Abstract

We show theoretical and experimental characterizations of a nanostructured gradient-index lens. The elliptical lens is a nonguiding element fabricated using the mosaic method, which is widely used for the fabrication of photonic crystal fibers. For the first time we show experimental data in the optics regime that confirm the effective medium approximation for discrete mosaic structures with subwavelength feature size. This opens the door for the development of general asymmetric gradient-index materials.

© 2010 Optical Society of America

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References

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  1. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).
  2. F. Hudelist, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, Opt. Express 17, 3255 (2009).
    [CrossRef] [PubMed]
  3. A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
    [CrossRef]
  4. E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).
  5. S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  6. L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
    [CrossRef]
  7. D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  9. W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill Professional, 2007).

2009

2008

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

1997

1983

S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Aranyosiova, M.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Buczynski, R.

F. Hudelist, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, Opt. Express 17, 3255 (2009).
[CrossRef] [PubMed]

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Bugar, I.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Hudelist, F.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Li, L.

Lorenc, D.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

Sihvola, A.

A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill Professional, 2007).

Stepien, R.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Taghizadeh, M. R.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Velic, D.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Vincze, A.

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

Waddie, A. J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Appl. Phys. B

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, Appl. Phys. B 93, 531 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Science

S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Other

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics (Springer, 2002).

A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
[CrossRef]

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill Professional, 2007).

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Figures (5)

Fig. 1
Fig. 1

Design of the nanostructured microlens; (a) shows the result of the design algorithm for an effective index profile with the design target shown in (b).

Fig. 2
Fig. 2

Phase-contrast images of the nanostructured microlens: (a) the intermediate preform after the second drawing step and (b) the final 2 × 2 array of the microlenses.

Fig. 3
Fig. 3

Comparison of (a) the intensity and (b) the phase and at the back plane of the nanostructured lens and the ideal gradient-index lens. The dotted curve marks the difference between the two structures. The amplitude of the incident light is 1 2 for x polarization.

Fig. 4
Fig. 4

Comparison of the measured and simulated intensity on the optical axis as a function of the distance.

Fig. 5
Fig. 5

Comparison of the measured and simulated intensity distribution at the distance with the highest intensity in the central point.

Equations (4)

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ϵ eff ( r ) = ϵ ( r ) = f ( U r ) ϵ 1 + ( 1 f ( U r ) ) ϵ 2 .
n ( x , y ) = n max ( 1 a x 2 2 b y 2 2 ) .
n ( x , y ) = max { n max [ 1 0.5 ( π x 2 p 1 4 x ) 2 0.5 ( π y 2 p 1 4 y ) 2 ] , n min } .
f = ( n 0 a tan ( a L ) ) 1 ,

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