Abstract

We propose a deterministic design method of a blazed grating consisting of a binary grating with subwavelength structures for a multilevel phase modulation. The feasible shapes of binary subwavelength microstructures are restricted to a few kinds of surface profiles by constraints in an actual fabrication technique. The relationship between the feasible shapes of binary subwavelength microstructures and their phase modulations can be calculated by an electromagnetic analysis and tabulated. Using the relationship, a deterministic design of a binary grating with subwavelength structures is simply realized. We have designed the binary blazed grating with subwavelength structures and investigated its performance. Its diffraction efficiency is in good agreement with that by a conventional statistical design method.

© 2007 Optical Society of America

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References

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2005 (2)

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

T. J. Suleski and R. D. Te Kolste, "Fabrication trends for free-space microoptics," J. Lightwave Technol. 23, 633-646 (2005).
[CrossRef]

2003 (1)

H. Kikuta, H. Toyota, and W. Yu, "Optical elements with subwavelength structure surface," Opt. Rev. 10, 63-73 (2003).
[CrossRef]

2000 (2)

1999 (1)

1998 (3)

1996 (1)

1995 (2)

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Z. Zhou and T. J. Drabik, "Optimized binary, phase-only, diffractive optical element with subwavelength features for 1.55 μm," J. Opt. Soc. Am. A 12, 1104-1112 (1995).
[CrossRef]

1994 (1)

1992 (1)

1983 (1)

D. C. Flanders, "Submicrometer periodicity grating as artificial anisotropic dielectrics," Appl. Phys. Lett. 42, 492-494 (1983).
[CrossRef]

1981 (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equation," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Astilean, S.

Cambril, E.

Chavel, P.

de Beaucoudrey, N.

Dial, O.

Drabik, T. J.

Farn, M. W.

Flanders, D. C.

D. C. Flanders, "Submicrometer periodicity grating as artificial anisotropic dielectrics," Appl. Phys. Lett. 42, 492-494 (1983).
[CrossRef]

Gao, X.

Ichioka, Y.

Iwata, K.

Johnson, E. G.

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Kikuta, H.

Konishi, T.

Kubo, H.

Lalanne, P.

Launois, H.

Mait, J. N.

Mehta, A.

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Miller, J. M.

Mirotznik, M. S.

Mur, G.

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equation," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Noponen, E.

Ohira, Y.

Prather, D. W.

Scherer, A.

Smith, R. E.

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Smolski, O. V.

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Suleski, T. J.

Takahara, K.

Te Kolste, R. D.

Toyota, H.

H. Kikuta, H. Toyota, and W. Yu, "Optical elements with subwavelength structure surface," Opt. Rev. 10, 63-73 (2003).
[CrossRef]

Turunen, J.

Vaissié, L.

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Vawter, G. A.

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Warren, M. E.

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Wendt, J. R.

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Yotsuya, T.

Yu, W.

Zhou, Z.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. C. Flanders, "Submicrometer periodicity grating as artificial anisotropic dielectrics," Appl. Phys. Lett. 42, 492-494 (1983).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Vaissié, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equation," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (1)

J. R. Wendt, G. A. Vawter, R. E. Smith, and M. E. Warren, "Nanofabrication of subwavelength, binary, high-efficiency diffractive optical elements in GaAs," J. Vac. Sci. Technol. B 13, 2705-2708 (1995).
[CrossRef]

Opt. Lett. (4)

Opt. Rev. (1)

H. Kikuta, H. Toyota, and W. Yu, "Optical elements with subwavelength structure surface," Opt. Rev. 10, 63-73 (2003).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Relationships between spatial resolution s and feasible number N Φ of b-SWMS at the maximum pitches p max = 500   nm , 1000   nm , and 1500   nm .

Fig. 2
Fig. 2

Representation of the computation domain.

Fig. 3
Fig. 3

Phase modulation of b-SWMS's.

Fig. 4
Fig. 4

Configurations of rectangular strips covering a period of the binary blazed gratings and phase modulations corresponding to individual b-SWMS's. Numbers on the ridges correspond to the label numbers in Table 1.

Fig. 5
Fig. 5

Surface structures of binary blazed gratings designed whose periods are (a) Λ = 6000   nm and (b) Λ = 10000   nm and their perspective views.

Fig. 6
Fig. 6

Phase distributions in the complex amplitudes of the electric fields of the wavefronts reached in the plane behind 1 .49   μm distant from the binary blazed gratings with (a) Λ = 6000   nm and (b) Λ = 10000   nm .

Fig. 7
Fig. 7

Illustration of allocation rule of b-SWMS.

Fig. 8
Fig. 8

Same as Fig. 3 but with the grating depth d = 2.22   μm .

Fig. 9
Fig. 9

Same as Fig. 6(b) but with d = 2.22   μm .

Fig. 10
Fig. 10

Same as Fig. 6(b) but with the spatial resolution s = 50   nm .

Fig. 11
Fig. 11

Diffraction efficiency as a function of a period Λ of the binary blazed grating.

Tables (2)

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Table 1 Look-Up Table and Perspective View a

Tables Icon

Table 2 Configurations of Rectangular Strips Describing the Feasible b-SWMS's

Equations (3)

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N Φ = i = 1 N p N w i ,
N p = p max s 1 ,
N w i = p i s 1 = i ,

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