Abstract

With computer-aided design and a digital-controlled lathe, shadow sputtering masks have been made with precisely tailored contour for the fabrication of guided-wave optical thin-film Luneburg lenses. Nearly diffraction-limited performance has been obtained reproducibly for a family of thin-film circular lenses ranging between F/4 and F/30 derived from generalized thin-film Luneburg lens profiles when only the center portion of the lens aperture is employed, in good agreement with numerical ray-tracing results. Both the design and construction of the mask and the analytical as well as experimental results of the thin-film generalized Luneburg lenses are reported. In addition, the fabrication tolerance for this guided-wave optical lens system is described.

© 1979 Optical Society of America

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References

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  1. D. B. Anderson, R. R. August, Trans. IECE Jpn E61, 140 (1978).
  2. D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
    [Crossref]
  3. M. C. Hamilton, D. A. Wille, W. J. Miceli, An Integrated Optical RF Spectrum Analyser, in Proceedings of the IEEE Ultrasonics Symposium (IEEE, New York, 1976), p. 218.
  4. R. Shubert, J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).
    [Crossref]
  5. F. Zernike, Opt. Commun. 12, 379 (1974).
    [Crossref]
  6. S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33(4), 307 (1978).
    [Crossref]
  7. G. C. Righini, V. Russo, S. Sottini, G. T. di Francia, Appl. Opt. 12, 1477 (1973).
    [Crossref] [PubMed]
  8. F. E. Vahey, V. E. Wood, IEEE J. Quantum Electron. QE-13, 129 (1977).
    [Crossref]
  9. D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.
  10. G. E. Betts, G. E. Marx, Appl. Opt. 17, 3969 (1978).
    [Crossref] [PubMed]
  11. R. K. Luneburg, The Mathematical Theory of Optics (U. California Press, Berkeley, 1954).
  12. S. E. Miller, IEEE J. Quantum Electron. QE-8, 199 (1972).
    [Crossref]
  13. W. H. Southwell, J. Opt. Soc. Am. 67, 1010 (1977).
    [Crossref]
  14. S. P. Morgan, J. Appl. Phys. 29, 1358 (1958).
    [Crossref]
  15. S. K. Yao, J. Appl. Phys. 50, 3390 (1979).
    [Crossref]
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), p. 137.
  17. T. C. Lee, J. D. Zook, IEEE J. Quantum Electron. QE-4, 442 (1968).
    [Crossref]
  18. E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

1979 (2)

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

E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

1978 (3)

D. B. Anderson, R. R. August, Trans. IECE Jpn E61, 140 (1978).

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33(4), 307 (1978).
[Crossref]

G. E. Betts, G. E. Marx, Appl. Opt. 17, 3969 (1978).
[Crossref] [PubMed]

1977 (3)

F. E. Vahey, V. E. Wood, IEEE J. Quantum Electron. QE-13, 129 (1977).
[Crossref]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

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

1974 (1)

F. Zernike, Opt. Commun. 12, 379 (1974).
[Crossref]

1973 (1)

1972 (1)

S. E. Miller, IEEE J. Quantum Electron. QE-8, 199 (1972).
[Crossref]

1971 (1)

1968 (1)

T. C. Lee, J. D. Zook, IEEE J. Quantum Electron. QE-4, 442 (1968).
[Crossref]

1958 (1)

S. P. Morgan, J. Appl. Phys. 29, 1358 (1958).
[Crossref]

Anderson, D. B.

D. B. Anderson, R. R. August, Trans. IECE Jpn E61, 140 (1978).

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33(4), 307 (1978).
[Crossref]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

August, R. R.

D. B. Anderson, R. R. August, Trans. IECE Jpn E61, 140 (1978).

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

Barnoski, M. K.

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

Betts, G. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), p. 137.

Boyd, J. T.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

Chen, B.

E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

di Francia, G. T.

Hamilton, M. C.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

M. C. Hamilton, D. A. Wille, W. J. Miceli, An Integrated Optical RF Spectrum Analyser, in Proceedings of the IEEE Ultrasonics Symposium (IEEE, New York, 1976), p. 218.

Harris, J. H.

Kassai, D.

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

Lee, T. C.

T. C. Lee, J. D. Zook, IEEE J. Quantum Electron. QE-4, 442 (1968).
[Crossref]

Luneburg, R. K.

R. K. Luneburg, The Mathematical Theory of Optics (U. California Press, Berkeley, 1954).

Marom, E.

E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

Marx, G. E.

Miceli, W. J.

M. C. Hamilton, D. A. Wille, W. J. Miceli, An Integrated Optical RF Spectrum Analyser, in Proceedings of the IEEE Ultrasonics Symposium (IEEE, New York, 1976), p. 218.

Miller, S. E.

S. E. Miller, IEEE J. Quantum Electron. QE-8, 199 (1972).
[Crossref]

Morgan, S. P.

S. P. Morgan, J. Appl. Phys. 29, 1358 (1958).
[Crossref]

Ramer, O. G.

E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

Righini, G. C.

Russo, V.

Shubert, R.

Sottini, S.

Southwell, W. H.

Vahey, F. E.

F. E. Vahey, V. E. Wood, IEEE J. Quantum Electron. QE-13, 129 (1977).
[Crossref]

Wille, D. A.

M. C. Hamilton, D. A. Wille, W. J. Miceli, An Integrated Optical RF Spectrum Analyser, in Proceedings of the IEEE Ultrasonics Symposium (IEEE, New York, 1976), p. 218.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), p. 137.

Wood, V. E.

F. E. Vahey, V. E. Wood, IEEE J. Quantum Electron. QE-13, 129 (1977).
[Crossref]

Yao, S. K.

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

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33(4), 307 (1978).
[Crossref]

Zernike, F.

F. Zernike, Opt. Commun. 12, 379 (1974).
[Crossref]

Zook, J. D.

T. C. Lee, J. D. Zook, IEEE J. Quantum Electron. QE-4, 442 (1968).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. K. Yao, D. B. Anderson, Appl. Phys. Lett. 33(4), 307 (1978).
[Crossref]

IEEE J. Quantum Electron. (4)

F. E. Vahey, V. E. Wood, IEEE J. Quantum Electron. QE-13, 129 (1977).
[Crossref]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, IEEE J. Quantum Electron., QE-13, 268 (1977).
[Crossref]

T. C. Lee, J. D. Zook, IEEE J. Quantum Electron. QE-4, 442 (1968).
[Crossref]

S. E. Miller, IEEE J. Quantum Electron. QE-8, 199 (1972).
[Crossref]

J. Appl. Phys. (2)

S. P. Morgan, J. Appl. Phys. 29, 1358 (1958).
[Crossref]

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

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

F. Zernike, Opt. Commun. 12, 379 (1974).
[Crossref]

Opt. Eng. (1)

E. Marom, B. Chen, O. G. Ramer, Opt. Eng. 18, 79 (1979).

Trans. IECE Jpn (1)

D. B. Anderson, R. R. August, Trans. IECE Jpn E61, 140 (1978).

Other (4)

M. C. Hamilton, D. A. Wille, W. J. Miceli, An Integrated Optical RF Spectrum Analyser, in Proceedings of the IEEE Ultrasonics Symposium (IEEE, New York, 1976), p. 218.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), p. 137.

D. Kassai, B. Chen, E. Marom, O. G. Ramer, M. K. Barnoski, in Digest of Topical Meeting on Integrated and Guided Wave Optics (Optical Society of America, Washington, D.C., 1978), paper MA2-1.

R. K. Luneburg, The Mathematical Theory of Optics (U. California Press, Berkeley, 1954).

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Figures (24)

Fig. 1
Fig. 1

(a) Ray trajectories through a generalized Luneburg lens. (b) Cross section of a waveguide Luneburg lens using an overlay thin film of high index of refraction material.

Fig. 2
Fig. 2

Cross section of rf sputtering deposition system used for Luneburg lens fabrication.

Fig. 3
Fig. 3

Cross section of the multilayer thin-film optical waveguide structure employed in theoretical treatment.

Fig. 4
Fig. 4

Dispersion characteristics of Ta2O5 waveguide on oxidized silicon.

Fig. 5
Fig. 5

Dispersion characteristics of 7059-glass waveguide on oxidized silicon.

Fig. 6
Fig. 6

Dispersion characteristics of 0.75-μm-thick 7059-glass waveguide on oxidized silicon with variable Ta2O5 overlay film thickness. Overlay n = 2.1, waveguide n = 1.565, t = 0.4 μm, substrate n = 1.47.

Fig. 7
Fig. 7

Normalized index of refraction profile for generalized Luneburg lens with S = 2, 3, 5, and 9. The parameter S is defined as focal length divided by lens radius.

Fig. 8
Fig. 8

Ta2O5 overlay film thickness profile for generalized Luneburg lens on 7059–SiO2–Si system, with S = 2, 3, 5, and 9.

Fig. 9
Fig. 9

Coordinate system for Luneburg lens shadow mask edge synthesis.

Fig. 10
Fig. 10

Theoretically calculated deposition profile through the two-section mask (dashed line) and the twelve-section mask (solid line) as compared with ideal (dotted line) S = 2 Luneburg lens profile.

Fig. 11
Fig. 11

Edge contour of the twelve-section shadow mask.

Fig. 12
Fig. 12

Dependence of the Luneburg lens focal length vs lens thickness, indicating the possibility of deriving circular lens families.

Fig. 13
Fig. 13

Computer-simulated focal property of S = 2 derived lenses (a) as generalized Luneburg lens, and (b) as a circular lens of long focal length, using the twelve-sectional mask and assuming 2-mm optical input aperture out of an 8-mm diam lens.

Fig. 14
Fig. 14

Guided-wave optical lens testing arrangement.

Fig. 15
Fig. 15

Guided-wave optical output couplers with reduced aberration using (a) a thin spinel wafer and (b) an aplanatic prism.

Fig. 16
Fig. 16

Guided-wave optical lens evaluation setup using cleaved edge and microscope objective lens.

Fig. 17
Fig. 17

Measured focal spot widths of the thin-film circular lenses using 2-mm optical aperture and showing diffraction-limited results.

Fig. 18
Fig. 18

Measured ray intercept error for the S = 2 lens deposited through the two-sectional mask, showing agreement with theoretical results. Calculated and experimental ray traces.

Fig. 19
Fig. 19

Focal intensity distribution obtained through the F/4.5 reimaging lens for (a) the S = 2 lens deposited through the two-sectional mask and (b) the S = 2 lens deposited through the twelve-sectional mask.

Fig. 20
Fig. 20

Focal intensity distribution of the S = 2 Luneburg lens deposited through the twelve-sectional mask, measured by the Zeiss F/0.6 lens.

Fig. 21
Fig. 21

Optical lens system misalignment definitions.

Fig. 22
Fig. 22

Normalized defocusing with lens thickness deviation of 10 Å for the S = 2 derived thin-film circular lens family, assuming optical aperture a = R/2 at 0.9-μm optical wavelength and α = 1.

Fig. 23
Fig. 23

Surface optical scattering trace on a 7059–SiO2–Si substrate containing an S = 2 thin-film Luneburg lens.

Fig. 24
Fig. 24

Focal plane scattering noise background of an S = 2 thin-film Luneburg lens.

Equations (23)

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E m 1 = A m exp [ - P m ( x - t ) ] sin ( h m t + ϕ m ) sin γ m exp ( - i β m z ) E m 2 = A m sin ( h m x + ϕ m ) sin γ m exp ( - i β m z ) E m 3 = A m sin ( l m x + γ m ) sin ϕ m exp ( - i β m z ) , E m 4 = A m exp [ q m ( x + d ) ] sin ( - l m d + γ m ) sin ϕ m exp ( - i β m z ) }
P m = ( β m 2 - k 2 n 1 2 ) 1 / 2 , h m = ( k 2 n 2 2 - β m 2 ) 1 / 2 l m = ( k 2 n 3 2 - β m 2 ) 1 / 2 . q m = ( β m 2 - k 2 n 4 2 ) 1 / 2 }
tan ( h m t + ϕ m ) = - h m / P m ,
tan ϕ m = ( h m / l m ) tan γ m ,
tan ( - l m d + γ m ) = l m / q m .
1 l m tan ( I m d + tan - 1 l m q m ) + 1 h m tan ( h m t + tan - 1 h m P m ) = 0.
n 3 2 l m tan [ l m d + tan - 1 ( n 4 2 n 3 2 l m q m ) ] + n 2 2 h m tan [ h m t + tan - 1 ( n 1 2 n 2 2 h m P m ) ] = 0.
n = n 0 exp ( w ) ,
w = 1 π 0 1 sin - 1 ( x / S ) ( x 2 - ρ 2 ) - 1 / 2 d x ,
T ( x 0 , y 0 ) = U A ( θ ) cos θ R 2 d x d y ,
θ = cos - 1 { D [ ( x 1 - x 0 ) 2 + ( y 1 - y 0 ) 2 ] 1 / 2 } , R = [ ( x 1 - x 0 ) 2 + ( y 1 - y 0 ) 2 + z 1 2 ] 1 / 2 ,
[ ( x 0 - x 1 ) z z 1 - x 0 ] 2 + [ ( y 0 - y 1 ) z z 1 - y 0 ] 2 - f 2 ( z ) = 0.
T ( x 0 , y 0 ) = W A ( θ ) G cos θ R 2 d x d y .
I = A 2 = | - exp ( - 4 x 2 / a 2 ) exp { - j [ ( k x 1 ) / f ] x } d x | 2 = C exp [ - 2 ( a k / 4 f ) 2 x 1 2 ]
F = f / a .
I / I 0 = - 8.69 ( a k / 4 f ) 2 x 1 2 dB , = - 21.44 ( x 1 / λ F ) 2             dB .
exp ( - 2 ) spot width = 1.27 λ F ,             - 3 dB spot width = 0.75 λ F .
I t = | A * sinc ( k D x 1 2 f ) | 2 ,
d f ( α λ f 2 ) / a 2 ) ,
d θ = a f ( f + d f ) d f ( a f ) ( d f f ) ,
d θ ( α λ a ) = d f ( α λ f 2 a 2 ) .
d θ ( α λ ) / a .
Δ f = ( i I d f i f i 2 / a i 2 ) / α λ 1 when aligned ,

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