Abstract

A polarization-independent wideband mixed metal dielectric grating with high efficiency of the 1st order is analyzed and designed in Littrow mounting. The mixed metal dielectric grating consists of a rectangular-groove transmission dielectric grating on the top layer and a highly reflective mirror composed of a connecting layer and a metal film. Simplified modal analysis is carried out, and it shows that when the phase difference accumulated by the two propagating modes is odd multiples of π/2, the diffraction efficiency of the 1st order will be high. Selecting grating depth and duty cycle for satisfying the phase difference condition for both TE (electric field parallel to grooves) and TM (magnetic field parallel to grooves) polarizations, a polarization-independent high-efficiency grating can be designed. Using rigorous coupled-wave analysis and a simulated annealing algorithm, geometric parameters of the reflective grating are exactly obtained. The optimized grating for operation around a wavelength of 800 nm exhibits diffraction efficiencies higher than 90% for both TE and TM polarizations over a 120 nm wavelength bandwidth. The simplified modal analysis can be applied in other types of reflective gratings if the top layer is a dielectric transmission grating.

© 2012 Optical Society of America

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References

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    [CrossRef]
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2012 (1)

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

2010 (3)

2009 (1)

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

2008 (2)

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]

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

2007 (2)

2006 (1)

N. Bonod and J. Néauport, “Optical performance and laser induced damage threshold improvement of diffraction gratings used as compressors in ultra high intensity lasers,” Opt. Commun. 260, 649–655 (2006).
[CrossRef]

2005 (1)

1998 (1)

1995 (4)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

Bonod, N.

J. Neauport, N. Bonod, S. Hocquet, S. Palmier, and G. Dupuy, “Mixed metal dielectric gratings for pulse compression,” Opt. Express 18, 23776–23783 (2010).
[CrossRef]

N. Bonod and J. Néauport, “Optical performance and laser induced damage threshold improvement of diffraction gratings used as compressors in ultra high intensity lasers,” Opt. Commun. 260, 649–655 (2006).
[CrossRef]

Boyd, R. D.

Britten, J. A.

Byer, R. L.

Canova, F.

Cao, H.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112 (2010).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

Chambaret, J.

Clady, R.

Clausnitzer, T.

Decker, D.

Decker, D. E.

Dupuy, G.

Fahr, S.

Fechner, R.

Feng, J.

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112 (2010).
[CrossRef]

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

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]

Flury, M.

Gaylord, T. K.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Grann, E. B.

Hocquet, S.

Hu, A.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

Jia, W.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

Käpfe, T.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Kley, E.

Kley, E. B.

Li, L.

Lu, P.

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112 (2010).
[CrossRef]

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

Lv, P.

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

Ma, J.

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112 (2010).
[CrossRef]

Moharam, M. G.

Neauport, J.

Néauport, J.

N. Bonod and J. Néauport, “Optical performance and laser induced damage threshold improvement of diffraction gratings used as compressors in ultra high intensity lasers,” Opt. Commun. 260, 649–655 (2006).
[CrossRef]

Palmier, S.

Parriaux, O.

Perry, M. D.

Peschel, U.

Pommet, D. A.

Shannon, C.

Shore, B. W.

Shults, E.

Stuart, B. C.

Sun, K. X.

Tishchenko, A. V.

Tonchev, S.

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

Tuennermann, A.

Tünermann, A.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Wang, B.

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

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]

Wu, J.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

Yu, J.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

Zheng, J.

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

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]

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

Zhou, C.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lu, and J. Ma, “Design and fabrication of a polarization-independent wideband transmission fused-silica grating,” Appl. Opt. 49, 4108–4112 (2010).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

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]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

J. Opt. (1)

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, “Modal analysis of high-efficiency wideband reflective gratings,” J. Opt. 14, 055705 (2012).
[CrossRef]

J. Opt. A (1)

J. Zheng, C. Zhou, J. Feng, H. Cao, and P. Lu, “A metal-mirror-based reflecting polarizing beam splitter,” J. Opt. A 11, 15710–15716 (2009).
[CrossRef]

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

Opt. Commun. (3)

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]

N. Bonod and J. Néauport, “Optical performance and laser induced damage threshold improvement of diffraction gratings used as compressors in ultra high intensity lasers,” Opt. Commun. 260, 649–655 (2006).
[CrossRef]

H. Cao, C. Zhou, J. Feng, P. Lv, and J. Ma, “Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550 nm,” Opt. Commun. 283, 4271–4273 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the mixed metal dielectric reflective grating: n1 and n2 are refractive indices of grating grooves and ridges, respectively; θi, incident angle; d, grating period; b, ridge width; hr, grating depth; hc, thickness of connecting layer.

Fig. 2.
Fig. 2.

Diffraction process of the mixed metal dielectric reflective grating. Mode 0 and mode 1, represented by the blue solid curve and green dashed curve, respectively, are excited by the incident wave in the transmission grating. The 1st order A and the 0th order B are reflected by the mirror and diffracted by the transmission grating again to form four possible diffraction waves C, D, E, and F. The interference between them will determine the diffraction efficiencies of the reflective grating.

Fig. 3.
Fig. 3.

Difference of effective indices for TE and TM polarizations and their ratio ΔnTM/ΔnTE as a function of duty cycle. The solid curve and the dash-dotted curve are difference of effective indices for TE (ΔnTE) and TM polarization (ΔnTM), respectively. The dashed curve is the ratio of effective indices differences ΔnTM/ΔnTE.

Fig. 4.
Fig. 4.

Reflectivity of the mirror as a function of the thickness of the connecting layer for different wavelengths. (a) TE polarization, (b) TM polarization.

Fig. 5.
Fig. 5.

Diffraction efficiencies of the 1st order for both TE and TM polarizations versus wavelengths.

Equations (6)

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cos(k2fd)cos[k1(1f)d]k22+k122k2k1sin(k2fd)sin[k1(1f)d]=cos(αd),
cos(k2fd)cos[k1(1f)d]n14k22+n24k122n12n22k2k1sin(k2fd)sin[k1(1f)d]=cos(αd).
η1=sin2(Δφ),
hr=2l+14(λn0effn1eff).
ΔφTMΔφTE=n0effTMn1effTMn0effTEn1effTE=2p+12q+1,
FSA={1Ni[1η1,mean(λi)]2}1/2,

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