Abstract

Surface-relief resonance-domain diffraction gratings with deep and dense grooves provide considerable changes in light propagation direction, wavefront curvature, and nearly 100% Bragg diffraction efficiency usually attributed only to volume optical holograms. In this paper, we present design, computer simulation, fabrication, and experimental results of binary resonance-domain diffraction gratings in the visible spectral region. Performance of imperfectly fabricated diffraction groove profiles was optimized by controlling the DC and the depth of the grooves. Indeed, more than 97% absolute Bragg diffraction efficiency was measured at the 635 nm wavelength with binary gratings having periods of 520 nm and groove depths of about 1000 nm, fabricated by direct electron-beam lithography and reactive ion etching.

© 2012 Optical Society of America

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References

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2012

2011

M. Oliva, T. Harzendorf, D. Michaelis, U. D. Zeitner, and A. Tünnermann, “Multilevel blazed gratings in resonance domain: an alternative to the classical fabrication approach,” Opt. Express 19, 14735–14745 (2011).
[CrossRef]

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

2010

2008

2007

2005

2004

M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, “Optimization of diffraction grating profiles in fabrication by electron-beam lithography,” Appl. Opt. 43, 5137–5142 (2004).
[CrossRef]

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).
[CrossRef]

2003

2002

2000

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

1999

1997

1995

1982

1980

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

Barlev, O.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

Beaucoudrey, N.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1993).

Cambril, E.

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambril, “Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection,” Appl. Opt. 36, 5717–5727 (1997).
[CrossRef]

Cao, H.

Chandezon, J.

Chavel, P.

Clausnitzer, T.

Collier, R. J.

R. J. Collier, Optical Holography (Academic, 1971).

Destouches, N.

Eisen, L.

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).
[CrossRef]

Feng, J.

Friesem, A. A.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

M. A. Golub and A. A. Friesem, “Analytic design and solutions for resonance domain diffractive optical elements,” J. Opt. Soc. Am. A 24, 687–695 (2007).
[CrossRef]

M. A. Golub and A. A. Friesem, “Effective grating theory for the resonance domain surface relief diffraction gratings,” J. Opt. Soc. Am. A 22, 1115–1126 (2005).
[CrossRef]

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).
[CrossRef]

Fuchs, H.-J.

Gaylord, T. K.

Glytsis, E. N.

Golub, M. A.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

M. A. Golub and A. A. Friesem, “Analytic design and solutions for resonance domain diffractive optical elements,” J. Opt. Soc. Am. A 24, 687–695 (2007).
[CrossRef]

M. A. Golub and A. A. Friesem, “Effective grating theory for the resonance domain surface relief diffraction gratings,” J. Opt. Soc. Am. A 22, 1115–1126 (2005).
[CrossRef]

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).
[CrossRef]

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC, 1994).

Granet, G.

Hamamoto, T.

Harzendorf, T.

Hirai, Y.

Jupe, M.

Kampfe, T.

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Kikuta, H.

Kley, E. B.

Kley, E.-B.

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Kuittinen, M.

K. Ventola, J. Tervo, S. Siitonen, H. Tuovinen, and M. Kuittinen, “High efficiency half-wave retardation in diffracted light by coupled waves,” Opt. Express 20, 4681–4689 (2012).
[CrossRef]

J. Turunen, M. Kuittinen, and F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2000), Vol. XL, pp. 343–388.

Lalanne, P.

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

Lee, M. L.

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

Li, L.

Limpert, J.

Loewen, E. G.

E. Popov and E. G. Loewen, Diffraction Gratings and Applications (Dekker, 1997).

Lu, P.

Ma, J.

Magnusson, R.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

Mahalu, D.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Michaelis, D.

Miller, J. M.

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

Morris, G. M.

Nathan, M.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Okano, M.

Oliva, M.

Parriau, O.

Parriaux, O.

Peng, S.

Plumey, J.-P.

Pommier, J. C.

Popov, E.

E. Popov and E. G. Loewen, Diffraction Gratings and Applications (Dekker, 1997).

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Reynaud, S.

Ristau, D.

Rodier, J.

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

Shiono, T.

Siitonen, S.

Soifer, V. A.

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC, 1994).

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

Takahara, K.

Tervo, J.

Tishchenko, A. V.

Tunnermann, A.

Tünnermann, A.

Tuovinen, H.

Turunen, J.

J. M. Miller, N. Beaucoudrey, P. Chavel, J. Turunen, and E. Cambril, “Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection,” Appl. Opt. 36, 5717–5727 (1997).
[CrossRef]

J. Turunen, M. Kuittinen, and F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2000), Vol. XL, pp. 343–388.

Ventola, K.

Wang, B.

Wang, S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1993).

Wu, S. D.

Wu, Y. M.

Wyrowski, F.

J. Turunen, M. Kuittinen, and F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2000), Vol. XL, pp. 343–388.

Yamamoto, K.

Yotsuya, T.

Zeitner, U. D.

Zellmer, H.

Zhou, C.

Zoellner, K.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

M. A. Golub, A. A. Friesem, and L. Eisen, “Bragg properties of efficient surface relief gratings in the resonance domain,” Opt. Commun. 235, 261–267 (2004).
[CrossRef]

Opt. Express

Opt. Let.

M. L. Lee, P. Lalanne, J. Rodier, and E. Cambril, “Wide field-angle behaviour of blazed-binary gratings in the resonance domain,” Opt. Let. 25, 1690–1692 (2000).
[CrossRef]

Opt. Lett.

Proc. SPIE

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication and testing of highly efficient resonance domain diffractive optical elements,” Proc. SPIE 8169, 81690D (2011).
[CrossRef]

Other

J. Turunen, M. Kuittinen, and F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, 2000), Vol. XL, pp. 343–388.

E. Popov and E. G. Loewen, Diffraction Gratings and Applications (Dekker, 1997).

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004).

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

V. A. Soifer and M. A. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC, 1994).

R. J. Collier, Optical Holography (Academic, 1971).

RSoft Design Group Inc., “DiffractMODTM software code,” www.rsoftdesign.com .

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1993).

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Figures (8)

Fig. 1.
Fig. 1.

Comparison of scalar and resonance-domain surface-relief diffraction gratings. (a) Scalar diffraction grating with sawtooth-shaped grooves and low aspect ratio, and (b) resonance-domain diffraction grating with high aspect ratio and grating period comparable to the incident wavelength.

Fig. 2.
Fig. 2.

Numerically calculated theoretical map of the first-order Bragg diffraction efficiency as a function of FS groove depths, in micrometers and DCs for a binary grating with period 520 nm, illuminated with a wavelength of 635 nm at the theoretical Bragg angle of θinc,B=37.63°. (a) TE polarization and (b) TM polarization.

Fig. 3.
Fig. 3.

Analytical and numerical calculations of diffraction efficiency as a function of angular orientation of the incident beam, for TE and TM polarizations at 635 nm wavelength and grating period 520 nm. Calculations were performed for a grating with binary-shaped FS grooves with DC= of 0.573 and groove depth 1114.4 nm.

Fig. 4.
Fig. 4.

ESEM images of magnified sections from the FS resonance-domain diffraction gratings with period 520 nm. (a) Top-view image after etching to the target depth of about 1000 nm; white color shows the top of the groove and dark gray shows the gaps between grooves; (b) cross section of the grating groove profile.

Fig. 5.
Fig. 5.

Rounded trapezoidal groove profile in normalized coordinates.

Fig. 6.
Fig. 6.

Numerically calculated theoretical map of the first-order Bragg diffraction efficiency as a function of FS groove depths and DCs, for a rounded trapezoidal grating with period 520 nm, parameters α=0.25, β=0.5, γ=0.25, illuminated with a wavelength of 635 nm at the theoretical Bragg angle of θinc,B=37.63°. (a) TE and (b) TM.

Fig. 7.
Fig. 7.

Experimental arrangement for measuring the diffraction efficiency of the resonance-domain diffraction gratings.

Fig. 8.
Fig. 8.

Experimental and best-fit calculated diffraction efficiencies as functions of the angle of incidence for TE and TM polarizations at the illumination wavelength 635 nm and grating period 520 nm. Calculations were performed for a grating with rounded trapezoidal grooves with parameters α=0.25, β=0.5, γ=0.25, DC=0.565 and groove depth 1100.0 nm.

Tables (3)

Tables Icon

Table 1. Calculated Optimal groove Depths in Nanometers (DC), and First-Order Optimal Diffraction Efficiencies Expressed as Percentages, for Binary-Shaped FS Grooves with Period of 520 nm at 635 nm Wavelength and the Bragg Angle of Incidence 37.63°

Tables Icon

Table 2. Calculated Optimal FS Groove Depths in Nanometers (DC) and First-Order Optimal Bragg Diffraction Efficiencies Expressed as Percentages, for Rounded Trapezoidal-Shaped FS Grooves with Period of 520 nm, and Parameters α=0.25, β=0.5, γ=0.25 at 635 nm Wavelength and Bragg Angle of Incidence 37.63°a

Tables Icon

Table 3. Experimental Results, Including Fresnel Transmittance, Aperture Transmittance and First-Order Diffracted Intensities

Equations (8)

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

nisinθinc,B=λ2Λtanφr[n¯21+tan2φr(jλ2Λ)2]1/2,
n¯2=ni2+ΔnM2·g¯,ΔnM2=nM2ni2
ηB=sin2(2πhλn¯κ¯01cosφrc0sB),
κ¯01TE=δnM2G1,δnM2=ΔnM2/2n¯2,
κ¯01TM=κ¯01TE[112(λn¯Λcosφr)2],c0sB=1(λ2Λn¯cosφr)2.
hoptλ=c0sBcosφr2πn¯κ¯01[π2±(π2asinηB)].
TFresnelTE/TM(θinc)=IFresnelTE/TM(θinc)/IrefTE/TMandTaper(θinc)=Iaper(θinc)/IrefTE/TM.
η1TE/TM(θinc)=I1TE/TM(θinc)IrefTE/TM·Taper(θinc)·TFresnelTE/TM(θinc).

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