medium theory of subwavelength periodic structures ,” J. of Mod. Opt.   43 , 2063 – 2086 ( 1996 ).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Vac. Sci. Technol. A (1)

H. Moussa , R. Daneau , C. Mériadec , L. Manin , I. Sagnes , and R. Raj , “ Deep in situ dry-etch monitoring of III-V multilayer structures using laser reflectometry and reflectivity modeling ,” J. Vac. Sci. Technol. A   20 , 748 – 753 ( 2002 ).
[Crossref]

J. Vac. Sci. Technol. B (2)

W. J. Zubrzycki , G. A. Vawter , and J. R. Wendt , “ High-aspect-ratio nanophotonic components fabricated by Cl 2 reactive ion beam etching ,” J. Vac. Sci. Technol. B   17 , 2740 – 2744 ( 1999 ).
[Crossref]

M. V. Kotlyar , L. O’Faolain , R. Wilson , and T. F. Krauss , “ High-aspect-ratio chemically assisted ion-beam etching for photonic crystals using a high beam voltage-current ratio ,” J. Vac. Sci. Technol. B   22 , 1788 – 1791 ( 2004 ).
[Crossref]

Opt. Commun. (1)

K. Knop , “ Reflection grating polarizer for the infrared ,” Opt. Commun.   26 , 281 – 283 ( 1978 )
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optica Acta (1)

J. M. Bell , G.H. Derrick , and R.C. McPhedran , “ Diffraction gratings in the quasi-static limit ,” Optica Acta   29 , 1475 ( 1982 ).
[Crossref]

Sov. Phys. JETP (1)

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

Other (1)

G. Bouchitté and R. Petit , Electromagnetics , 5 , 17 – 36 ( 1985 ).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of a Wollaston Prism-like Device (WPD), using a variation of phaseshift between 0 and 2 π.

Fig. 2.
Fig. 2.

Coding a linearly-varying effective index (or similarly, a linearly-varying phaseshift) with subwavelength gratings of varying fill-factor, for a given polarization state.

Fig. 3.
Fig. 3.

Cross-view of a subwavelength grating. f is the fill factor, f Λ represents the wall width, and (1 - f)Λ is the slit width.

Fig. 4.
Fig. 4.

Effective index of subwavelength gratings on a GaAs substrate as a function of the fill-factor f. We also draw the induced birefringence δ n = nTE - nTM (λ = 5μm and Λ = λ/2nGaAs )

Fig. 5.
Fig. 5.

WPD geometries : (a) the phaseshift is coded between 0 and π on each side of the plate, for both the TE and TM polarization state; (b) the phaseshift is coded between 0 and 2π on one side for TM and between 0 and π on each side for the TE state.

Fig. 6.
Fig. 6.

Phaseshift coding by various binary subwavelength grating geometries (scatter triangle: TM, joined box: TE). Each period is devided into 12 miniperiods. The case of Fig. 5(a) is a poor approximation of the desired geometry, since both TE and TM polarizations undergo the same phaseshift on the second half of the period. The case of Fig. 5(b) is similar to the case of Fig. 1, except that it provides a better approximation for the TM polarization on the first half of the period.

Fig. 7.
Fig. 7.

In case of a mis-calculated thickness of the substrate, the upper and lower diffraction patterns could be mis-aligned.

Fig. 8.
Fig. 8.

Diffraction pattern of various binary subwavelength grating geometries (TM : dashed lines; TE : straight lines). The extinction ratio is evaluated with the two first useful orders in each case (see rectangular boxes).

Fig. 9.
Fig. 9.

Optimized WPD geometry based on Fig. 5(b). The phaseshift is coded between 0 and 2π on one side for TM and between 0 and π on each side for the TE state. A supplementary phaseshift of π is periodically added, in order to annihilate the 0th transmitted order.

Fig. 10.
Fig. 10.

Phaseshift introduced by a 5μm-designed WPD in the 4.25μm-5.75μm range within each period. This illustrates that the WPD is naturally spectrally broadband.

Tables (3)

Tables Icon

Table 1. (a) The grating follows the geometry of Fig. 5b. These are the computed values for the TE State (λ = 5μm,h = 2.17 μm, Λ = 0.76μm).

Tables Icon

Table 1. (b) The grating follows the geometry of Fig. 5b. These are the computed values for the TM State (λ = 5μm,h = 2.17 μm, Λ = 0.76μm).

Tables Icon

Table 2. The grating follows the geometry of Fig. 1. These are the computed values for the TE State (λ = 5μm, h = 2.17μm, Λ = 0.76μm ). The values for the TM state are the same as in Table 1(b).

Equations (8)

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n T E = f ε 1 + ( 1 f ) ε 2 1 + 1 f ε 1 + ( 1 f ) ε 2 ( Λ λ ) 2 r 0 ε r ε r r 2
n T M = ε 1 ε 2 f ε 2 + ( 1 f ) ε 1 1 + ( ε 1 ε 2 f ε 2 + ( 1 f ) ε 1 ) 2 ( Λ λ ) 2 r 0 m 0 a r a m ε r m m r
ε ( x ) = q ε q e i 2 π Λ q x
n T E = f ε 1 + ( 1 f ) ε 2 1 + π 2 3 ( f ε 1 + ( 1 f ) ε 2 ) ( f ( 1 f ) Λ λ ) 2 ( ε 1 ε 2 f ε 1 + ( 1 f ) ε 2 ) 2
n T M = ε 1 ε 2 f ε 2 + ( 1 f ) ε 1 1 + π 2 3 ( f ε 1 + ( 1 f ) ε 2 ) ( f ( 1 f ) Λ λ ) 2 ( ε 1 ε 2 f ε 2 + ( 1 f ) ε 1 ) 2
n GaAs ( E n ) = 7.1 + 3.78 1 0.180 En 2 1.97 ( 30.08 En ) 2 1
t θ ( x ) = v c v , θ exp ( i v 2 π Λ x )
E R T E = c v , T M c v , T E 2

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