Abstract

A sinusoidal-shaped fused-silica grating as a highly efficient polarizing beam splitter (PBS) is investigated based on the simplified modal method. The grating structure depends mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These ratios can be used as a guideline for the grating design at different wavelengths. A sinusoidal-groove PBS grating is designed at a wavelength of 1310nm under Littrow mounting, and the transmitted TM and TE polarized waves are mainly diffracted into the zeroth order and the 1st order, respectively. The grating profile is optimized by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient (>95.98%) over the O-band wavelength range (12601360nm) for both TE and TM polarizations. The sinusoidal grating can exhibit higher diffraction efficiency, larger extinction ratio, and less reflection loss than the rectangular-groove PBS grating. By applying wet etching technology on the rectangular grating, which was manufactured by holographic recording and inductively coupled plasma etching technology, the sinusoidal grating can be approximately fabricated. Experimental results are in agreement with theoretical values.

© 2010 Optical Society of America

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2009

2008

2007

2005

2004

2000

1999

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

1995

1982

Aasen, M. D.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

Baets, R.

Britten, J. A.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

Byer, R. L.

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

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.

Carlson, T. C.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

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.

Delbeke, D.

Dobrowolski, J. A.

Feng, J.

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]

Hoaglan, C. R.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

Jia, W.

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]

Larson, C. C.

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[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]

Li, L.

Lu, P.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

Lu, P. P.

Lv, P.

Moharam, M. G.

Morris, G. M.

Muys, P.

Nguyen, H. T.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

Nissen, J. D.

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

Parriaux, O.

Peschel, U.

Pommet, D. A.

Sun, K.-X.

P. P. Lu, K.-X. Sun, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Precise diffraction efficiency measurements of large-area greater-than-99%-efficient dielectric gratings at the Littrow angle,” Opt. Lett. 34, 1708-1710(2009).
[CrossRef] [PubMed]

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, A.

Wang, B.

Wang, S.

Zheng, J.

Zhou, C.

Appl. Opt.

J. Opt. A Pure Appl. Opt.

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.

J. Opt. Soc. Am. A

J. Phys. Conf. Ser.

K.-X. Sun, P. Lu, R. L. Byer, J. A. Britten, H. T. Nguyen, J. D. Nissen, C. C. Larson, M. D. Aasen, T. C. Carlson, and C. R. Hoaglan, “Characterization of polarization sensitive, high efficiency dielectric gratings for formation flight interferometry,” J. Phys. Conf. Ser. 154, 012031(2009).
[CrossRef]

Opt. Commun.

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

Opt. Lett.

Opt. Quantum Electron.

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

Fig. 2
Fig. 2

(a) Average difference of mode indices and (b) ratios of accumulated phase difference for TM polarization to that for TE polarization as a function of grating period for sinusoidal, triangular, and rectangular (with duty cycle of 0.5) groove gratings at a wavelength of 1310 nm .

Fig. 3
Fig. 3

Contour of the extinction ratio of the sinusoidal-groove PBS grating for different profile parameters at a wavelength of 1310 nm .

Fig. 4
Fig. 4

Diffraction efficiency of the designed grating as a function of incident wavelength under Littrow mounting.

Fig. 5
Fig. 5

Scanning electron micrograph image of the manufactured grating (a) before and (b) after the wet etching process.

Fig. 6
Fig. 6

Theoretical (curves) and experimental (dots) diffraction efficiencies of the manufactured grating for different incident angles at a wavelength of 1310 nm .

Tables (1)

Tables Icon

Table 1 Corresponding Diffractive Efficiencies of the Sinusoidal Grating at Different Wavelengths with λ / Λ = 1.731 and h / Λ = 2.723 by Use of RCWA

Equations (7)

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 ,
Δ n ¯ eff = 1 h 0 h ( n even ( z ) n odd ( z ) ) d z ,
Δ n ¯ eff = π 2 0 1 ( n even ( Λ , f ) n odd ( Λ , f ) ) sin ( π f ) d f ,
n ¯ eff = 0 1 ( n even ( Λ , f ) n odd ( Λ , f ) ) d f ,
Δ n ¯ eff = n even ( Λ , 0.5 ) n odd ( Λ , 0.5 ) .

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