Abstract

A general design rule of deep-etched subwavelength sinusoidal-groove fused-silica grating as a highly efficient polarization-independent or polarization-selective device is studied based on the simplified modal method, which shows that the device structure depends little on the incident wavelength, but mainly on the ratio of groove depth to incident wavelength and the ratio of wavelength to grating period. These two ratios could be used as the design guidelines for wavelength-independent structure from deep ultraviolet to far infrared. The optimized grating profile with a different function as a polarizing beam splitter, a polarization-independent two-port beam splitter, or a polarization-independent grating with high efficiency of -1st order is obtained at a wavelength of 1064nm, and verified by using the rigorous coupled-wave analysis. The performance of the sinusoidal grating is better than a conventional rectangular one, which could be useful for practical applications.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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2010 (1)

2009 (2)

2008 (5)

2007 (3)

2006 (3)

2005 (3)

2004 (1)

2003 (1)

1999 (2)

S. Pelissier, D. Blanc, M. P. Andrews, S. I. Najafi, A. V. Tishchenko, and O. Parriaux, “Single-step UV recording of sinusoidal surface gratings in hybrid solgel glasses,” Appl. Opt. 38, 6744–6748 (1999).
[CrossRef]

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

1996 (1)

1995 (1)

1982 (1)

Andrews, M. P.

Baets, R.

Blanc, D.

Bouchut, P.

Braga, E. D. S.

Bu, J.

Cambril, E.

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

Cao, H.

Carvalho, E. J. D.

Cescato, L. H.

Chavel, P.

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

Clausnitzer, T.

Dai, E.

David, C.

Delbeke, D.

Ekinci, Y.

Fahr, S.

Feng, J.

Fuchs, H.-J.

Gaborit, G.

Gaylord, T. K.

Grann, E. B.

Hazart, J.

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

He, M.

Jia, W.

Journot, E.

Jupé, M.

Kämpfe, T.

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: Pure Appl. Opt. 1, 215–219 (1999).
[CrossRef]

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

Launois, H.

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

Limpert, J.

Lv, P.

Moharam, M. G.

Morris, G. M.

Muys, P.

Najafi, S. I.

Néauport, J.

Niu, H.

Parriaux, O.

Pelissier, S.

Peng, X.

Pommet, D. A.

Ristau, D.

Ru, H.

Sigg, H.

Solak, H. H.

Tishchenko, A.

Tishchenko, A. V.

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
[CrossRef]

S. Pelissier, D. Blanc, M. P. Andrews, S. I. Najafi, A. V. Tishchenko, and O. Parriaux, “Single-step UV recording of sinusoidal surface gratings in hybrid solgel glasses,” Appl. Opt. 38, 6744–6748 (1999).
[CrossRef]

Tünnermann, A.

Wang, B.

Wang, S.

Yuan, X.

Zellmer, H.

Zhang, Y.

Zheng, J.

Zhou, C.

J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep-etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743(2010).
[CrossRef] [PubMed]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Design and fabrication of a polarization-independent two-port beam splitter,” Appl. Opt. 48, 5636–5641 (2009).
[CrossRef] [PubMed]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Dual-function beam splitter of a subwavelength fused-silica grating,” Appl. Opt. 48, 2697–2701 (2009).
[CrossRef] [PubMed]

W. Jia, C. Zhou, J. Feng, and E. Dai, “Miniature pulse compressor of deep-etched gratings,” Appl. Opt. 47, 6058–6063 (2008).
[CrossRef] [PubMed]

B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused-silica phase grating,” Appl. Opt. 47, 4004–4008 (2008).
[CrossRef] [PubMed]

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

J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298–5301 (2008).
[CrossRef]

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

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550nm,” Appl. Opt. 45, 2567–2571 (2006).
[CrossRef] [PubMed]

Zöllner, K.

Appl. Opt. (13)

D. Delbeke, R. Baets, and P. Muys, “Polarization-selective beam splitter based on a highly efficient simple binary diffraction grating,” Appl. Opt. 43, 6157–6165 (2004).
[CrossRef] [PubMed]

E. J. D. Carvalho, E. D. S. Braga, and L. H. Cescato, “Study of the injection molding of a polarizing beam splitter,” Appl. Opt. 45, 100–103 (2006).
[CrossRef]

S. Fahr, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, “Reflective diffractive beam splitter for laser interferometers,” Appl. Opt. 46, 6092–6095 (2007).
[CrossRef] [PubMed]

B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused-silica phase grating,” Appl. Opt. 47, 4004–4008 (2008).
[CrossRef] [PubMed]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Design and fabrication of a polarization-independent two-port beam splitter,” Appl. Opt. 48, 5636–5641 (2009).
[CrossRef] [PubMed]

J. Néauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization, and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152 (2005).
[CrossRef] [PubMed]

S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550nm,” Appl. Opt. 45, 2567–2571 (2006).
[CrossRef] [PubMed]

J. Feng, C. Zhou, H. Cao, and P. Lv, “Deep-etched sinusoidal polarizing beam splitter grating,” Appl. Opt. 49, 1739–1743(2010).
[CrossRef] [PubMed]

T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. Tishchenko, and O. Parriaux, “Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmission gratings illuminated in Littrow mounting,” Appl. Opt. 46, 819–826 (2007).
[CrossRef] [PubMed]

T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped-pulse amplification systems,” Appl. Opt. 42, 6934–6938(2003).
[CrossRef] [PubMed]

W. Jia, C. Zhou, J. Feng, and E. Dai, “Miniature pulse compressor of deep-etched gratings,” Appl. Opt. 47, 6058–6063 (2008).
[CrossRef] [PubMed]

S. Pelissier, D. Blanc, M. P. Andrews, S. I. Najafi, A. V. Tishchenko, and O. Parriaux, “Single-step UV recording of sinusoidal surface gratings in hybrid solgel glasses,” Appl. Opt. 38, 6744–6748 (1999).
[CrossRef]

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Dual-function beam splitter of a subwavelength fused-silica grating,” Appl. Opt. 48, 2697–2701 (2009).
[CrossRef] [PubMed]

J. Opt. A: Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298–5301 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of a deep-etched sinusoidal-groove grating ( n 1 and n 2 : refractive indices of air and fused-silica, respectively; Λ: period; h: depth; θ i : incident angle (under Littrow mounting); θ 0 and θ 1 : diffraction angles of the zeroth and -1st orders, respectively).

Fig. 2
Fig. 2

Reflection of a sinusoidal-groove fused-silica grating as a function of grating period, and the corresponding Fresnel reflection at a plane air/fused-silica interface (wavelength λ = 1064 nm , TE polarization).

Fig. 3
Fig. 3

Average difference of mode indices and ratios of accumulated phase difference for TM polarization to that for TE polarization as a function of grating period for sinusoidal-groove grating at a wavelength of 1064 nm .

Fig. 4
Fig. 4

Extinction ratio contour of a sinusoidal PBS grating at a wavelength of 1064 nm with (a) TM- and TE-polarized waves being respectively diffracted to the zeroth and -1st order, and (b) TE- and TM-polarized waves respectively to the zeroth and -1st orders.

Fig. 5
Fig. 5

Diffraction efficiency contour as functions of grating period and groove depth at a wavelength of 1064 nm for (a) TM and (b) TE polarization.

Fig. 6
Fig. 6

Diffraction efficiency as a function of groove depth with a period of 1100 nm at a wavelength of 1064 nm .

Tables (4)

Tables Icon

Table 1 Diffractive Efficiencies of the Sinusoidal Grating at Different Wavelengths for a Polarizing Beam Splitter with p = 1.733 and q = 1.563 by Using RCWA

Tables Icon

Table 2 Diffractive Efficiencies of the Sinusoidal Grating at Different Wavelengths for a Polarizing Beam Splitter with p = 1.267 and q = 3.889 by Using RCWA

Tables Icon

Table 3 Diffractive Efficiencies of the Sinusoidal Grating at Different Wavelengths for a 1 × 2 Beam Splitter with p = 1.440 and q = 2.733 by Using RCWA

Tables Icon

Table 4 Diffractive Efficiencies of the Sinusoidal Grating at Different Wavelengths for High Efficiency at the -1st Diffractive Order with p = 1.440 and q = 5.466 by Using RCWA

Equations (11)

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

η 0 = cos 2 Δ φ 2 ,
η 1 = sin 2 Δ φ 2 ,
Δ φ = Δ n ¯ eff k 0 h ,
cos [ k 1 ( 1 f ) Λ ] cos ( k 2 f Λ ) k 1 2 + k 2 2 2 k 1 k 2 sin [ k 1 ( 1 f ) Λ ] sin ( k 2 f Λ ) = cos ( α Λ ) ,
cos [ k 1 ( 1 f ) Λ ] cos ( k 2 f Λ ) n 2 4 k 1 2 + k 2 2 2 n 2 2 k 1 k 2 sin [ k 1 ( 1 f ) Λ ] sin ( k 2 f Λ ) = cos ( α Λ ) .
p = λ / Λ
q = h / λ ,
n eff = n eff ( p , f )
Δ φ = 2 π Δ n ¯ eff q .
Δ n ¯ eff = π 2 0 1 ( n even ( p , f ) n odd ( p , f ) ) sin ( π f ) d f ,
Δ φ = { ( 2 l + 1 ) π , η 0 = 0 , η 1 = 1 , 2 l π , ( l = 0 , 1 , 2 , ) η 0 = 1 , η 1 = 0 , ( 2 l + 1 ) π / 2 η 0 = η 1 = 50 % .

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