Abstract

We present a theoretical and experimental study on the diffraction characteristics of gratings, with particular attention focused on the effects of polarization. The goal of our study is to develop multifunctional devices for use in a pickup head for optical storage systems. Experiments and numerical calculations are carried out systematically to determine the effects of the grating parameters of depth, period, and duty cycle and also the effects of the incident-wave parameters of incident angle, wavelength, and polarization. It is shown that, theoretically, the diffraction efficiency can reach 100% for both TE and TM polarizations that are incident at the Bragg angle. The simple dispersion characteristics of the Floquet modes are invoked to explain the different diffraction behaviors between the two polarizations. We conclude that a suitably designed grating may split an incident light beam of mixed polarizations into two beams of the opposite polarizations, each propagating in a different direction. Based on the numerical results, simple criteria are suggested for the design of the grating structures for both polarizing and nonpolarizing beam splitters.

© 1993 Optical Society of America

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References

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  1. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 898 (1985).
    [Crossref]
  2. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [Crossref]
  3. M. Moaveni, “Plane wave diffraction by dielectric gratings, finite-difference formulations,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
    [Crossref]
  4. Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).
  5. K. Yokomori, “Dielectric surface relief gratings with high diffraction efficiency,” Appl. Opt. 23, 2303–2310 (1984).
    [Crossref] [PubMed]
  6. S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. A 6, 1869–1883 (1989).
    [Crossref]
  7. H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

1989 (3)

M. Moaveni, “Plane wave diffraction by dielectric gratings, finite-difference formulations,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[Crossref]

S. T. Peng, “Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence,” J. Opt. Soc. Am. A 6, 1869–1883 (1989).
[Crossref]

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

1987 (1)

Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 898 (1985).
[Crossref]

1984 (1)

1983 (1)

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 898 (1985).
[Crossref]

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[Crossref]

Inokuchi, T.

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Kitabayashi, J.

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Koshiba, M.

Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).

Maeda, H.

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Moaveni, M.

M. Moaveni, “Plane wave diffraction by dielectric gratings, finite-difference formulations,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[Crossref]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 898 (1985).
[Crossref]

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[Crossref]

Nakata, Y.

Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).

Ohuchida, S.

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Peng, S. T.

Sumi, Y.

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Suzuki, M.

Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).

Yokomori, K.

Appl. Opt. (1)

Electron. Commun. Jpn. (1)

Y. Nakata, M. Koshiba, M. Suzuki, “Finite-element analysis of plane wave diffraction from dielectric gratings,” Electron. Commun. Jpn. 70, 42–52 (1987).

IEEE Trans. Antennas Propag. (1)

M. Moaveni, “Plane wave diffraction by dielectric gratings, finite-difference formulations,” IEEE Trans. Antennas Propag. 37, 1026–1031 (1989).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

H. Maeda, Y. Sumi, S. Ohuchida, J. Kitabayashi, T. Inokuchi, “A high density dual type grating for magneto-optical disk head,” Jpn. J. Appl. Phys. 28, 193–195 (1989).

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 898 (1985).
[Crossref]

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Figures (13)

Fig. 1
Fig. 1

Scanning electron micrograph of grating lines etched into quartz substrate (ns = 1.46).

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Theoretical model of plane-wave scattering by a grating.

Fig. 4
Fig. 4

Results of dispersion calculation for TE and TM incident light on a multilayer stack: (a) period d = 0.36 μm, (b) period d = 0.6 μm.

Fig. 5
Fig. 5

Experimental and theoretical results of variation of diffraction efficiency versus incident angle. Grating period d = 0.36 μm, grating depth tg = 0.68 μm.

Fig. 6
Fig. 6

Variation of diffraction efficiency versus grating depth for TE incidence. Grating period d = 0.36 and θ = 65°: (a) experimental results, (b) theoretical results.

Fig. 7
Fig. 7

Variation of diffraction efficiency versus grating depth for TM incidence. Grating period d = 0.36 μm and θ = 65°: (a) experimental results, (b) theoretical results.

Fig. 8
Fig. 8

Variation of diffraction efficiency versus grating period for TE incidence. Grating depth tg = 0.7 μm and θ = 65°: (a) experimental results, (b) theoretical results.

Fig. 9
Fig. 9

Variation of diffraction efficiency versus grating period for TM incidence. Grating depth tg = 0.7 μm and θ = 65°: (a) experimental results, (b) theoretical results.

Fig. 10
Fig. 10

Theoretical results of variation of diffraction efficiency versus wavelength for grating period d = 0.36 μm and tg = 0.68 μm: (a) TE incidence, (b) TM incidence.

Fig. 11
Fig. 11

Experimental measurement of diffraction efficiency with polarization angle; λ = 0.6328 μm, θ = 65°, d = 0.36 μm, and tg = 0.7 μm.

Fig. 12
Fig. 12

Diffraction efficiency versus incident angle: λ = 0.6328 μm, d = 0.5 μm, n1 = 1.53, n2 = 1.50, and tg = 15 μm.

Fig. 13
Fig. 13

Diffraction efficiency versus grating depth for TE and TM polarizations: λ = 0.6328 μm, θ = 39.25°, d = 0.5 μm, n1 = 1.04, and n2 = 1.0.

Equations (11)

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k x = k 0 sin θ 0 ,             k z = k 0 cos θ 0 ,
k x n = k x + 2 n π / d for n = , - 2 , - 1 , 0 , 1 , 2 , ,
sin θ n = sin θ 0 + n λ / d
E ( x ) = exp ( - j k x x ) n E n exp [ - j ( 2 n π / d ) x ] ,
cos k x d = cos κ 1 d 1 cos κ 2 d 2 - 1 2 ( Z 1 Z 2 + Z 2 Z 1 ) sin κ 1 d 1 sin κ 2 d 2 ,
κ i = ( k 0 2 ɛ i - k z 2 ) 1 / 2 ,
Z i = ω μ 0 / κ i for TE modes , Z i = κ i / ω 0 i for TM modes ,
Δ k z = 4 Δ ɛ λ ɛ ave [ 1 - ( λ 2 d ) 2 ] - 1 / 2             for TE polarization ,
Δ k z = 4 Δ ɛ λ ɛ ave [ 1 - ( λ 2 d ) 2 ] 1 / 2             for TM polarization ,
E ( x , z ) cos π k x x sin Δ k z z ,
L = π / Δ k z .

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