Abstract

We propose achromatic quarter-wave plates of a subwavelength grating structure. When the period of the grating structure is smaller than the wavelengths of the incident light, the structure is considered to be an optically anisotropic medium. The effective refractive indices strongly depend on the wavelengths, especially when the period is close to the wavelength. Using this feature, we can design a grating quarter-wave plate whose phase retardation is maintained at π/2 for a wide wavelength range. A design method using the effective medium theory is described, and the wave plates designed were evaluated by numerical calculation with a rigorous electromagnetic grating theory. The calculation results led to the possibility of an achromatic quarter-wave plate whose retardation errors are smaller than 3° for a ±10% change in wavelength.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. For example, M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), p. 705.
  2. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [CrossRef] [PubMed]
  3. S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multi-layer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 241–250 (1991).
    [CrossRef]
  4. F. T. Chen, H. G. Craighead, “Diffractive phase elements based on two-dimensional artificial dielectrics,” Opt. Lett. 20, 121–123 (1995).
    [CrossRef] [PubMed]
  5. M. E. Warren, R. E. Smith, G. A. Vawter, J. R. Wendt, “High-efficiency subwavelength diffractive optical element in GaAs for 975 nm,” Opt. Lett. 20, 1441–1443 (1995).
    [CrossRef] [PubMed]
  6. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  7. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  8. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter wave plates,” Appl. Opt. 29, 3286–3290 (1990).
    [CrossRef] [PubMed]
  9. A. Yariv, P. Yhe, Optical Waves in Crystals (Wiley, New York, 1984), pp. 165–174.
  10. C. W. Haggans, L. Li, R. K. Kostuk, “Effective-medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993).
    [CrossRef]
  11. H. Kikuta, H. Yoshida, K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
    [CrossRef]
  12. D. H. Raguin, G. H. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  13. K. Matsumoto, K. Rokushima, J. Yamakita, “Three-dimensional rigorous analysis of dielectric grating wave guides for general cases oblique propagation,” J. Opt. Soc. Am. A 10, 269–276 (1993).
    [CrossRef]
  14. P. Blair, M. R. Taghizadeh, W. Parkes, C. D. W. Wilkinson, “High-efficiency binary fan-out gratings by modulation of a high-frequency carrier grating,” Appl. Opt. 34, 2406–2413 (1995).
    [CrossRef] [PubMed]
  15. For example, Z. Zhou, T. J. Drabik, “Optimized binary phase-only diffractive element with subwavelength features for 1.55 µm,” J. Opt. Soc. Am. A12, 1104–1112 (1995).

1995 (5)

1993 (3)

1990 (1)

1987 (1)

1983 (2)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef] [PubMed]

Aoyama, S.

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multi-layer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 241–250 (1991).
[CrossRef]

Blair, P.

Born, M.

For example, M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), p. 705.

Case, S. K.

Cescato, L. H.

Chen, F. T.

Craighead, H. G.

Drabik, T. J.

For example, Z. Zhou, T. J. Drabik, “Optimized binary phase-only diffractive element with subwavelength features for 1.55 µm,” J. Opt. Soc. Am. A12, 1104–1112 (1995).

Enger, R. C.

Flanders, D. C.

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Gluch, E.

Haggans, C. W.

Iwata, K.

H. Kikuta, H. Yoshida, K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Kikuta, H.

H. Kikuta, H. Yoshida, K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Kimura, Y.

Kostuk, R. K.

Li, L.

Matsumoto, K.

Morris, G. H.

Nishida, N.

Ohta, Y.

Ono, Y.

Parkes, W.

Raguin, D. H.

Rokushima, K.

Smith, R. E.

Streibl, N.

Taghizadeh, M. R.

Vawter, G. A.

Warren, M. E.

Wendt, J. R.

Wilkinson, C. D. W.

Wolf, E.

For example, M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), p. 705.

Yamakita, J.

Yamashita, T.

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multi-layer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 241–250 (1991).
[CrossRef]

Yariv, A.

A. Yariv, P. Yhe, Optical Waves in Crystals (Wiley, New York, 1984), pp. 165–174.

Yhe, P.

A. Yariv, P. Yhe, Optical Waves in Crystals (Wiley, New York, 1984), pp. 165–174.

Yoshida, H.

H. Kikuta, H. Yoshida, K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Zhou, Z.

For example, Z. Zhou, T. J. Drabik, “Optimized binary phase-only diffractive element with subwavelength features for 1.55 µm,” J. Opt. Soc. Am. A12, 1104–1112 (1995).

Appl. Opt. (5)

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

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

Opt. Lett. (2)

Opt. Rev. (1)

H. Kikuta, H. Yoshida, K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2, 92–99 (1995).
[CrossRef]

Other (3)

A. Yariv, P. Yhe, Optical Waves in Crystals (Wiley, New York, 1984), pp. 165–174.

For example, M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), p. 705.

S. Aoyama, T. Yamashita, “Grating beam splitting polarizer using multi-layer resist method,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 241–250 (1991).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Light wave propagating along the lamellar plates in a one-dimensional periodic structure. Its wave number is β. The lamellae have thicknesses a and b, Λ = a + b, with refractive indices n 1 and n 2 respectively. The duty cycle α is defined as b/Λ in case n 1 < n 2.

Fig. 2
Fig. 2

Dispersion of effective refractive indices: (a) dependence of the effective refractive indices on normalized wavelengths, (b) differences in the effective indices. n 1 = 1.0, n 2 = 2.0, Λ = 0.4λ0, and α = 0.7.

Fig. 3
Fig. 3

Ideal refractive–index difference for the broadband quarter–wave plate: h, wave-plate thickness.

Fig. 4
Fig. 4

Index difference curve tangent to an ideal dispersion line.

Fig. 5
Fig. 5

Index difference curves with respect to duty cycle α and some ideal dispersion curves.

Fig. 6
Fig. 6

Lamellar subwavelength gratings: (a) simple lamellar grating, (b) gating structure sandwiched by materials whose refractive indices are near the effective refractive indices of the periodic structure, (c) quasi-sandwich structure.

Fig. 7
Fig. 7

Performance of the simple lamellar grating: (a) phase retardation, (b) transmittances of the TE and TM waves with respect to wavelength. n 1 = 1.0, n 2 = 2.0, Λ = 0.4λ0, α = 0.7, h = 1.146.

Fig. 8
Fig. 8

Performance of the sandwiched grating with a duty cycle of 0.7. (a) phase retardation, (b) transmittance. The refractive indices of the upper and lower material are n 0 = n 3 = 1.8. Other parameters are the same as those in Fig. 7.

Fig. 9
Fig. 9

Performance of the sandwiched grating with a duty cycle of 0.8: (a) phase retardation, (b) transmittance. n 1 = 1.0, n 2 = 2.0, n 0 = n 3 = 1.8; Λ = 0.4λ0, α = 0.8, h = 1.49.

Fig. 10
Fig. 10

Performance of the sandwiched grating with a duty cycle of 0.8: (a) phase retardation, (b) transmittance. n 1 = 1.0, n 2 = 2.0, n 0 = n 3 = 1.8; Λ = 0.4λ0, α = 0.8, h = 1.49.

Fig. 11
Fig. 11

Dependence of phase retardation on the angle of incidence with the normal of the grating plate. The incident rays lie on the plane containing the normal and the grating vector.

Fig. 12
Fig. 12

Phase retardation for different groove depths. Other parameters are the same as those in Fig. 10.

Fig. 13
Fig. 13

Phase retardation for different duty cycles. Other parameters are the same as those in Fig. 10.

Equations (5)

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

neff=cω β,
k1z=n1ωc2-β21/2, k2z=n2ωc2-β21/2,
1=cos k1za cos k2zb-12k2zk1z+k1zk2zsin k1za sin k2zb,
1=cos k1za cos k2zb-12n22k2 zn12k1z+n12k1zn22k2z×sin k1za sink2zb.
Δnλ=λ4h,

Metrics