Abstract

We report the manufacturing and characterization of a refractive linear axicon producing a linearly increasing axial intensity Bessel-type beam over a predetermined range starting away from the axicon and without central blocking when illuminated by a plane wave. This is in contrast to a classical axicon that generates a diffraction-free beam starting from the axicon tip and extending to a range limited by the input beam aperture. The measured characteristics of the beam produced by the linear axicon, including its intensity distribution and spot size, are in good agreement with the theoretical predictions. Together with logarithmic axicon and exicon, this is another element of the axicon family that can generate a prescribed intensity distribution over a chosen range/depth of field.

© 2013 Optical Society of America

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References

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  1. A. Saikaley, B. Chebbi, and I. Golub, “Imaging properties of three refractive axicons,” Appl. Opt. 52, 6910–6918 (2013).
    [CrossRef]
  2. J. H. Mcleod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  3. Z. Jaroszewicz, A. Burvall, and T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
    [CrossRef]
  4. B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
    [CrossRef]
  5. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
    [CrossRef]
  6. A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A 13, 743–750 (1996).
  7. D. Brousseau, J. Drapeau, M. Piché, and E. Borra, “Generation of Bessel beams using a magnetic liquid deformable mirror,” Appl. Opt. 50, 4005–4010 (2011).
    [CrossRef]
  8. S. K. Tiwari, S. R. Mishra, S. P. Ram, and H. S. Rawat, “Generation of a Bessel beam of variable spot size,” Appl. Opt. 51, 3718–3725 (2012).
    [CrossRef]
  9. Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).
  10. G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
    [CrossRef]
  11. K. Gourley, I. Golub, and B. Chebbi, “Demonstration of a Fresnel axicon,” Appl. Opt. 50, 303–306 (2011).
    [CrossRef]
  12. I. Golub, B. Chebbi, D. Shaw, and D. Nowacki, “Characterization of a refractive logarithmic axicon,”Opt. Lett. 35, 2828–2830 (2010).
    [CrossRef]
  13. J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  14. Z. Cao, K. Wang, and Q. Wu, “Logarithmic axicon characterized by scanning optical probe system,” Opt. Lett. 38, 1603–1605 (2013).
    [CrossRef]
  15. J. Sochacki, Z. Jaroszewicz, L. R. Staroński, and A. Kołodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
  16. I. Golub, T. Mirtchev, J. Nuttall, and D. Shaw, “The taming of absorption: generating a constant intensity beam in a lossy medium,” Opt. Lett. 37, 2556–2558 (2012).
    [CrossRef]

2013 (2)

2012 (2)

2011 (2)

2010 (2)

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[CrossRef]

I. Golub, B. Chebbi, D. Shaw, and D. Nowacki, “Characterization of a refractive logarithmic axicon,”Opt. Lett. 35, 2828–2830 (2010).
[CrossRef]

2007 (1)

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

2005 (2)

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Z. Jaroszewicz, A. Burvall, and T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

1996 (1)

1993 (1)

1992 (1)

1954 (1)

Al-Akwaa, N.

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[CrossRef]

Bará, S.

Borra, E.

Brousseau, D.

Burvall, A.

Z. Jaroszewicz, A. Burvall, and T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Cao, Z.

Chebbi, B.

Drapeau, J.

Friberg, A. T.

Friberg, T.

Z. Jaroszewicz, A. Burvall, and T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Golub, I.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Gourley, K.

Jaroszewicz, Z.

Kolodziejczyk, A.

Li, F.

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

Liu, H.

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

Liu, Y.

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

Lu, Z.

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

Makowski, M.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Mcleod, J. H.

Mikula, G.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Minko, S.

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[CrossRef]

Mirtchev, T.

Mishra, S. R.

Nowacki, D.

Nuttall, J.

Piché, M.

Prokopowicz, C.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Ram, S. P.

Rawat, H. S.

Saikaley, A.

Shaw, D.

Sochacki, J.

Staronski, L. R.

Sypek, M.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Tiwari, S. K.

Wang, K.

Wang, R.

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

Wu, Q.

Appl. Opt. (5)

J. Opt. A (1)

Z. Lu, H. Liu, R. Wang, F. Li, and Y. Liu, “Diffractive axicons fabricated by laser direct writer on curved surface,” J. Opt. A 9, 160–164 (2007).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[CrossRef]

Opt. Eng. (1)

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001 (2005).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

Z. Jaroszewicz, A. Burvall, and T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Other (1)

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Profiles (sags) of axicons and lenses.

Fig. 2.
Fig. 2.

Measured on-axis intensity distribution generated by a linear axicon.

Fig. 3.
Fig. 3.

Simulated on-axis intensity distribution generated by a linear axicon.

Fig. 4.
Fig. 4.

Transverse intensity distribution at z=95mm: (a) obtained from CMOS image and (b) obtained from numerical simulation.

Fig. 5.
Fig. 5.

Linear axicon generated spot size variation according to Eq. (4) (solid line), numerical simulation using Eq. (3) (dotted line) and experimental measurement (closed circles).

Fig. 6.
Fig. 6.

Effect of central blocking on on-axis intensity. Rcb=0mm (no central blocking). Rcb=2.08mm (optimal blocking). Rcb=3mm and Rcb=4mm (nonoptimal blocking).

Equations (4)

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φ(r)=1a+1(f12+(a+1)r2),
s=const1(n1)(a+1)(f12+(a+1)r2),
E(x,y,z)=1jλAE(x,y,0)exp[jkR(x,x,y,y,z)]R(x,x,y,y,z)cos(n⃗,R⃗(x,x,y,y,z))dxdy,
r0=2.4048zkf22f12(z2f12)R2,

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