Abstract

Utilization of second-, third-, and fourth-order diffraction is discussed for providing a single reflection grating lens that yields the same wave-front conversions for wavelengths of 420, 280, and 210 nm, which are used to sense NOx and SO2 gas densities. A blazed grating lens was fabricated by a planar process and characterized by use of UV lamps. The same wave-front conversion was observed at the three UV wavelengths. Efficiencies were measured to be 80%, 70%, and 30% for second-, third-, and fourth-order diffractions, respectively, at wavelengths of 420, 280, and 210 nm, respectively.

© 1999 Optical Society of America

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References

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  1. D. W. Sweeney, G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. 34, 2469–2475 (1995).
    [CrossRef] [PubMed]
  2. D. Faklis, G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462–2468 (1995).
    [CrossRef] [PubMed]
  3. J. A. Furthey, M. Beal, S. Saxe, “Superzone diffractive optics,” in OSA Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.
  4. R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
    [CrossRef]
  5. T. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
    [CrossRef] [PubMed]
  6. H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1.
    [CrossRef]
  7. T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-apertured micro-Fresnel lens arrays fabricated by electron-beam lithography,” Appl. Opt. 26, 587–591 (1987).
    [CrossRef] [PubMed]
  8. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4.

1995 (2)

1993 (1)

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

1987 (1)

1982 (1)

Beal, M.

J. A. Furthey, M. Beal, S. Saxe, “Superzone diffractive optics,” in OSA Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Bennett, J. M.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4.

Faklis, D.

Fujita, T.

Furthey, J. A.

J. A. Furthey, M. Beal, S. Saxe, “Superzone diffractive optics,” in OSA Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Koyama, J.

Kunz, R. E.

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4.

Morris, G. M.

Nishihara, H.

T. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
[CrossRef] [PubMed]

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1.
[CrossRef]

Rossi, M.

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

Saxe, S.

J. A. Furthey, M. Beal, S. Saxe, “Superzone diffractive optics,” in OSA Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Setsune, K.

Shiono, T.

Sommargren, G. E.

Suhara, T.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1.
[CrossRef]

Sweeney, D. W.

Wasa, K.

Yamazaki, O.

Appl. Opt. (3)

Opt. Commun. (1)

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

Opt. Lett. (1)

Other (3)

J. A. Furthey, M. Beal, S. Saxe, “Superzone diffractive optics,” in OSA Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1.
[CrossRef]

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), Chap. 4.

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Figures (7)

Fig. 1
Fig. 1

Example configuration of a gas-sensing head that uses a grating lens with three UV wavelengths.

Fig. 2
Fig. 2

Schematic view of a reflection-type grating lens.

Fig. 3
Fig. 3

Cross-sectional view of a blazed grating and an imaginary flat reflection surface constructed by means of shifting each blazed segment by mt along the z direction and connecting them.

Fig. 4
Fig. 4

Theoretical prediction of the wavelength dependence of the qth-order diffraction efficiency.

Fig. 5
Fig. 5

Microphotograph of a cross section of the grating lens, cleaved after characterization.

Fig. 6
Fig. 6

Focal-spot position of the wave as a result of qth-order diffraction. The open circles represent the measurements, and the solid curves indicate the theoretical predictions.

Fig. 7
Fig. 7

Measured diffraction efficiency at several wavelengths. The single-line bars show the second-order diffraction; the double-line bars show the third-order diffraction; the triple-line (solid-appearing) bars show the fourth-order diffraction. The solid curves represent the calculated results with the tooth profile of Eq. (4). The dashed curve shows an efficiency-reduction factor calculated by use of a surface-scattering model.

Equations (5)

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ψGx, y=2π/λ1ΦDFx, y-ΦINx, y=2mπ+constant,
ΦINx, y=x2+y+fIN sin θIN2+fIN cos θIN21/2, ΦDFx, y=-x2+y-fDF sin θDF2+fDF cos θDF21/2,
expj2π/λ2ΦDFx, y=expjqψGx, yexpj2π/λ2ΦINx, y.
η=1Λ0Λexpj2π cos θIN+cos θDFλ fGy-2qπ yΛdy2.
fGy=t yΛ0y<0.8Λ0.8t0.8Λy<0.9Λ8t1-yΛ0.9ΛyΛ.

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