Abstract

Thin film Fresnel lenses have been achieved on SiO2/Si substrates covered with a waveguide layer of Si3N4 grown by low pressure chemical vapor deposition (LPCVD). The phase shift between the different zones is induced by a SiO2 top layer chemically etched. The use of this additional layer having a smaller refractive index than the waveguide results in a saturation of the lens characteristics vs the thickness of the SiO2 layer; this feature associated with the good reproducibility of the LPCVD technology allows good control of the lens characteristics.

© 1981 Optical Society of America

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References

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  1. S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33, 307 (1978).
    [CrossRef]
  2. W. H. Southwell, J. Opt. So. Am. 67, 1004 (1977).
    [CrossRef]
  3. W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).
    [CrossRef]
  4. G. E. Betts, J. C. Bradley, G. E. Marx, D. C. Schubert, H. A. Trenchard, Appl. Opt. 17, 2346 (1978).
    [CrossRef] [PubMed]
  5. G. C. Righini, V. Russo, S. Sottini, G. Toraldo di Francia, Appl. Opt. 12, 1477 (1973).
    [CrossRef] [PubMed]
  6. B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
    [CrossRef]
  7. D. Kassai, E. Marom, J. Opt. Soc. Am. 69, 1242 (1979).
    [CrossRef]
  8. A. Naumaan, J. T. Boyd, Appl. Phys. Lett. 35, 324 (1979).
    [CrossRef]
  9. P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
    [CrossRef]
  10. G. I. Hatakoshi, S. I. Tanaka, Opt. Lett. 2, 142 (1978).
    [CrossRef] [PubMed]
  11. S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
    [CrossRef]
  12. A. Papoulis, Systems and Transforms with Application in Optics (McGraw-Hill, New York, 1968).

1979 (2)

A. Naumaan, J. T. Boyd, Appl. Phys. Lett. 35, 324 (1979).
[CrossRef]

D. Kassai, E. Marom, J. Opt. Soc. Am. 69, 1242 (1979).
[CrossRef]

1978 (5)

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

G. I. Hatakoshi, S. I. Tanaka, Opt. Lett. 2, 142 (1978).
[CrossRef] [PubMed]

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33, 307 (1978).
[CrossRef]

G. E. Betts, J. C. Bradley, G. E. Marx, D. C. Schubert, H. A. Trenchard, Appl. Opt. 17, 2346 (1978).
[CrossRef] [PubMed]

1977 (3)

W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).
[CrossRef]

W. H. Southwell, J. Opt. So. Am. 67, 1004 (1977).
[CrossRef]

B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
[CrossRef]

1973 (1)

Anderson, D. B.

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33, 307 (1978).
[CrossRef]

Ashley, P. R.

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

Betts, G. E.

Boyd, J. T.

A. Naumaan, J. T. Boyd, Appl. Phys. Lett. 35, 324 (1979).
[CrossRef]

Bradley, J. C.

Chang, W. S. C.

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

Chen, B.

B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
[CrossRef]

Hatakoshi, G. I.

Kassai, D.

Lee, A.

B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
[CrossRef]

Marom, E.

D. Kassai, E. Marom, J. Opt. Soc. Am. 69, 1242 (1979).
[CrossRef]

B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
[CrossRef]

Marx, G. E.

Naumaan, A.

A. Naumaan, J. T. Boyd, Appl. Phys. Lett. 35, 324 (1979).
[CrossRef]

Papoulis, A.

A. Papoulis, Systems and Transforms with Application in Optics (McGraw-Hill, New York, 1968).

Righini, G. C.

Russo, V.

Schubert, D. C.

Sottini, S.

Southwell, W. H.

W. H. Southwell, J. Opt. So. Am. 67, 1004 (1977).
[CrossRef]

W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).
[CrossRef]

Tanaka, S. I.

Thompson, D. E.

S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

Toraldo di Francia, G.

Trenchard, H. A.

Yao, S. K.

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33, 307 (1978).
[CrossRef]

S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (5)

B. Chen, E. Marom, A. Lee, Appl. Phys. Lett. 31, 263 (1977).
[CrossRef]

A. Naumaan, J. T. Boyd, Appl. Phys. Lett. 35, 324 (1979).
[CrossRef]

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
[CrossRef]

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33, 307 (1978).
[CrossRef]

J. Opt. So. Am. (1)

W. H. Southwell, J. Opt. So. Am. 67, 1004 (1977).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (1)

A. Papoulis, Systems and Transforms with Application in Optics (McGraw-Hill, New York, 1968).

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Figures (8)

Fig. 1
Fig. 1

Schematic drawing of the digitized Fresnel lens.

Fig. 2
Fig. 2

Theoretical effective index change of the waveguide mode vs the SiO2 overlayer thickness (λ = 0.6328 μm).

Fig. 3
Fig. 3

Theoretical effective index change and corresponding additional absorption of the waveguide mode vs the aluminum overlayer thickness. In these two figures the waveguide structure is: Si refractive index at 0.6328μm: n = 3.85–0.07i, thickness ∞; SiO2: n = 1.458, thickness 1.2 μm; Si3N4: n = 1.975, thickness 0.165 μm.

Fig. 4
Fig. 4

Theoretical maximum effective index change of the waveguide mode induced by the SiO2 overlayer vs the Si3N4 film thickness and corresponding length L of the Fresnel zones.

Fig. 5
Fig. 5

Theoretical intensity distribution in the focal line for (a) a perfect digitized Fresnel lens and for (b) digitized Fresnel lenses exhibiting an underetching and (c) overetching error of 0.5 μm (N.A., 0.1).

Fig. 6
Fig. 6

Theoretical intensity distribution in the focal line for (a) a perfect digitized Fresnel lens (c) and for (b) digitized Fresnel lenses exhibiting an underetching and (c) overetching error of 0.5 μm (N.A., 0.3).

Fig. 7
Fig. 7

Observed focusing effect.

Fig. 8
Fig. 8

Experimental intensity distribution of the digitized Fresnel lens in the focal line.

Tables (1)

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Table I Computed Characteristics of the Focal Line vs the Numerical Aperture and Etching Error of a Digitized Fresnel Lens

Equations (2)

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2 π λ 0 · L · Δ n eff = π ,
U ( P 0 ) = | exp [ j ( π / 4 ) ] 2 λ + V ( x ) ( 1 + z 0 ρ ) exp ( j k ρ ) ρ d x | 2 ,

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