Abstract

The application of thin-film Luneburg lenses to integrated optical circuits will require accurate control of their focal length to permit the necessary alignment between the various circuit elements. Of particular interest is the design of lenses for application to a silicon-based integrated optical rf spectrum analyzer. This study analyzes the sensitivity of the focal length of Luneburg lenses to thickness variation at the lens center resulting from fabrication process tolerances. It is shown that this sensitivity can be minimized by properly selecting the refractive index of the waveguide material, using a larger focal length and employing a longer optical wavelength.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. B. Anderson, IEEE Spectrum 15, 22 (1978).
  2. S. K. Yao, J. Appl. Phys. 50, 3390 (1979).
    [CrossRef]
  3. S. K. Yao et al., Appl. Opt. 18, 4067 (1979).
    [CrossRef] [PubMed]
  4. W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).
    [CrossRef]
  5. S. K. Yao, D. E. Thompson, Appl. Phys. Lett. 33, 635 (1978).
    [CrossRef]
  6. D. Mergerian et al., in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper ME4.
  7. E. Colombini, “Index profile computation for the generalized Luneburg lens,” to be published in J. Opt. Soc. Am.
  8. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [CrossRef] [PubMed]
  9. D. B. Anderson et al., IEEE J. Quantum Electron. QE-13, 268 (1977).
    [CrossRef]

1979 (2)

1978 (2)

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

D. B. Anderson, IEEE Spectrum 15, 22 (1978).

1977 (2)

D. B. Anderson et al., IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

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

1971 (1)

Anderson, D. B.

D. B. Anderson, IEEE Spectrum 15, 22 (1978).

D. B. Anderson et al., IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

Colombini, E.

E. Colombini, “Index profile computation for the generalized Luneburg lens,” to be published in J. Opt. Soc. Am.

Mergerian, D.

D. Mergerian et al., in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper ME4.

Southwell, W. H.

Thompson, D. E.

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

Tien, P. K.

Yao, S. K.

S. K. Yao et al., Appl. Opt. 18, 4067 (1979).
[CrossRef] [PubMed]

S. K. Yao, J. Appl. Phys. 50, 3390 (1979).
[CrossRef]

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

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

D. B. Anderson et al., IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

IEEE Spectrum (1)

D. B. Anderson, IEEE Spectrum 15, 22 (1978).

J. Appl. Phys. (1)

S. K. Yao, J. Appl. Phys. 50, 3390 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (2)

D. Mergerian et al., in Digest of Topical Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1980), paper ME4.

E. Colombini, “Index profile computation for the generalized Luneburg lens,” to be published in J. Opt. Soc. Am.

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 (8)

Fig. 1
Fig. 1

Cross section of the thin-film Luneburg lens and layered waveguide structure.

Fig. 2
Fig. 2

Normalized index profiles for generalized Luneburg lenses.

Fig. 3
Fig. 3

Effective index dependence on waveguide thickness for single-mode operation of thin-film guide and lens.

Fig. 4
Fig. 4

Optimum material index for waveguide lens which minimizes focal length sensitivity to thickness variations.

Fig. 5
Fig. 5

Single TE0 mode dispersion curves for varying normalized focal length.

Fig. 6
Fig. 6

Dependence of focal length on the overlay film thickness at the center of the Luneburg lens for varying optimum waveguide material index.

Fig. 7
Fig. 7

Evaluation of depth of focus from lens geometry.

Fig. 8
Fig. 8

Percent change in focal length at specific lens thickness tolerances assuming an optimum material index at each value of normalized focal length. Lens design constraints are indicated as horizontal lines.

Equations (9)

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

tan ( K 2 d + m π ) = K 2 ( γ 1 + γ 3 ) K 2 2 - γ 1 γ 3 ,
k 0 d = 1 ( n 2 2 - n 3 2 ) 1 / 2 [ tan - 1 ( n 3 2 - n 1 2 n 2 2 - n 3 2 ) 1 / 2 + π ] .
f ( n 2 ) = tan K 2 d - K 2 ( γ 1 + γ 3 ) K 2 2 - γ 1 γ 3 = 0 ,
Δ s Δ ( d / λ 0 ) = Δ s λ 0 Δ d .
Δ F = α λ 0 n g ( F a ) 2 ,
Δ F = Δ s ( D / 2 ) ,
N D = Δ s D 2 α λ 0 n g ( F a ) 2 1.
Δ s s F a 2 α λ 0 n g .
a = ( ν a ) / ( δ f ) ,

Metrics