Abstract

We describe a design methodology for synthesizing polarization-sensitive diffractive optical elements based on two-dimensional form-birefringent microstructures. Our technique yields a single binary element capable of producing independent phase transformations for horizontally and vertically polarized illumination. We designed two elements for operation at 10.6 μm and fabricated them in silicon. Qualitative experimental results agree with design predictions.

© 2004 Optical Society of America

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References

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    [CrossRef]
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2002 (1)

2001 (1)

2000 (1)

1998 (1)

1997 (2)

1996 (1)

1995 (3)

1994 (1)

1993 (1)

1986 (1)

Ashok, V.

Borghi, R.

Bräuer, R.

Bryngdahl, O.

Cheng, C.

Deguzman, P.

G. P. Nordin, P. Deguzman, J. Jiang, J. T. Meier, “Polarization sensitive diffractive optics for integration with infrared photodetector arrays,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 88–90.

Dereniak, E.

Descour, M.

Fainman, Y.

Ford, J.

Hamamoto, T.

Hugonin, J.

Ichioka, Y.

Jiang, J.

G. P. Nordin, P. Deguzman, J. Jiang, J. T. Meier, “Polarization sensitive diffractive optics for integration with infrared photodetector arrays,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 88–90.

Kirk, A.

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681–4686 (1997).
[CrossRef] [PubMed]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

Konishi, T.

Krishnamoorthy, A.

Lalanne, P.

Lohmann, A.

Mait, J. N.

M. S. Mirotznik, J. N. Mait, D. W. Prather, “Design of two-dimensional polarization selective computer generated holograms using form-birefringence,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 231–233.

Meier, J. T.

G. P. Nordin, P. Deguzman, J. Jiang, J. T. Meier, “Polarization sensitive diffractive optics for integration with infrared photodetector arrays,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 88–90.

Mirotznik, M. S.

M. S. Mirotznik, J. N. Mait, D. W. Prather, “Design of two-dimensional polarization selective computer generated holograms using form-birefringence,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 231–233.

Morlion, B.

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681–4686 (1997).
[CrossRef] [PubMed]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

Nieuborg, N.

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681–4686 (1997).
[CrossRef] [PubMed]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

Noponen, E.

Nordin, G. P.

G. P. Nordin, P. Deguzman, J. Jiang, J. T. Meier, “Polarization sensitive diffractive optics for integration with infrared photodetector arrays,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 88–90.

Pajewski, L.

Prather, D. W.

M. S. Mirotznik, J. N. Mait, D. W. Prather, “Design of two-dimensional polarization selective computer generated holograms using form-birefringence,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 231–233.

Richter, I.

Sabatke, D.

Scherer, A.

Schettini, G.

Schmitz, M.

Sun, P.

Thienpont, H.

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681–4686 (1997).
[CrossRef] [PubMed]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

Toyota, H.

Turunen, J.

Tyan, R.

Urquhart, K.

Veretennicoff, I.

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681–4686 (1997).
[CrossRef] [PubMed]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

Xu, F.

Yotsuya, T.

Yu, W.

Appl. Opt. (7)

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

Opt. Lett. (3)

Other (4)

S. Tao, X. Yuan, W. Cheong, J. Bu, V. Kudryashov, “Optimized polarization-selective computer-generated hologram with fewer phase combinations,” Opt. Exp.11, 1252–1257 (2003), http://www.opticsexpress.org .
[CrossRef]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, I. Veretennicoff, “Highly polarization-selective diffractive optical elements in calcite with an index-matching gap material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S.-H. Lee, eds., SPIE Proc.3010, 124–133 (1997).
[CrossRef]

M. S. Mirotznik, J. N. Mait, D. W. Prather, “Design of two-dimensional polarization selective computer generated holograms using form-birefringence,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 231–233.

G. P. Nordin, P. Deguzman, J. Jiang, J. T. Meier, “Polarization sensitive diffractive optics for integration with infrared photodetector arrays,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 88–90.

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of a form-birefringent DOE. A subwavelength grating at each pixel location produces polarization-dependent effective optical properties. Effective properties are a function of the x and y fill factors, the x and y grating periods, and the etch depth.

Fig. 2
Fig. 2

Geometry used to calculate effective properties of subwavelength gratings.

Fig. 3
Fig. 3

Effective phase and amplitude transmission as a function of x and y fill factor. (a) Phase variations for Λ x = Λ y = (0.5) λ0/n s , (b) phase variations for Λ x = Λ y = (0.9) λ0/n s , (c) amplitude variations for Λ x = Λ y = (0.5) λ0/n s , (d) amplitude variations for Λ x = Λ y = (0.9) λ0/n s .

Fig. 4
Fig. 4

Graphical representation of form-birefringent cell encoding. (a) Relationship between a single binary subwavelength grating and the pair of polarization-sensitive phase values. (b) The encoding of a desired phase pair by a subwavelength grating.

Fig. 5
Fig. 5

Graphical representation of the algorithm used to design polarization-selective DOEs. (a) Desired phase profiles for x- and y-polarized illumination, (b) sampled phase profiles, (c) encoding, (d) binary cell-encoded polarization-sensitive DOE.

Fig. 6
Fig. 6

Binary phase polarization-selective binary grating. (a) Desired phase profiles for x- and y-polarized illumination. (b) Scanning electron microscope image of the fabricated element.

Fig. 7
Fig. 7

Experimental setup used to characterize the polarization-selective DOEs.

Fig. 8
Fig. 8

Experimental results for the binary phase polarization-selective binary grating. Measured and simulated results for (a) x polarization, (b) linear polarization at 45°, (c) y polarization.

Fig. 9
Fig. 9

Multiple-phase polarization-selective blazed binary grating. Desired phase profiles for (a) x- and (b) y-polarized illumination. Realizable phase profiles for (c) x- and (d) y-polarized illumination. (e) Images of the fabricated element.

Fig. 10
Fig. 10

Experimental results for the multiple-phase polarization-selective blazed binary grating. Measured and simulated results for (a) x polarization, (b) y polarization, (c) linear polarization at 45°.

Tables (3)

Tables Icon

Table 1 Design Specifications for Binary Phase Polarization-Selective Binary Grating

Tables Icon

Table 2 Measured and Simulated Diffraction Efficiencies (in percent) for the Example Problem Described in Figs. 6 and 8

Tables Icon

Table 3 Measured and Simulated Diffraction Efficiencies (in percent) for the Example Problem Described in Figs. 9 and 10

Equations (4)

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Einc=û exp-jksz,
ER=m,nRm,n expjαmx+βny-rmnz,ET=m,nTm,n expjαmx+βny+tmnz-h.
ϕ=T0,0-k0h,
Δϕ=ϕdesiredx-ϕactualx2+ϕdesiredy-ϕactualy21/2.

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