Abstract

The thickness profile of deposits obtained from Lambertian evaporation sources is highlighted concerning its transmission optical functionality, in the case of dielectric materials. Fresnel diffraction is used to characterize the lateral resolution and intensity on the optical axis of an input gaussian laser beam. Functionality similar to logarithmic axicons, with uniform lateral resolution and also uniform on-axis intensity, is theoretically derived. It is also shown for this particular optical structure that the intensity slope along the optical axis can be changed from positive to negative values by only changing the input beam width.

© 2007 Optical Society of America

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References

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  1. R. Glang, in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds., (McGraw-Hill, New York, 1983).
  2. M. Born, E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1989) p. 752.
  3. J. M. González-Leal, R. Prieto-Alcón, J. A. Ángel, D. A. Minkov, E. Márquez, "Influence of the substrate absorption on the optical and geometrical characterization of thin dielectric films," Appl. Opt. 41, 7300 (2002).
    [CrossRef] [PubMed]
  4. A. T. Friberg, "Stationary-phase analysis of generalized axicons," J. Opt. Soc. Am. A 13, 743 (1996).
    [CrossRef]
  5. J. H. McLeod, "The axicon: A new type of optical element," J. Opt. Soc. Am. 44, 592 (1954).
    [CrossRef]
  6. A. Burvall, K. Kolacz, Z. Jaroszewicz, A. T. Friberg, "Simple lens axicon," Appl. Opt. 43, 4838 (2004).
    [CrossRef]
  7. Z. Jaroszewicz, A. Burvall, A. T. Friberg, "Axicon: the most important optical element," Opt. Photon. News 16, 34 (2005).
    [CrossRef]
  8. B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, H. Wang, "Design and fabrication of a double-axicon for generation of tailored self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987 (2006).
    [CrossRef] [PubMed]
  9. J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
    [CrossRef]
  10. J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, and S. Bará, "Nonparaxial designing of generalized axicons," Appl. Opt. 31, 5326 (1992).
    [CrossRef]
  11. R. Grunwald, U. Neumann, A. Rosenfeld, J. Li, P. R. Herman, "Scalable multichannel micromachining with pseudo-nondiffracting vacuum ultraviolet beam arrays generated by thin-film axicons," Opt. Lett. 31, 1666 (2006).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Singapore, 1996).
  13. H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909 (1969).

2006 (2)

2005 (1)

Z. Jaroszewicz, A. Burvall, A. T. Friberg, "Axicon: the most important optical element," Opt. Photon. News 16, 34 (2005).
[CrossRef]

2004 (1)

2002 (1)

2000 (1)

J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
[CrossRef]

1996 (1)

1992 (1)

1969 (1)

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909 (1969).

1954 (1)

Ahluwalia, B. P. S.

Ángel, J. A.

Bará, S.

Bu, J.

Burvall, A.

Z. Jaroszewicz, A. Burvall, A. T. Friberg, "Axicon: the most important optical element," Opt. Photon. News 16, 34 (2005).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, A. T. Friberg, "Simple lens axicon," Appl. Opt. 43, 4838 (2004).
[CrossRef]

Cheong, W. C.

Friberg, A. T.

González-Leal, J. M.

Grunwald, R.

Herman, P. R.

Jaroszewicz, Z.

Kogelnik, H.

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909 (1969).

Kolacz, K.

Kolodziejczyk, A.

Li, J.

Márquez, E.

McLeod, J. H.

Minkov, D. A.

Nemoto, S.

J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
[CrossRef]

Neumann, U.

Prieto-Alcón, R.

Pu, J. X.

J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
[CrossRef]

Rosenfeld, A.

Sochacki, J.

Tao, S.-H.

Wang, H.

Yuan, X.-C.

Zhang, H. H.

J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
[CrossRef]

Zhang, L.-S.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled-wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909 (1969).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

J. X. Pu, H. H. Zhang, and S. Nemoto, "Lens axicons illuminated by Gaussian beams for generation of uniform-axial intensity Bessel fields," Opt. Eng. 39, 803 (2000).
[CrossRef]

Opt. Lett. (2)

Opt. Photon. News (1)

Z. Jaroszewicz, A. Burvall, A. T. Friberg, "Axicon: the most important optical element," Opt. Photon. News 16, 34 (2005).
[CrossRef]

Other (3)

R. Glang, in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds., (McGraw-Hill, New York, 1983).

M. Born, E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, 6th ed. (Pergamon Press, Oxford, 1989) p. 752.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Singapore, 1996).

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of the cosine law for the evaporated-mass distribution from Lambertian evaporation source. A flat substrate is also drawn and relevant deposition parameters are indicated: a being the distance from the centre of the source to the substrate, ρ the modulus of the vector from the centre of the source to any point on the substrate surface, θ is the angle between a and ρ, and Ψ is the angle between ρ and the normal vector to the surface substrate.

Fig. 2.
Fig. 2.

Thickness profile, t(r), corresponding to a deposit obtained from a Lambertian evaporation source. The analytical formula for t(r) and design parameters A and a are conveniently indicated.

Fig. 3.
Fig. 3.

Lateral resolution (thick solid line) and light intensity (thick dashed line) along the axis for a representative refractive optical structure with design and input gaussian-beam parameters shown in the figure. Thin dashed line indicates the minimum lateral resolution, w min, reached at distance f 0, and thin solid line at a value of the resolution 5 % above w min, is also plotted to characterize the focal region Δf as described in the text (f 0 = 86 mm, w min = 74 μm, and Δf ≈ 43 mm).

Fig. 4.
Fig. 4.

Lateral resolution (thick solid line) and light intensity (thick dashed line) along the axis for a refractive optical structure with design and input gaussian-beam parameters shown in the figure. Values for f 0 , wmin, and Δf are, respectively, 43 mm, 37 μm and 20 mm (a), 22 mm, 18.5 μm and 10 mm (b), 173 mm, 148 μm and 85 mm (c), and 58 mm, 49 μm and 28 mm (d).

Fig. 5.
Fig. 5.

Lateral resolution (thick solid line) and light intensity (thick dashed line) along the axis for a refractive optical structure with design and input gaussian-beam parameters shown in the figure. Values for f 0 , w min, and Δf are, respectively, 777 mm, 222 μm and 400 mm (a), and 1382 mm, 296 μm and 680 mm (b).

Fig. 6.
Fig. 6.

Lateral resolution (thick solid line) and light intensity (thick dashed line) along the axis for a refractive optical structure with design and input gaussian-beam parameters shown in the figure. Values for f 0 , w min, and Δf are, respectively, 50 mm, 12 μm and 37 mm.

Equations (18)

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dM e = M e cos ( θ ) π :
dM c dA c = M e π ρ 2 cos ( θ ) cos ( ψ ) ,
dM c dA c = M e π a 2 ( a 2 + r 2 ) 2 .
t ( r ) = A ( 1 + ( r a ) 2 ) 2 ,
φ ( r ) = A ( n 1 ) ( 1 t ( r ) ) = A ( n 1 ) ( 1 1 ( 1 + ( r a ) 2 ) 2 ) .
U ( ρ , z ) = e ikz iλz e i k 2 z ρ 2 s U ( r , z ) e i k 2 z r 2 e i k z r ρ co s ( ϕ ) d ϕ dr .
U ( r , z ) = U ( r ) = e ( r σ ) 2 e ikφ ( r ) .
U ( ρ , z ) = e ikz ikz e i k 2 z ρ 2 s e ( r σ ) 2 e ik ( r 2 2 z φ ( r ) ) J 0 ( kρr 2 z ) rdr =
= e ikz ikz e i k 2 z ρ 2 s e ( r σ ) 2 e ikf ( r ) J 0 ( kρr 2 z ) rdr ,
r c = a ( ( 4 A ( n 1 ) z a 2 ) 1 3 1 ) 1 2
I ( r ' , z ) e 2 ( r c σ ) 2 r c 2 z 2 1 1 z + φ ' ' ( r c ) J 0 2 ( k r c r ' 2 z ) .
J 0 2 ( k r c w 4 z ) = 1 2 ,
d dz ( J 0 2 ( k r c w 4 z ) ) | f 0 = d dz ( r c z ) | f 0 = 0 ,
f 0 = 54 125 a 2 A ( n 1 ) .
w min = w ( f 0 ) 1.13 216 a 25 5 kA ( n 1 ) .
I ( 0 , z ) e 2 ( r c σ ) 2 r c 2 z 2 1 1 z + φ ' ' ( r c ) ,
dI ( 0 , z ) dz | f 0 A 2 ( n 1 ) 2 e 2 5 ( a σ ) 2 σ 2 ( 10 σ 2 3 a 2 ) .
σ 0 = ( 3 10 ) 1 2 a .

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