Abstract

A multireflection modal method is proposed to give a clear physical picture for explanation of the diffraction process that takes place in a wideband fused-silica transmission grating. Using rigorous coupled-wave analysis, the optimized grating exhibits diffraction efficiency greater than 93.9% for TE polarization over a bandwidth of 126 nm (from 735 to 861 nm). The designed wideband fused-silica transmission grating is fabricated using holographic interference recording and inductively coupled plasma etching technology. Experimental results are in agreement with the theoretical values.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
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  23. 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]
  24. S. Wang, C. Zhou, H. Ru, and Y. Zhang, “Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology,” Appl. Opt. 44, 4429–4434(2005).
    [CrossRef]

2012 (1)

2011 (1)

C. J. Chang-Hasnain, “High-contrast gratings as a new platform for integrated optoelectronics,” Semicond. Sci. Technol. 26, 014043 (2011).
[CrossRef]

2010 (1)

2009 (3)

2008 (6)

2007 (2)

2006 (1)

2005 (3)

1995 (2)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

1983 (1)

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

1981 (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Alessi, D.

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Boyd, R. D.

Britten, J. A.

Cao, H.

Chang-Hasnain, C. J.

Chavel, P.

Clausnitzer, T.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Dai, E.

Decker, D. E.

Feng, J.

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]

George, J.

Grann, E. B.

Hugonin, J. P.

Jia, W.

Kämpfe, T.

Karagodsky, V.

Kirkpatrick, S.

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

Kley, E.-B.

Knollenberg, B.

Krous, E.

Lalanne, P.

Larotonda, M. A.

Li, L.

Luther, B. M.

Lv, P.

Martz, D. H.

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Menoni, C. S.

Moharam, M. G.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Nguyen, H. T.

Parriaux, O.

Patel, D.

Perry, M. D.

Peschel, U.

Pommet, D. A.

Rocca, J. J.

Ru, H.

Sedgwick, F. G.

Shore, B. W.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Stuart, B. C.

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, 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.

Wang, S.

Wang, Y.

Yang, W.

Zhang, Y.

Zheng, J.

Zheng, J. J.

J. J. Zheng, “Simplified modal method of gratings and applications,” Ph.D. dissertation (Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences, 2009).

Zhou, C.

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]

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]

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]

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

J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused-silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[CrossRef]

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]

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

S. Wang, C. Zhou, H. Ru, and Y. Zhang, “Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology,” Appl. Opt. 44, 4429–4434(2005).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (8)

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]

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

R. D. Boyd, J. A. Britten, D. E. Decker, B. W. Shore, B. C. Stuart, M. D. Perry, and L. Li, “High-efficiency metallic diffraction gratings for laser applications,” Appl. Opt. 34, 1697–1706 (1995).
[CrossRef]

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]

J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused-silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[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]

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]

S. Wang, C. Zhou, H. Ru, and Y. Zhang, “Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology,” Appl. Opt. 44, 4429–4434(2005).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

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]

Optica Acta (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Optica Acta 28, 413–428 (1981).
[CrossRef]

Science (1)

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

Semicond. Sci. Technol. (1)

C. J. Chang-Hasnain, “High-contrast gratings as a new platform for integrated optoelectronics,” Semicond. Sci. Technol. 26, 014043 (2011).
[CrossRef]

Other (1)

J. J. Zheng, “Simplified modal method of gratings and applications,” Ph.D. dissertation (Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences, 2009).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic illustration of a binary fused-silica grating (n1 and n2, refractive indices of air and fused-silica, respectively; θin, incident angle; θ0 and θ1, diffraction angles of the zeroth and 1st diffractive orders, respectively; Λ, grating period; b, ridge width; g, groove width; h, groove depth).

Fig. 2.
Fig. 2.

(a) Mean and (b) standard deviation of diffraction efficiency versus groove depth and grating period.

Fig. 3.
Fig. 3.

Diffraction efficiency versus incident wavelength under Littrow mounting for the wavelength of 800 nm, with optimum grating parameters: duty cycle f=0.5, Λ=665nm, and h=1273nm. The inset shows the magnified part of the diffraction efficiency.

Fig. 4.
Fig. 4.

Squares of the first four effective indices (0, 1, 2, and 3) versus the incident wavelength. Parameters used in calculation are the same as those used in Fig. 3.

Fig. 5.
Fig. 5.

Energy exchange between the incident wave and the first four grating modes versus the incident wavelength. Parameters used in calculation are the same as those used in Fig. 3.

Fig. 6.
Fig. 6.

Schematic illustration of the physical mechanism of multireflection interference taking place inside the wideband fused-silica grating.

Fig. 7.
Fig. 7.

Diffraction efficiency by using MRMM versus incident wavelength. Parameters used in calculation are the same as those used in Fig. 3.

Fig. 8.
Fig. 8.

Diffraction efficiencies of the 1st transmission order obtained using MRMM, SMM, and RCWA.

Fig. 9.
Fig. 9.

Scanning electron micrograph image of the fabricated wideband grating.

Fig. 10.
Fig. 10.

Theoretical (solid curves) and experimental (dashed curves) diffraction efficiency of the wideband grating at different incident wavelength.

Equations (20)

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

η¯=1Nλiη(λi),
ηstd=5log10(1N1λi(η(λi)η¯)2),
cos(βb)cos(γg)12(β2+γ2)βγsin(βb)sin(γg)=cos(α0Λ),
Eyin(x)um(x)=|0ΛEyin(x)um(x)dx|20Λ|Eyin(x)|2dx0Λ|um(x)|2dx,
Eyin(x,z=0)=ejk⃗·r⃗=ejkxx·ejkzz=ej·n1cos(θin)k0z(a0inu0(x)+a1inu1(x))=ejk0neffinz(a0inu0(x)+a1inu1(x))Eyin(x,z=0+)=a0u0(x)ejneffk0z0+a1u1(x)ejneffk0z1,
amin=1Λ0Λejkxxum(x)dx.
rin/m=neffinneffmneffin+neffm=n1cosθinneffmn1cosθin+neffm,
tin/m=2neffinneffin+neffm=2n1cosθinn1cosθin+neffm.
am=amintin/m.
neffrp=n12(kxp/k0)2,
nefftp=n22(kxp/k0)2,
kxp=k0[n1sin(θin)+p(λ/Λ)].
rm/rp=neffmneffrpneffm+neffrp,tm/rp=2neffmneffm+neffrp,rm/tp=neffmnefftpneffm+nefftp,tm/tp=2neffmneffm+nefftp.
Eyoutrp(x,z)=Arpejkxpx·ejkzz=ejneffrpk0z(a0rpu0(x)+a1rpu1(x))(z=0),
Eyouttp(x,z)=Atpejkxpx·ejkzz=ejnefftpk0z(a0tpu0(x)+a1tpu1(x))(z=h+),
amrp=amin(rin/m+tin/mrm/tptm/rpe2jδ1rm/rprm/tpe2jδ),
amtp=amin(tin/mtm/tpejδ1rm/rprm/tpe2jδ),
Arp=1Λ0Λ(a0rpu0(x)+a1rpu1(x))ejkxpxdx,
Atp=1Λ0Λ(a0tpu0(x)+a1tpu1(x))ejkxpxdx.
ηp=neffp|Ap|2n1cos(θin),

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