Abstract

Early expectations for a role of diffractive lenses were dramatically lessened by their high order overlapping foci, low optical powers, and competing advances in refractive micro-optics. By bringing the Bragg properties of volume holograms to diffractive lenses we got rid of ghost diffractive orders and the critical trade-off between diffraction efficiency, number of phase levels, and spatial feature-size. Binary off-axis resonance domain diffractive lens with high numerical aperture of 0.16 was designed with analytical effective grating theory, fabricated by direct e-beam writing, etched in fused silica and experimentally investigated. More than 81% measured diffraction efficiency exceeds twice the limits of thin binary optics.

© 2013 Optical Society of America

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2012 (5)

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication of high-aspect-ratio resonance domain diffraction grating in fused silica,” Opt. Eng. 51, 118002 (2012).
[CrossRef]

H. Zappe, “Micro-optics: a micro-tutorial,” Adv. Opt. Tech. 1, 117–126 (2012).
[CrossRef]

R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Tech. 1, 117–126 (2012).
[CrossRef]

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]

O. Barlev, M. A. Golub, and A. A. Friesem, “Design and experimental investigation of highly efficient resonance domain diffraction gratings in the visible spectral region,” Appl. Opt. 51, 8074–8080 (2012).
[CrossRef]

2011 (4)

K. Ventola, J. Tervo, P. Laakkonen, and M. Kuittinen, “High phase retardation by waveguiding in slanted photonic nanostructures,” Opt. Express 19, 241–246 (2011).
[CrossRef]

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. Sandfuchs, C. Schwanke, M. Burkhardt, F. Wyrowski, A. Gatto, and R. Brunner, “Modelling adapted to manufacturing aspects of holographic grating structures,” J. Eur. Opt. Soc. 6, 11006 (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 (4)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

L. Chrostowski, “Nano-engineered lenses,” Nat. Photonics 4, 413–415 (2010).
[CrossRef]

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 4, 188–193 (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]

2009 (1)

2008 (1)

2007 (2)

2005 (3)

2004 (2)

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 (2)

2002 (1)

2001 (1)

2000 (2)

1999 (5)

1998 (2)

1997 (4)

1996 (1)

1995 (4)

1993 (1)

1984 (1)

1980 (1)

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

1970 (1)

1969 (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Astilean, S.

Barlev, O.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication of high-aspect-ratio resonance domain diffraction grating in fused silica,” Opt. Eng. 51, 118002 (2012).
[CrossRef]

O. Barlev, M. A. Golub, and A. A. Friesem, “Design and experimental investigation of highly efficient resonance domain diffraction gratings in the visible spectral region,” Appl. Opt. 51, 8074–8080 (2012).
[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]

Beaucoudrey, N.

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
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Bona, G. L.

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O. Sandfuchs, C. Schwanke, M. Burkhardt, F. Wyrowski, A. Gatto, and R. Brunner, “Modelling adapted to manufacturing aspects of holographic grating structures,” J. Eur. Opt. Soc. 6, 11006 (2011).
[CrossRef]

Burkhardt, M.

O. Sandfuchs, C. Schwanke, M. Burkhardt, F. Wyrowski, A. Gatto, and R. Brunner, “Modelling adapted to manufacturing aspects of holographic grating structures,” J. Eur. Opt. Soc. 6, 11006 (2011).
[CrossRef]

Cambril, E.

Cao, H.

Chandezon, J.

Chavel, P.

Chrostowski, L.

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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]

Elias, Y.

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Feng, D.

Feng, J.

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Friesem, A. A.

O. Barlev, M. A. Golub, and A. A. Friesem, “Design and experimental investigation of highly efficient resonance domain diffraction gratings in the visible spectral region,” Appl. Opt. 51, 8074–8080 (2012).
[CrossRef]

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication of high-aspect-ratio resonance domain diffraction grating in fused silica,” Opt. Eng. 51, 118002 (2012).
[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]

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]

M. A. Golub and A. A. Friesem, “Analytical theory for efficient surface relief gratings in the resonance domain,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H. John Caulfield, ed. (SPIE, 2004) Chap. 19, pp. 307–328.

Fuchs, H.-J.

Gao, X.

Gatto, A.

O. Sandfuchs, C. Schwanke, M. Burkhardt, F. Wyrowski, A. Gatto, and R. Brunner, “Modelling adapted to manufacturing aspects of holographic grating structures,” J. Eur. Opt. Soc. 6, 11006 (2011).
[CrossRef]

Gaylord, T. K.

S. D. Wu, T. K. Gaylord, E. N. Glytsis, and Y. M. Wu, “Angular sensitivities of volume gratings for substrate-mode optical interconnects,” Appl. Opt. 44, 4447–4453 (2005).
[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]

Gaylord, Thomas K.

Gerke, T. D.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics 4, 188–193 (2010).
[CrossRef]

Glytsis, E. N.

Glytsis, N.

Golub, M. A.

O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication of high-aspect-ratio resonance domain diffraction grating in fused silica,” Opt. Eng. 51, 118002 (2012).
[CrossRef]

O. Barlev, M. A. Golub, and A. A. Friesem, “Design and experimental investigation of highly efficient resonance domain diffraction gratings in the visible spectral region,” Appl. Opt. 51, 8074–8080 (2012).
[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]

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]

M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1194–1201 (1999).
[CrossRef]

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

M. A. Golub and A. A. Friesem, “Analytical theory for efficient surface relief gratings in the resonance domain,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H. John Caulfield, ed. (SPIE, 2004) Chap. 19, pp. 307–328.

Granet, G.

Guofan, J.

Hamamoto, T.

Harrigan, Michael E.

Harzendorf, T.

Herzig, H. P.

Hirai, Y.

Hirayama, Koichi

Hirsch, P. M.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Holswade, S. C.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Technologies (Marcel Dekker, 2000).

Ichikawa, H.

Jordan, J. A.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

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, 2003).

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 (John Wiley & Sons, 2000).

B. Kress and P. Meyrueis, Applied Digital Optics: From Micro-optics to Nanophotonics (John Wiley & Sons, 2009).

Kuittinen, M.

Kunz, R. E.

Laakkonen, P.

Lalanne, P.

Larochelle, S.

Lesem, L. B.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[CrossRef]

Li, L.

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O. Barlev, M. A. Golub, A. A. Friesem, D. Mahalu, and M. Nathan, “Fabrication of high-aspect-ratio resonance domain diffraction grating in fused silica,” Opt. Eng. 51, 118002 (2012).
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Proc. SPIE (1)

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]

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M. A. Golub and A. A. Friesem, “Analytical theory for efficient surface relief gratings in the resonance domain,” in The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H. John Caulfield, ed. (SPIE, 2004) Chap. 19, pp. 307–328.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (John Wiley & Sons, 1998).

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

V. A. Soifer, ed., Methods for Computer Design of Diffractive Optical Elements, Wiley Series in Lasers and Applications (John Wiley & Sons, 2001).

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

B. Kress and P. Meyrueis, Applied Digital Optics: From Micro-optics to Nanophotonics (John Wiley & Sons, 2009).

F. M. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Technologies (Marcel Dekker, 2000).

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

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DiffractMODTM software code, Rsoft Design Group, www.rsoftdesign.com .

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Figures (13)

Fig. 1.
Fig. 1.

Geometry of the diffractive lens design and polarization states of the electric field E of the incident plane wave. (a) Virtual larger zone plate and (b) ray tracing of plane parallel beam.

Fig. 2.
Fig. 2.

First-order diffraction efficiency as function of the groove depth, for a basic resonance domain diffraction grating with period 520 nm and DC q = 0.575 . Intersection of the TE and TM curves in Fig. 2 provides the polarization independent solution. (a) Analytical calculations and (b) numerical calculations.

Fig. 3.
Fig. 3.

Numerically calculated local first-order TE diffraction efficiency η 1 ( x , 0 ) at fixed incident angle θ B = 37.6 ° as a function of the local grating period, for binary gratings with DC q = 0.575 and wavelength λ = 635 nm . Solid curve-analytic with groove depth of 1031 nm; dashed curve-numeric with groove depth of 1114 nm.

Fig. 4.
Fig. 4.

Local first-order diffracted beam angle at points ( x , 0 ) as a function of the local grating period, for wavelength λ = 635 nm .

Fig. 5.
Fig. 5.

Numerically calculated local first-order TE diffraction efficiency as a function of the local grating period for different the DCs, at the wavelength λ = 635 nm and n M = 1.45695 .

Fig. 6.
Fig. 6.

ESEM image of a mechanically cut cross section of the etched FS calibration sample of a RD gratings with period 520 nm.

Fig. 7.
Fig. 7.

Top view ESEM images of edges of the FS etched RDDL at about 8000 × magnification. (a) Top left and (b) bottom left.

Fig. 8.
Fig. 8.

Top view ESEM images of different sections of the FS etched RDDL at 30 , 000 × magnification. (a) Top left and (b) center.

Fig. 9.
Fig. 9.

Optical arrangement for RDDL measurements, F relay = 75 mm , f = 5.63 mm .

Fig. 10.
Fig. 10.

Measured first-order RDDL diffraction efficiency as a function of angle of incidence for TE polarization at the illumination wavelength 635 nm.

Fig. 11.
Fig. 11.

First-order image and zero diffraction order of the RDDL.

Fig. 12.
Fig. 12.

Image intensity patterns of the mask. (a) Designed, (b) and (c) experimental photos from diffusing screen with different distances of 123 and 250 mm from the RDDL. The adjacent minor lines of the ruler indicate 1 mm scale both at (b) and (c).

Fig. 13.
Fig. 13.

Image magnification versus the distance d from the RDDL plane.

Tables (1)

Tables Icon

Table 1. Measured Image Size and Magnification at Various Distances d from RDDL for the Mask with Width 1.52 mm

Equations (26)

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

Δ x = f sin θ B ,
F = f cos θ B ,
S = sin θ B x ,
S = F 2 + ( x + Δ x ) 2 + y 2 = f l ,
l = ( 1 + 2 sin θ B x f + x 2 + y 2 f 2 ) 1 2 .
φ RDDL ( x , y ) = k ( S S ) + const = k f ( 1 l sin θ B x f ) ,
ν ( x , y ) = 1 2 π φ RDDL ( x , y ) ,
Λ ( x , y ) = 1 | ν ( x , y ) | = λ l { [ sin θ B ( l + 1 ) + x f ] 2 + y 2 f 2 } 1 2 .
Λ ( 0 , 0 ) = λ 2 sin θ B ,
φ RDDL = 2 π · m ,
( x x m ) 2 a m 2 + y 2 b m 2 = 1 ,
x m = f sin θ B ( C m cos 2 θ B 1 ) ,
b m 2 = f 2 ( C m 2 cos 2 θ B cos 2 θ B ) , a n 2 = 1 cos 2 θ B b n 2 ,
C m = m λ f 1 sin 2 θ B .
n ¯ 2 = n i 2 ( 1 q ) + n M 2 · q ,
G 1 s = q sinc ( q ) , sinc ( t ) = sinc ( π t ) π t .
sin θ B = 1 2 Λ ^ ,
Λ ^ = Λ ( 0 , 0 ) λ ,
h TE = n ¯ λ c 2 G 1 s ( n M 2 n i 2 ) , h TM = h TE κ ,
κ = 1 1 2 n ¯ 2 Λ ^ 2 , c = 1 1 4 n ¯ 2 Λ ^ 2 .
η B TE , TM = sin ( π 2 h h TE , TM ) 2 .
h ± TE , TM = h TE , TM [ 1 ± ( 1 2 π a sin η B TE , TM ) ] ,
h indep = h TE c 2 ,
η B indep = sin 2 ( π 2 κ c 2 ) .
η lens = I inc ( x , y ) η 1 ( x , y ) d x d y I inc ( x , y ) d x d y ,
M = d f f = d 1 f 1 .

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