Abstract

The development of a solution deposited optical waveguide lens, whose focusing effect is produced by an effective index gradient with a hyperbolic secant variation, is described. The lenses are fabricated by a microcontrolled dip coating procedure from colloidal SiO2:TiO2 solutions. Both the design and construction of the lens, along with the analytical and experimental results of the focusing properties, are described. The best lenses had speeds of ∼f/10 and focal spots ∼1.2 times the diffraction limit at apertures of 2.0 mm.

© 1989 Optical Society of America

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References

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  1. F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).
    [Crossref]
  2. S. K. Yao, D. B. Anderson, R. R. August, B. R. Youmans, and C. M. Oania, "Guided-Wave Optical Thin-Film Luneburg Lenses: Fabrication Technique and Properties," Appl. Opt. 18, 4067–4079 (1979).
    [Crossref] [PubMed]
  3. V. E. Wood, J. R. Busch, D. T. Moore, C. B. Wooley, and W. H. Southwell, "Rectangular Luneburg-Type Lenses for Integrated Optics," Opt. Lett. 8, 226–228 (1983).
    [Crossref] [PubMed]
  4. D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
    [Crossref]
  5. D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).
  6. D. W. Hewak and J. W. Y. Lit, "Fabrication of Tapers and Lenslike Waveguides by a microcontrolled Dip Coating Procedure," Appl. Opt. 28, 4562–4564 (1988).
    [Crossref]
  7. D. W. Hewak and J. W. Y. Lit, "Standardization and Control of a Dip Coating Procedure for Thin Films Deposited from Solution," Can. J. Phys. 66, 861–867 (1988).
    [Crossref]
  8. G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
    [Crossref]
  9. D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.
  10. A. L. Mikaelian, "Self-Focusing Media with Variable Index of Refraction," Prog. Opt. 17, 283–345 (1980).
  11. S. Kawakami and J. Nishizawa, "An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion," IEEE Trans. Microwave Theory MTT-16, 814–818 (1968).
    [Crossref]
  12. E. G. Rawson, D. R. Herriott, and J. McKenna, "Analysis of Refractive Index Distributions in Cylindrical, Graded-Index Glass Rods (GRIN Rods) Used as Image Relays," Appl. Opt. 9, 753–759 (1970).
    [Crossref] [PubMed]
  13. E. W. Marchand, "Gradient Index Lenses," Prog. Opt. 11,305–337 (1973).
    [Crossref]
  14. K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).
  15. R. Ulrich and H. P. Weber, "Solution-Deposited Thin Films as Passive and Active Light-Guides," Appl. Opt. 11, 428–434 (1972).
    [Crossref] [PubMed]
  16. K. Heuberger and W. Lubosz, "Embossing Technique for Fabricating Surface Relief Gratings on Hard Oxide Waveguides," Appl. Opt. 25, 1499–1504 (1986).
    [Crossref] [PubMed]
  17. D. W. Hewak and J. W. Y. Lit, "Numerical RayTracing Methods for Gradient Index Media," Can. J. Phys. 63, 234–239 (1985).
    [Crossref]
  18. A. Sharma, D. V. Kumar, and A. K. Ghatak, "Tracing Rays Through Graded-Index Media: A New Method," Appl. Opt. 21, 984–987 (1982).
    [Crossref] [PubMed]
  19. W. Y. Jiang and V. M. Ristic, "Experimental Study of Anisotropy Dependent Geodesic Lenses," IEEE/OSA J. Lightwave Technol. JT-6, 353–356 (1988).
    [Crossref]

1988 (3)

D. W. Hewak and J. W. Y. Lit, "Fabrication of Tapers and Lenslike Waveguides by a microcontrolled Dip Coating Procedure," Appl. Opt. 28, 4562–4564 (1988).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Standardization and Control of a Dip Coating Procedure for Thin Films Deposited from Solution," Can. J. Phys. 66, 861–867 (1988).
[Crossref]

W. Y. Jiang and V. M. Ristic, "Experimental Study of Anisotropy Dependent Geodesic Lenses," IEEE/OSA J. Lightwave Technol. JT-6, 353–356 (1988).
[Crossref]

1986 (1)

1985 (1)

D. W. Hewak and J. W. Y. Lit, "Numerical RayTracing Methods for Gradient Index Media," Can. J. Phys. 63, 234–239 (1985).
[Crossref]

1983 (2)

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

V. E. Wood, J. R. Busch, D. T. Moore, C. B. Wooley, and W. H. Southwell, "Rectangular Luneburg-Type Lenses for Integrated Optics," Opt. Lett. 8, 226–228 (1983).
[Crossref] [PubMed]

1982 (2)

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

A. Sharma, D. V. Kumar, and A. K. Ghatak, "Tracing Rays Through Graded-Index Media: A New Method," Appl. Opt. 21, 984–987 (1982).
[Crossref] [PubMed]

1980 (1)

A. L. Mikaelian, "Self-Focusing Media with Variable Index of Refraction," Prog. Opt. 17, 283–345 (1980).

1979 (2)

1977 (1)

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

1974 (1)

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).
[Crossref]

1973 (1)

E. W. Marchand, "Gradient Index Lenses," Prog. Opt. 11,305–337 (1973).
[Crossref]

1972 (1)

1970 (1)

1968 (1)

S. Kawakami and J. Nishizawa, "An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion," IEEE Trans. Microwave Theory MTT-16, 814–818 (1968).
[Crossref]

Anderson, D. B.

S. K. Yao, D. B. Anderson, R. R. August, B. R. Youmans, and C. M. Oania, "Guided-Wave Optical Thin-Film Luneburg Lenses: Fabrication Technique and Properties," Appl. Opt. 18, 4067–4079 (1979).
[Crossref] [PubMed]

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

August, R. R.

S. K. Yao, D. B. Anderson, R. R. August, B. R. Youmans, and C. M. Oania, "Guided-Wave Optical Thin-Film Luneburg Lenses: Fabrication Technique and Properties," Appl. Opt. 18, 4067–4079 (1979).
[Crossref] [PubMed]

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

Boyd, J. T.

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

Bradely, J. C.

D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.

Briguet, V.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Bryan, D. A.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Busch, J. R.

Buser, E.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Chubbs, C. R.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Dalke, E. A.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Davis, R. L.

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

Ghatak, A. K.

Hatakoshi, G.

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Herriott, D. R.

Heuberger, K.

Hewak, D. W.

D. W. Hewak and J. W. Y. Lit, "Fabrication of Tapers and Lenslike Waveguides by a microcontrolled Dip Coating Procedure," Appl. Opt. 28, 4562–4564 (1988).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Standardization and Control of a Dip Coating Procedure for Thin Films Deposited from Solution," Can. J. Phys. 66, 861–867 (1988).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Numerical RayTracing Methods for Gradient Index Media," Can. J. Phys. 63, 234–239 (1985).
[Crossref]

Horisberger, M.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Inoue, H.

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Jiang, W. Y.

W. Y. Jiang and V. M. Ristic, "Experimental Study of Anisotropy Dependent Geodesic Lenses," IEEE/OSA J. Lightwave Technol. JT-6, 353–356 (1988).
[Crossref]

Kawakami, S.

S. Kawakami and J. Nishizawa, "An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion," IEEE Trans. Microwave Theory MTT-16, 814–818 (1968).
[Crossref]

Kumar, D. V.

Lit, J. W. Y.

D. W. Hewak and J. W. Y. Lit, "Standardization and Control of a Dip Coating Procedure for Thin Films Deposited from Solution," Can. J. Phys. 66, 861–867 (1988).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Fabrication of Tapers and Lenslike Waveguides by a microcontrolled Dip Coating Procedure," Appl. Opt. 28, 4562–4564 (1988).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Numerical RayTracing Methods for Gradient Index Media," Can. J. Phys. 63, 234–239 (1985).
[Crossref]

Lubosz, W.

Lukosz, W.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Malarkey, E. C.

D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.

Marchand, E. W.

E. W. Marchand, "Gradient Index Lenses," Prog. Opt. 11,305–337 (1973).
[Crossref]

McKenna, J.

Mergerian, D.

D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.

Mikaelian, A. L.

A. L. Mikaelian, "Self-Focusing Media with Variable Index of Refraction," Prog. Opt. 17, 283–345 (1980).

Moore, D. T.

Naito, K.

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Nishizawa, J.

S. Kawakami and J. Nishizawa, "An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion," IEEE Trans. Microwave Theory MTT-16, 814–818 (1968).
[Crossref]

Oania, C. M.

Pautienus, R. P.

D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.

Powers, J. K.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Rawson, E. G.

Reed, W. R.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Ristic, V. M.

W. Y. Jiang and V. M. Ristic, "Experimental Study of Anisotropy Dependent Geodesic Lenses," IEEE/OSA J. Lightwave Technol. JT-6, 353–356 (1988).
[Crossref]

Sharma, A.

Southwell, W. H.

Tanaka, S.

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Tiefenthaler, K.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Tomaschke, H. E.

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

Ulrich, R.

Umegaki, S.

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Weber, H. P.

Wood, V. E.

Wooley, C. B.

Yao, S. K.

Youmans, B. R.

Zernike, F.

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).
[Crossref]

Appl. Opt. (6)

Can. J. Phys. (2)

D. W. Hewak and J. W. Y. Lit, "Numerical RayTracing Methods for Gradient Index Media," Can. J. Phys. 63, 234–239 (1985).
[Crossref]

D. W. Hewak and J. W. Y. Lit, "Standardization and Control of a Dip Coating Procedure for Thin Films Deposited from Solution," Can. J. Phys. 66, 861–867 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

D. B. Anderson, R. L. Davis, J. T. Boyd, and R. R. August, "Comparison of Optical Waveguide Lens Technologies," IEEE J. Quantum Electron. QE-13, 275–282 (1977).
[Crossref]

IEEE Trans. Microwave Theory (1)

S. Kawakami and J. Nishizawa, "An Optical Waveguide with the Optimum Distribution of the Refractive Index with Reference to Waveform Distortion," IEEE Trans. Microwave Theory MTT-16, 814–818 (1968).
[Crossref]

IEEE/OSA J. Lightwave Technol. (1)

W. Y. Jiang and V. M. Ristic, "Experimental Study of Anisotropy Dependent Geodesic Lenses," IEEE/OSA J. Lightwave Technol. JT-6, 353–356 (1988).
[Crossref]

Opt. Acta (1)

G. Hatakoshi, H. Inoue, K. Naito, S. Umegaki, and S. Tanaka, "Optical Waveguide Lenses," Opt. Acta 26, 961–968 (1979).
[Crossref]

Opt. Commun. (1)

F. Zernike, "Luneburg Lens for Optical Waveguide Use," Opt. Commun. 12, 379–381 (1974).
[Crossref]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

D. A. Bryan, C. R. Chubbs, J. K. Powers, H. E. Tomaschke, W. R. Reed, and E. A. Dalke, "Development of a Tantalum Pentoxide Luneburg Lens," Proc. Soc. Photo-Opt. Instrum. Eng. 321, 2–8 (1982).

D. Mergerian, E. C. Malarkey, R. P. Pautienus, and J. C. Bradely, "Diamond Machined Geodesic Lenses in LiNbO3," Proc. Soc. Photo-Opt. Instrum. Eng. 176, 85–94.

K. Tiefenthaler, V. Briguet, E. Buser, M. Horisberger, and W. Lukosz, "Preparation of Planar Optical SiO2-TiO2 and LiNbO3 Guides with a Dip Coating Method and an Embossing Technique for Fabricating Grating Couplers and Channel Wave Guides," Proc. Soc. Photo-Opt. Instrum. Eng. 401, 165–173 (1983).

Prog. Opt. (2)

A. L. Mikaelian, "Self-Focusing Media with Variable Index of Refraction," Prog. Opt. 17, 283–345 (1980).

E. W. Marchand, "Gradient Index Lenses," Prog. Opt. 11,305–337 (1973).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1

Top view of the planar optical waveguide lens illustrating (a) a conventional structure of a localized lens and (b) a proposed lens based on an axial index gradient.

Fig. 2
Fig. 2

Thickness profiles for a family of hyperbolic secant lenses with focal lengths of 10–50 mm and apertures of 5 mm (design parameters: n1 = 1.522, n2 = 1.80, n3 = 1.80, n4 = 1.0, d1 = 0.2 μm, λ = 0.633 μm).

Fig. 3
Fig. 3

Geometry and coordinate system used in the analysis of the hyperbolic secant lens.

Fig. 4
Fig. 4

Thin film thickness as a function of the withdrawal speed for a SiO2:TiO2 solution which yields n = 1.8.

Fig. 5
Fig. 5

Withdrawal speed pattern used in an attempt to achieve a lens with focal length f = 20 mm.

Fig. 6
Fig. 6

Thickness profile of the first lens attempt fabricated with the withdrawal pattern illustrated in Fig. 5.

Fig. 7
Fig. 7

Modified withdrawal speed pattern.

Fig. 8
Fig. 8

Improved lens prototype fabricated with the withdrawal speed pattern illustrated in Fig. 7.

Fig. 9
Fig. 9

Ray trace through the first lens attempt illustrated in Fig. 6.

Fig. 10
Fig. 10

Ray trace through the lens illustrated in Fig. 8.

Fig. 11
Fig. 11

Schematic diagram of the thin film lens testing arrangement.

Fig. 12
Fig. 12

Experimental and theoretical thickness profiles for lens r4.

Fig. 13
Fig. 13

Intensity distribution in the focal plane of lens r4.

Fig. 14
Fig. 14

Diffraction pattern of lens s2 magnified by ∼58 times.

Tables (3)

Tables Icon

Table I Lens Materials and Peak Overlay Thickness for the Three Lens Structures Experimentally Measured

Tables Icon

Table II Comparison of the Theoretical Focal Length, Determined by Ray Tracing and the Experimental Focal Length

Tables Icon

Table III Comparison of Measured Focal Spot Size with the Diffraction Limited Spot Size

Equations (11)

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

n ( x ) = n 0 sech ( g x )
/ s ( n r ̅ / s ) = n
d 2 r ̅ d z 2 = ( 1 / n ) d n d x .
sinh ( g x ) = A sin [ B ± g ( z z 0 ) ] ,
A = [ ( n 0 / q 0 ) 2 1 ] 1 / 2 ,
B = sin 1 [ ( 1 / A ) sinh ( g x 0 ) ] ,
p 0 = n ( x 0 ) sin θ 0 ,
q 0 = n ( x 0 ) cos θ 0 ,
N . A . = sin θ a = ( 1 / n a ) n ( x 0 ) sin θ .
N . A . = ( 1 / n a ) [ n 2 ( x 0 ) n 2 ( a ) ] 1 / 2 .
δ = 0.75 λ f / a .

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