Abstract

The application of rectangular-groove fused-silica gratings as polarizing beam splitters (PBSs) under Littrow incidence is investigated. Based on the simple modal method, two different cases of PBS gratings are designed. The achieved solutions, which are independent on the incident wavelength, are verified by the rigorous coupled-wave analysis and expressed in several polynomials instead of listing one or two numerical solutions. More importantly, on the basis of the designed PBS gratings, a porous fused silica antireflective film is introduced to improve their performances. Theoretical results indicate that such modified rectangular-groove PBS gratings exhibit higher diffraction efficiencies (over 0.99) and larger spectral bandwidths.

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  22. C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
    [CrossRef]
  23. Y. Tang, H. Xiong, H. Li, and Z. Chen, “Preparation method for a porous SiO2 reducing film with controllable refractive index” (in Chinese) C.N. Patent (2009).
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2010

2008

2007

2006

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. A 8, 511–517 (2006).
[CrossRef]

2005

2004

D. Yi, Y. B. Yan, H. T. Liu, S. Lu, and G. F. Jin, “Broadband polarizing beam splitter based on the form birefringence of a subwavelength grating in the quasi-static domain,” Opt. Lett. 29(7), 754–756 (2004).
[CrossRef] [PubMed]

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

1999

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

1997

1996

1995

1994

P. F. Belleville and H. G. Floch, “Ammonia-hardening of porous silica antireflective coatings,” Proc. SPIE 2288, 25–32 (1994).
[CrossRef]

1993

1987

1986

1956

R. E. Collin, “Reflection and Transmission at a Slotted Dielectric Interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

S. M. Rytov, “Electromagnetic Properties of a Finely Stratified Medium,” Sov. Phys. JETP 2, 466–475 (1956).

Ballif, C.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

Belleville, P. F.

P. F. Belleville and H. G. Floch, “Ammonia-hardening of porous silica antireflective coatings,” Proc. SPIE 2288, 25–32 (1994).
[CrossRef]

Borchert, D.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

Bouchut, P.

Boyd, R. D.

Britten, J. A.

Bryan, S. J.

Cambril, E.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

Cescato, L.

Chavel, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

Clausnitzer, T.

Collin, R. E.

R. E. Collin, “Reflection and Transmission at a Slotted Dielectric Interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

Dicker, J.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

Doumuki, T.

Drauschke, A.

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. A 8, 511–517 (2006).
[CrossRef]

Fainman, Y.

Feng, J. J.

Floch, H. G.

P. F. Belleville and H. G. Floch, “Ammonia-hardening of porous silica antireflective coatings,” Proc. SPIE 2288, 25–32 (1994).
[CrossRef]

Gaborit, G.

Gaylord, T. K.

Gobbi, A. L.

Golub, M. A.

Grann, E. B.

Habraken, S.

Haggans, C. W.

Hazart, J.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

Hofmann, T.

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

Hutter, T.

Jin, G. F.

Journot, E.

Kampfe, T.

Kämpfe, T.

Kimura, Y.

Kley, E. B.

Lalanne, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

Launois, H.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

Li, L. F.

Lima, C. R. A.

Lion, Y.

Liu, H. T.

Liu, W.

Lu, S.

Matsumoto, S.

Michaux, O.

Moharam, M. G.

Néauport, J.

Nguyen, H. T.

Nishida, N.

Ohta, Y.

Ono, Y.

Parriaux, O.

Perry, M. D.

Peschel, U.

Pommet, D. A.

Renotte, Y.

Ruschin, S.

Rytov, S. M.

S. M. Rytov, “Electromagnetic Properties of a Finely Stratified Medium,” Sov. Phys. JETP 2, 466–475 (1956).

Scherer, A.

Shore, B. W.

Soares, L. L.

Sun, P. C.

Tamada, H.

Thomas, I. M.

Tishchenko, A.

Tishchenko, A. V.

Tunnermann, A.

Tünnermann, A.

Tyan, R. C.

Wang, B.

Wang, S. Q.

Yamaguchi, T.

Yan, Y. B.

Yi, D.

Zheng, J. J.

Zhou, C. H.

Zhou, L. B.

Appl. Opt.

Can. J. Phys.

R. E. Collin, “Reflection and Transmission at a Slotted Dielectric Interface,” Can. J. Phys. 34, 398–411 (1956).
[CrossRef]

J. Opt. A

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A 1, 215–219 (1999).
[CrossRef]

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. A 8, 511–517 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

J. J. Zheng, C. H. Zhou, J. J. Feng, and B. Wang, “Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings,” Opt. Lett. 33(14), 1554–1556 (2008).
[CrossRef] [PubMed]

B. Wang, C. H. Zhou, S. Q. Wang, and J. J. Feng, “Polarizing beam splitter of a deep-etched fused-silica grating,” Opt. Lett. 32(10), 1299–1301 (2007).
[CrossRef] [PubMed]

H. T. Nguyen, B. W. Shore, S. J. Bryan, J. A. Britten, R. D. Boyd, and M. D. Perry, “High-efficiency fused-silica transmission gratings,” Opt. Lett. 22(3), 142–144 (1997).
[CrossRef] [PubMed]

H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, “Al wire-grid polarizer using the s-polarization resonance effect at the 0.8-µm-wavelength band,” Opt. Lett. 22(6), 419–421 (1997).
[CrossRef] [PubMed]

C. R. A. Lima, L. L. Soares, L. Cescato, and A. L. Gobbi, “Reflecting polarizing beam splitter,” Opt. Lett. 22(4), 203–205 (1997).
[CrossRef] [PubMed]

L. B. Zhou and W. Liu, “Broadband polarizing beam splitter with an embedded metal-wire nanograting,” Opt. Lett. 30(12), 1434–1436 (2005).
[CrossRef] [PubMed]

R. C. Tyan, P. C. Sun, A. Scherer, and Y. Fainman, “Polarizing beam splitter based on the anisotropic spectral reflectivity characteristic of form-birefringent multilayer gratings,” Opt. Lett. 21(10), 761–763 (1996).
[CrossRef] [PubMed]

D. Yi, Y. B. Yan, H. T. Liu, S. Lu, and G. F. Jin, “Broadband polarizing beam splitter based on the form birefringence of a subwavelength grating in the quasi-static domain,” Opt. Lett. 29(7), 754–756 (2004).
[CrossRef] [PubMed]

S. Habraken, O. Michaux, Y. Renotte, and Y. Lion, “Polarizing holographic beam splitter on a photoresist,” Opt. Lett. 20(22), 2348–2350 (1995).
[CrossRef] [PubMed]

Proc. SPIE

P. F. Belleville and H. G. Floch, “Ammonia-hardening of porous silica antireflective coatings,” Proc. SPIE 2288, 25–32 (1994).
[CrossRef]

Sol. Energy Mater. Sol. Cells

C. Ballif, J. Dicker, D. Borchert, and T. Hofmann, “Solar glass with industrial porous SiO2 antireflection coating: measurements of photovoltaic module properties improvement and modelling of yearly energy yield gain,” Sol. Energy Mater. Sol. Cells 82(3), 331–344 (2004).
[CrossRef]

Sov. Phys. JETP

S. M. Rytov, “Electromagnetic Properties of a Finely Stratified Medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other

Y. Tang, H. Xiong, H. Li, and Z. Chen, “Preparation method for a porous SiO2 reducing film with controllable refractive index” (in Chinese) C.N. Patent (2009).

M. Krzyzak, G. Helsch, and G. H. Frischat, “Method of making a glass body with a phosphorous-and porous SiO2-containing coating, glass body made thereby and solution for making same,” U.S.Patent (2006)

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Figures (7)

Fig. 1
Fig. 1

Schematic of two polarizing split ways of transmission PBS gratings based on different designing principles: a) △n eff,TM = 0; b)△n eff,TE/△n eff,TM = 2.

Fig. 2
Fig. 2

Grating parameters (PVW and f) satisfying different designing principles for PBS gratings: a) △n eff,TM < 0.001; b) 1.98 < △n eff,TE/△n eff,TM < 2.01.

Fig. 3
Fig. 3

Diffraction efficiencies of the supposed orders for gratings with different constructive parameters described by: (a) Eqs. (3) and (4); (b) Eqs. (5) and (6); (c) and (d) are partial enlarged detail with efficiencies larger than 0.9 of (a) and (b), respectively.

Fig. 4
Fig. 4

Diffraction efficiency of the designed PBS gratings with the largest bandwidth under constant incident angle as a function of the ratio of wavelength to the central wavelength: a) PVW = 0.731 for the first polarizing split way; b) PVW = 1.03 for the second one.

Fig. 5
Fig. 5

Schematic of an improved PBS grating from an original one with rectangular- groove.

Fig. 6
Fig. 6

Diffraction efficiencies of the supposed orders for improved PBS gratings with different constructive parameters described by: (a) Eqs. (3) and (4); (c) Eqs. (5) and (6); (d) the shorter line in Fig. 2(b); (b) is the partial enlarged detail with efficiencies larger than 0.99 of (a).

Fig. 7
Fig. 7

Diffraction efficiency of the improved PBS grating with the largest bandwidth under constant incident angle as a function of the ratio of wavelength to the central wavelength: a) PVW = 0.655 for the first polarizing split way; b) PVW = 1.18 for the second one.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

cos ( 2 π n 1 p sin θ inc λ ) = F ( n eff m 2 ) ,
F ( n eff m 2 ) = cos ( β ) cos ( γ ) 1 2 ξ sin ( β ) sin ( γ ) ,
β = 2 π p f λ n 2 2 n eff m 2 ,
γ = 2 π p ( 1 f ) λ n 1 2 n eff m 2 ,
ξ = { β γ + γ β n 1 2 β n 2 2 γ + n 2 2 γ n 1 2 β for TE-waves for TM-waves .
f = 3.3098 ( P V W ) 2 6.2731 ( P V W ) + 2.991 ,
Δ n eff, TE = 1.9076 f 2 + 1.8060 f 0.0214 ,
f = 1.0228 ( P V W ) 4 - 5.1384 ( P V W ) 3 + 10.0316 ( P V W ) 2 - 9.2527 P V W + 3.6559 ,
Δ n eff,TE = 1.1568 f 2 + 1.0310 f + 0.1005 ,

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