Abstract

We introduce a design method for diffractive cylindrical microlenses fabricated with a new technology similar to the fabrication of all-solid photonic crystal fibers. Unlike conventional microlenses that are fabricated with etching methods and thus have a step-index profile, the refractive index of each layer can be individually designed. We study the transmitted field of such nonperiodic lamellar phase grating. By using the field-stitching method we can suppress the effect of periodic boundary conditions of the Fourier modal method when calculating the transmitted field of nonperiodic lamellar phase elements. We suggest an algorithm to design multilayer phase elements, which act as cylindrical lenses. We show experimental and theoretical data for a diffraction-limited lens.

© 2009 Optical Society of America

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References

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  1. F. Hudelist, R. Buczynski, A. J. Waddie, and M. R. Taghizadeh, Opt. Express 17, 3255 (2009).
    [CrossRef] [PubMed]
  2. D. Feng, P. Ou, L.-S. Feng, S.-L. Hu, and C.-X. Zhang, Opt. Express 16, 20968 (2008).
    [CrossRef] [PubMed]
  3. L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
    [CrossRef]
  4. J. P. Hugonin and P. Lalanne, J. Opt. Soc. Am. A 22, 1844 (2005).
    [CrossRef]
  5. B. Layet and M. R. Taghizadeh, Opt. Lett. 21, 1508, 1996.
    [CrossRef] [PubMed]
  6. D. W. Prather, S. Shi, and J. S. Bergey, Opt. Lett. 24, 273 (1999).
    [CrossRef]
  7. R. F. Harrington, Field Computation by Moment Methods (Krieger Publishing Co., Inc., 1982).
  8. J. Chandezon, G. Rauolt, and D. Maystre, J. Opt. 11, 235 (1980).
    [CrossRef]
  9. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  10. J. H. Li, G. J. Burke, D. A. White, C. A. Thompson, and K. J. Webb, Opt. Lett. 31, 1181 (2006).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

2006 (1)

2005 (1)

1999 (1)

1997 (1)

1996 (1)

1983 (1)

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

1980 (1)

J. Chandezon, G. Rauolt, and D. Maystre, J. Opt. 11, 235 (1980).
[CrossRef]

Bergey, J. S.

Buczynski, R.

Burke, G. J.

Chandezon, J.

J. Chandezon, G. Rauolt, and D. Maystre, J. Opt. 11, 235 (1980).
[CrossRef]

Feng, D.

Feng, L.-S.

Gelatt, C. D.

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

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Krieger Publishing Co., Inc., 1982).

Hu, S.-L.

Hudelist, F.

Hugonin, J. P.

Kirkpatrick, S.

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

Lalanne, P.

Layet, B.

Li, J. H.

Li, L.

Maystre, D.

J. Chandezon, G. Rauolt, and D. Maystre, J. Opt. 11, 235 (1980).
[CrossRef]

Ou, P.

Prather, D. W.

Rauolt, G.

J. Chandezon, G. Rauolt, and D. Maystre, J. Opt. 11, 235 (1980).
[CrossRef]

Shi, S.

Taghizadeh, M. R.

Thompson, C. A.

Vecchi, M. P.

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

Waddie, A. J.

Webb, K. J.

White, D. A.

Zhang, C.-X.

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the microstructured lamellar grating. The gray area is the cladding, which has been removed from two sides.

Fig. 2
Fig. 2

Element embedded in an absorbing padding with dimension d padd on either side.

Fig. 3
Fig. 3

Error of the field in the focal plane as a function of the padding size.

Fig. 4
Fig. 4

Transmitted field distribution for the periodic case with (a) no added frame and (b) a frame added with six times the period on either side of the structure.

Fig. 5
Fig. 5

Structure of the microwave lens. The white parts represent perspex, and the black parts represent air.

Fig. 6
Fig. 6

Comparison of the theoretical and experimental results.

Equations (5)

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U T ( x , z ) = m T m exp [ i ( α m x t m z ) ] ,
T m = d 1 n = 1 N p = P P T p n exp [ i γ p ( x n x s ) ] × x n x n + 1 exp [ i ( γ p γ m ) x ] dx ,
T m = 1 p p T p exp [ i γ p d padd ] × d padd d padd + p exp [ i ( γ p γ m ) x ] dx .
σ N = [ x = 1 X ( F x ( N ) F x ( 10 ) ) 2 ] 1 2 ,
c = α [ I ( x , f ) d x x F I ( x , f ) d x I ( x , f ) d x ] β + γ R ,

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