Abstract

We describe a novel scheme for obtaining a superhigh numerical aperture gradient-index (SHNA GRIN) lens from multiple thin layers of two or more materials with large refractive-index contrast. Design procedures for the lens are described, including variation of the layer thickness to achieve focusing and of the thickness limit to reduce scattering loss. We use an exact numerical solution by the finite-difference time-domain method to evaluate the lens’s performance. Specific examples of a SHNA GRIN lens with a SiO2TiO2 material system designed for fiber coupling to a nanowaveguide are shown to have focusing FWHM spot sizes of 0.530.7μm at λ=1.55μm (corresponding to a NA of approximately 1.6–1.1) with 2.7–2.4% more loss than an ideal continuous index profile GRIN lens. With this approach, a SHNA GRIN lens with a NA of >1.5 and a length of <20μm can be achieved with currently available thin-film deposition techniques.

© 2005 Optical Society of America

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References

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  1. J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
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    [CrossRef]
  7. K. S. Yee, IEEE Trans. Antennas Propag. 41, 302 (1966).
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    [CrossRef]
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    [CrossRef]

1998 (1)

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

1997 (1)

D. Rafizadeh and S. T. Ho, Opt. Commun. 141, 17 (1997).
[CrossRef]

1995 (1)

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

1990 (1)

1980 (2)

1966 (1)

K. S. Yee, IEEE Trans. Antennas Propag. 41, 302 (1966).

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002).
[CrossRef]

Bi, W. G.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Chu, D. Y.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002).
[CrossRef]

Ho, S. T.

D. Rafizadeh and S. T. Ho, Opt. Commun. 141, 17 (1997).
[CrossRef]

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Iga, K.

Messerschmidt, B.

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

Moore, D. T.

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002).
[CrossRef]

Pfeil, A.

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

Possner, T.

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

Possner, U.

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

Rafizadeh, D.

D. Rafizadeh and S. T. Ho, Opt. Commun. 141, 17 (1997).
[CrossRef]

Samuels, J. E.

Tiberio, R. C.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Tu, C. W.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Wu, S. L.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).

Yee, K. S.

K. S. Yee, IEEE Trans. Antennas Propag. 41, 302 (1966).

Zhang, J. P.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Antennas Propag. (1)

K. S. Yee, IEEE Trans. Antennas Propag. 41, 302 (1966).

Opt. Commun. (1)

D. Rafizadeh and S. T. Ho, Opt. Commun. 141, 17 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, Phys. Rev. Lett. 75, 2678 (1995).
[CrossRef] [PubMed]

Proc. SPIE (1)

B. Messerschmidt, U. Possner, A. Pfeil, and T. Possner, Proc. SPIE 3424, 88 (1998).
[CrossRef]

Other (2)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Parabolic refractive-index profile (dashed curve) of a 13 - μ m -thick GRIN lens and the approximate step refractive-index profile of a SHNA MLGRIN lens (solid curve). (b) TiO 2 and SiO 2 layers (solid curve) used to approximate a certain step refractive index (dashed line).

Fig. 2
Fig. 2

(a) Layer structure used in estimation of scattering loss by the transfer matrix method. (b) Total scattering loss calculated by the transfer matrix method for three total structure thicknesses: 3 μ m (B, solid curve), 5 μ m (C, dashed curve), and 7 μ m (D, dashed–dotted curve).

Fig. 3
Fig. 3

FDTD simulated field pattern for a fiber mode propagating inside lenses [vertical size (V), 13 μ m ; horizontal size (H), 25 μ m : (a) TE light (E field) in the continuous-index GRIN lens, (b) TE light (E field) in the SHNA MLGRIN lens with TiO 2 SiO 2 , (c) TM light (H field) in the SHNA MLGRIN lens with TiO 2 SiO 2 , (d) mode profile at the focusing point of the SHNA MLGRIN lens and the continuous GRIN lens compared with the mode profile of the matched III–V waveguide (core thickness, 1.1 μ m ; core–cladding refractive index, 3 2.8 ).

Fig. 4
Fig. 4

Focusing in a SHNA MLGRIN lens from the optical fiber mode to a III–V waveguide with an air gap and an antireflection (AR) coating: (a) structure, (b) FDTD simulated TE-light E-field pattern ( V × H = 13 μ m × 28 μ m ) .

Fig. 5
Fig. 5

FDTD simulation of a SHNA MLGRIN lens with n R = 1.45 and n 0 = 2.17 . (a) Simulated TE light E-field pattern ( V × H = 13 μ m × 22 μ m ) , showing the optical fiber mode focused to a 0.5 - μ m III–V waveguide (core–cladding refractive index, 3.35 3.2 ; core thickness, 0.5 μ m ). (b) Mode profile at the focusing point of the SHNA MLGRIN lens and the continuous GRIN lens compared with the mode profile of the matched III–V waveguide.

Equations (1)

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n step = ( n 1 L 1 + n 2 L 2 ) ( L 1 + L 2 ) .

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