Abstract

Both continuously tapered and discrete multilevel subwavelength grating structures are examined to determine the optimum method of designing antireflection surfaces. Continuously tapered gratings are designed with use of the optimal Klopfenstein graded index technique, while discrete multilevel stair-step gratings are designed with use of the Tschebyscheff quarter-wave synthesis technique. It is shown that a continuous design is always deeper than a discrete design. It is determined that since a subwavelength grating structure produces a bandpass surface, the high-pass (short-wave) performance of the continuous taper design cannot be realized. Therefore the discrete method of designing antireflection subwavelength gratings will always produce a shallower spatial profile or a smaller aspect ratio for any specified maximum reflection threshold level over a given passband.

© 1996 Optical Society of America

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References

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  1. R. E. Collins, Foundations for Microwave Engineering (McGraw Hill, New York, 1966), Chap. 5, pp. 221–254.
  2. Henry J. Riblet, “General synthesis of quarter-wave impedance transformers,” IRE Trans. on Microwave Theory Techniques MTT-5, 36–43 (1957).
    [Crossref]
  3. Leo Young, “Synthesis of multiple antireflection films over a prescribed band,” J. Opt. Soc. Am. 51, 967–974 (1961).
    [Crossref]
  4. R. W. Klopfenstein, “A transmission line taper of improved design,” Proc. IRE 44, 31–35 (January1956).
    [Crossref]
  5. D. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [Crossref] [PubMed]
  6. D. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
    [Crossref] [PubMed]
  7. W. Stork, N. Striebl, H. Hainer, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
    [Crossref] [PubMed]
  8. Y. Ono, Y. Kimura, Y. Ohta, N. Nishida, “Antireflection effect in ultrahigh spatial-frequency holographic relief gratings,” Appl. Opt. 26, 1142–1146 (1987).
    [Crossref] [PubMed]
  9. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [Crossref] [PubMed]
  10. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [Crossref] [PubMed]
  11. D. C. Flanders, “Submicrometer periodicity gratings as artificial anisotropic dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [Crossref]
  12. C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. 10, 2217–2225 (1993).
    [Crossref]
  13. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).
  14. Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
    [Crossref]
  15. M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE883, 8–11 (1988).
    [Crossref]
  16. 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]
  17. E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
    [Crossref]

1995 (1)

E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
[Crossref]

1994 (1)

Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
[Crossref]

1993 (3)

1992 (1)

1991 (1)

1987 (1)

1986 (1)

1983 (2)

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

1961 (1)

1957 (1)

Henry J. Riblet, “General synthesis of quarter-wave impedance transformers,” IRE Trans. on Microwave Theory Techniques MTT-5, 36–43 (1957).
[Crossref]

1956 (2)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

R. W. Klopfenstein, “A transmission line taper of improved design,” Proc. IRE 44, 31–35 (January1956).
[Crossref]

Baird, W. E.

Collins, R. E.

R. E. Collins, Foundations for Microwave Engineering (McGraw Hill, New York, 1966), Chap. 5, pp. 221–254.

Flanders, D. C.

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

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
[Crossref]

Grann, Eric B.

Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
[Crossref]

Haggans, C. W.

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. 10, 2217–2225 (1993).
[Crossref]

Hainer, H.

Kimura, Y.

Kipfer, P.

Klopfenstein, R. W.

R. W. Klopfenstein, “A transmission line taper of improved design,” Proc. IRE 44, 31–35 (January1956).
[Crossref]

Kostuk, R. K.

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. 10, 2217–2225 (1993).
[Crossref]

Li, L.

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. 10, 2217–2225 (1993).
[Crossref]

Moharam, M. G.

E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
[Crossref]

Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
[Crossref]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[Crossref] [PubMed]

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]

M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE883, 8–11 (1988).
[Crossref]

Morris, G. M.

Nishida, N.

Ohta, Y.

Ono, Y.

Pommet, Drew A.

E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
[Crossref]

Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
[Crossref]

Raguin, D.

Riblet, Henry J.

Henry J. Riblet, “General synthesis of quarter-wave impedance transformers,” IRE Trans. on Microwave Theory Techniques MTT-5, 36–43 (1957).
[Crossref]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Stork, W.

Striebl, N.

Young, Leo

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]

IRE Trans. on Microwave Theory Techniques (1)

Henry J. Riblet, “General synthesis of quarter-wave impedance transformers,” IRE Trans. on Microwave Theory Techniques MTT-5, 36–43 (1957).
[Crossref]

J. Opt. Soc. Am. (5)

Leo Young, “Synthesis of multiple antireflection films over a prescribed band,” J. Opt. Soc. Am. 51, 967–974 (1961).
[Crossref]

C. W. Haggans, L. Li, R. K. Kostuk, “Effective medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. 10, 2217–2225 (1993).
[Crossref]

Eric B. Grann, M. G. Moharam, Drew A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. 11, 2695–2703 (1994).
[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]

E. B. Grann, M. G. Moharam, Drew A. Pommet, “Optimal design for antireflective tapered two-dimensional subwavelength grating structures,” J. Opt. Soc. Am. 12, 333–339 (1995).
[Crossref]

Opt. Lett. (1)

Proc. IRE (1)

R. W. Klopfenstein, “A transmission line taper of improved design,” Proc. IRE 44, 31–35 (January1956).
[Crossref]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–474 (1956).

Other (2)

M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE883, 8–11 (1988).
[Crossref]

R. E. Collins, Foundations for Microwave Engineering (McGraw Hill, New York, 1966), Chap. 5, pp. 221–254.

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Figures (6)

Fig. 1
Fig. 1

Power spectrum for a Klopfenstein taper (continuous) and a Tschebyscheff quarter-wave transformer (discrete), with two and six layers, versus normalized depth. (b) is an enlargement of the lower left-hand part of (a).

Fig. 2
Fig. 2

Klopfenstein tapered subwavelength grating structure profile.

Fig. 3
Fig. 3

Five-layer (six-level) subwavelength grating structure profile.

Fig. 4
Fig. 4

Reflectivity as function of wavelength for the Klopfenstein tapered subwavelength grating structure as well as the ideal inhomogeneous thin film structure.

Fig. 5
Fig. 5

Reflectivity as function of the wavelength for the discrete six-level (five-layer) stair-step subwavelength grating structure as well as the ideal five-layer thin film layer.

Fig. 6
Fig. 6

Reflectivity as function of angle of incidence for both the continuous and the discrete (five-layer) design subwavelength grating structures.

Tables (2)

Tables Icon

Table 1 Normalized Depth and Normalized Minimum Wavelength Bandwidth for Several Multilayer Discrete and Continuous Klopfenstein AR Design Techniques

Tables Icon

Table 2 Depth, Effective Refractive Index, and the Grating Duty Cycle for Each Layer of the Six-Level (Five-Layer) Discrete SWG Structure

Equations (2)

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Λ max λ min n s + n i sin θ i ,
Λ max = λ min n s + n i = 0.75 μ m .

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