Abstract

The performance characteristics of focusing diffractive mirrors designed with various methods are evaluated by using the rigorous boundary element method. Quantitative results are presented for (1) conventional-zero-thickness mirror designs, (2) alternative-zero-thickness designs that incorporate an off-axis correction factor and (3) finite-thickness designs. For TM polarization, the mirrors designed by using the alternative-zero-thickness method perform considerably worse than those designed by using the conventional-zero-thickness method, which contradicts predictions made in an earlier paper [J. Opt. Soc. Am. A 17, 1132 (2000)].

© 2001 Optical Society of America

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References

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  1. Feature issue on diffractive optics applications, Appl. Opt. 34, 2399–2559 (1995).
  2. J. M. Bendickson, E. M. Glytsis, T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
    [CrossRef]
  3. M. Testorf, “On the zero-thickness model of diffractive optical elements,” J. Opt. Soc. Am. A 17, 1132–1133 (2000).
    [CrossRef]
  4. V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
    [CrossRef]
  5. D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
    [CrossRef] [PubMed]
  6. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
    [CrossRef]
  7. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
    [CrossRef]
  8. E. N. Glytsis, M. E. Harrigan, K. Hirayama, T. K. Gaylord, “Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation,” Appl. Opt. 37, 34–43 (1998).
    [CrossRef]
  9. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
    [CrossRef]
  10. D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).
    [CrossRef]
  11. G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

2000 (1)

1999 (1)

1998 (2)

1997 (3)

1996 (1)

1995 (1)

1989 (1)

Bendickson, J. M.

Buralli, D. A.

Gaylord, T. K.

Glytsis, E. M.

Glytsis, E. N.

Hadley, L.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

Harrigan, M. E.

Hass, G.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

Hirayama, K.

Mait, J. N.

Mirotznik, M. S.

Moreno, V.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Morris, G. M.

Prather, D. W.

Rogers, J. R.

Román, J. F.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Salgueiro, J. R.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Testorf, M.

Am. J. Phys. (1)

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. A (6)

Other (1)

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

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Figures (5)

Fig. 1
Fig. 1

(a) Geometry used for the design and analysis of focusing diffractive cylindrical mirrors. The boundary Γ divides all space into the open, semi-infinite regions S1 with real refractive index n1 and S2 with complex refractive index n˜2. A wave is incident at an arbitrary angle α from region S1 and is to be focused by the metallic diffractive mirror to the point (xf,f), which makes an angle β with the positive y axis. The surface-relief profile of the metallic diffractive mirror is given by h(x). The quantity x0 gives the location of the center of the central Fresnel zone, and xm- and xm+ are Fresnel zone boundaries. (b) Geometry used to determine the surface-relief profile for the zero-thickness mirror design. The shaded gray strip represents an infinitesimally thin phase-shifting foil.

Fig. 2
Fig. 2

Normalized focal-plane intensity profiles for TE polarization and f/0.75 focusing diffractive mirrors designed for α=45° and β=0°, 25°, and 45°. The conventional-zero-thickness (γ=2), alternative-zero-thickness (γ=2 cos α), and finite-thickness design methods are compared.

Fig. 3
Fig. 3

Same as Fig. 2, but for TM polarization.

Fig. 4
Fig. 4

Normalized focal-plane intensity profiles for TE polarization and f/5 focusing diffractive mirrors designed for α=45° and β=0°, 25°, and 45°. The conventional-zero-thickness (γ=2), alternative-zero-thickness (γ=2 cosα), and finite-thickness design methods are compared.

Fig. 5
Fig. 5

Same as Fig. 4, but for TM polarization.

Equations (9)

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xm±=x0+[-mλ1sin α±(m2λ12+2mλ1f cos α)1/2]sec2 α.
hzt(x)=1γ{x sin α+[(x-xf)2+f2]1/2-f(cos α+tan β sin α)-mλ1}
for xm+xmin(xm+1+, D/2) ifxx0max(xm+1-, -D/2)xxm- ifxx0.
hft(x)=-B-B2-4AC2A,
A=sin2 α
B=-2f(1+cos2 α)-2(cos α)(f tan β sin α-x sin α+mλ1),
C=(x-f tan β)2+f2-(f cos α+f tan β sin α-x sin α+mλ1)2.
ϕinc(r1)=ϕ0w(x)exp(-jk1x sin α)exp(jk1y cos α),
r1S1,

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