Abstract

New waveguide grating lenses for coupling a guided wave to a spherical wave, focusing in the air, have been designed. The lenses have the advantages. of high efficiency and high practicability for fabrication. Chirped and curved grating lenses were fabricated on PMMA waveguides by an electron beam exposure system.

© 1984 Optical Society of America

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References

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  1. A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
    [CrossRef]
  2. A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
    [CrossRef]
  3. M. Miler, Opt. Quantum Electron. 11, 359 (1979).
    [CrossRef]
  4. M. Miler, M. Skalsky, Electron. Lett. 15, 275 (1979).
    [CrossRef]
  5. D. Heitmann, R. V. Pole, Appl. Phys. Lett. 37, 585 (1980).
    [CrossRef]
  6. D. Heitmann, C. Ortiz, IEEE J. Quantum Electron. QE-17, 1257 (1981).
    [CrossRef]
  7. J. H. Harris, R. K. Winn, D. G. Dalgoutte, Appl. Opt. 11, 2234 (1972).
    [CrossRef] [PubMed]
  8. K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
    [CrossRef]
  9. D. G. Dalgoutte, Opt. Commun. 8, 124 (1973).
    [CrossRef]
  10. R. Ulrich, J. Opt. Soc. Am. 63, 1419 (1973).
    [CrossRef]
  11. T. Tamir, Integrated Optics (Springer, Berlin, 1979), Chap. 3.
  12. P. K. Tien, Opt. Lett. 1, 64 (1977).
    [CrossRef] [PubMed]
  13. A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
    [CrossRef]
  14. J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
    [CrossRef]
  15. D. A. Bryan, J. K. Powers, Opt. Lett. 5, 407 (1980).
    [CrossRef] [PubMed]
  16. G. Hatakoshi, S. Tanaka, Opt. Lett. 2, 142 (1978).
    [CrossRef] [PubMed]
  17. P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
    [CrossRef]
  18. Y. Handa, T. Suhara, H. Nishihara, J. Koyama, Appl. Opt. 19, 2842 (1980).
    [CrossRef] [PubMed]
  19. G. Hatakoshi, M. Yoshimi, K. Goto, in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

1981 (1)

D. Heitmann, C. Ortiz, IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

1980 (3)

1979 (2)

M. Miler, Opt. Quantum Electron. 11, 359 (1979).
[CrossRef]

M. Miler, M. Skalsky, Electron. Lett. 15, 275 (1979).
[CrossRef]

1978 (2)

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

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

1977 (5)

P. K. Tien, Opt. Lett. 1, 64 (1977).
[CrossRef] [PubMed]

A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
[CrossRef]

J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

1973 (3)

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

D. G. Dalgoutte, Opt. Commun. 8, 124 (1973).
[CrossRef]

R. Ulrich, J. Opt. Soc. Am. 63, 1419 (1973).
[CrossRef]

1972 (1)

Ashley, P. R.

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

Bryan, D. A.

Chang, W. S. C.

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

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

Dalgoutte, D. G.

Goto, K.

G. Hatakoshi, M. Yoshimi, K. Goto, in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

Handa, Y.

Harris, J. H.

Hatakoshi, G.

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

G. Hatakoshi, M. Yoshimi, K. Goto, in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

Heitmann, D.

D. Heitmann, C. Ortiz, IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

D. Heitmann, R. V. Pole, Appl. Phys. Lett. 37, 585 (1980).
[CrossRef]

Hong, C. S.

J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
[CrossRef]

Katzir, A.

A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
[CrossRef]

Koyama, J.

Livanos, A. C.

A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
[CrossRef]

Miler, M.

M. Miler, Opt. Quantum Electron. 11, 359 (1979).
[CrossRef]

M. Miler, M. Skalsky, Electron. Lett. 15, 275 (1979).
[CrossRef]

Nishihara, H.

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

Ortiz, C.

D. Heitmann, C. Ortiz, IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

Pole, R. V.

D. Heitmann, R. V. Pole, Appl. Phys. Lett. 37, 585 (1980).
[CrossRef]

Powers, J. K.

Rosenbaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

Shellan, J. B.

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
[CrossRef]

Skalsky, M.

M. Miler, M. Skalsky, Electron. Lett. 15, 275 (1979).
[CrossRef]

Sopoli, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

Suhara, T.

Tamir, T.

T. Tamir, Integrated Optics (Springer, Berlin, 1979), Chap. 3.

Tanaka, S.

Tien, P. K.

Ulrich, R.

Winn, R. K.

Yariv, A.

A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
[CrossRef]

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
[CrossRef]

J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
[CrossRef]

Yoshimi, M.

G. Hatakoshi, M. Yoshimi, K. Goto, in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

A. Katzir, A. C. Livanos, A. Yariv, Appl. Phys. Lett. 30, 225 (1977).
[CrossRef]

D. Heitmann, R. V. Pole, Appl. Phys. Lett. 37, 585 (1980).
[CrossRef]

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

Electron. Lett. (1)

M. Miler, M. Skalsky, Electron. Lett. 15, 275 (1979).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. Heitmann, C. Ortiz, IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

A. Katzir, A. C. Livanos, J. B. Shellan, A. Yariv, IEEE J. Quantum Electron. QE-13, 296 (1977).
[CrossRef]

K. Ogawa, W. S. C. Chang, B. L. Sopoli, F. J. Rosenbaum, IEEE J. Quantum Electron. QE-9, 29 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (3)

D. G. Dalgoutte, Opt. Commun. 8, 124 (1973).
[CrossRef]

A. C. Livanos, A. Katzir, A. Yariv, Opt. Commun. 20, 179 (1977).
[CrossRef]

J. B. Shellan, C. S. Hong, A. Yariv, Opt. Commun. 23, 398 (1977).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

M. Miler, Opt. Quantum Electron. 11, 359 (1979).
[CrossRef]

Other (2)

T. Tamir, Integrated Optics (Springer, Berlin, 1979), Chap. 3.

G. Hatakoshi, M. Yoshimi, K. Goto, in Technical Digest, Fourth International Conference on Integrated Optics and Optical Fiber Communication (IECE, Tokyo, 1983), paper 29A2-2.

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Figures (8)

Fig. 1
Fig. 1

Momentum conservation for wave vectors. The upper figures show top views of the wave vectors.

Fig. 2
Fig. 2

Waveguide grating lens configuration.

Fig. 3
Fig. 3

Variation in grating pitch Λ as a function of ϕ and ψ.

Fig. 4
Fig. 4

Optical waveguide structure for the experiment: (a) top view (x-y plane); (b) side view (η-ξ plane); (c) cross-sectional view.

Fig. 5
Fig. 5

Microscopic photograph of the grating lens.

Fig. 6
Fig. 6

SEM photographs of the grating lens.

Fig. 7
Fig. 7

Intensity profiles at the focal plane measured in the (a) η and (b) ξ directions.

Fig. 8
Fig. 8

Intensity profiles near the focal plane.

Equations (15)

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

k 0 < k 1 + K < k 0 n
K x = - k 0 ( cos α cos ϕ sin ψ - sin α n 2 - sin 2 ψ + N cos θ ) ,
K y = - k 0 ( sin ϕ sin ψ + N sin θ ) ,
x = r cos ϕ / cos α ,
y = r sin ϕ ,
r = f tan ψ + h 0 sin ψ / n 2 - sin 2 ψ 1 + tan α cos ϕ sin ψ / n 2 - sin 2 ψ ,
1 < ( cos α cos ϕ sin ψ - sin α n 2 - sin 2 ψ ) 2 + sin 2 ϕ sin 2 ψ < n 2 .
Λ = 2 π / K x 2 + K y 2 .
Ω = k 0 [ l + N ( x cos θ + y sin θ ) ] ,
l = f sec ψ + n 2 ( h 0 - x sin α ) / n 2 - sin 2 ψ .
x 2 cos 2 α + y 2 = f tan ψ + ( h 0 - x sin α ) sin ψ / n 2 - sin 2 ψ .
γ L = 1 ,
γ 2 n N ( n f 2 - 1 ) ( n f 2 - N 2 ) sin ψ s N ( n sin ψ s + n f 2 - n 2 cos 2 ψ s ) 2 ( δ t ) 2 λ 2 t ,
k 0 n < k 1 + 2 K
cos θ < ( N 2 - n 2 - n 2 + 4 n 2 sin 2 α ) / ( 4 n N sin α ) .

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