Abstract

We generalize the shape of the traditional axicon by analytically finding the function of the output surface when the input surface is not flat but an arbitrary continuous function that possesses rotational symmetry. Several illustrative examples are presented and tested using ray tracing techniques without the paraxial approximation.

© 2018 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration

Tae Moon Jeong, Do-Kyeong Ko, and Jongmin Lee
Opt. Lett. 30(22) 3009-3011 (2005)

Design of aberrationless aspheric unstable resonators

Robert J. Lang
J. Opt. Soc. Am. A 9(12) 2176-2181 (1992)

Generalized Aldis theorem for calculating aberration contributions in freeform systems

Bo Chen and Alois M. Herkommer
Opt. Express 24(23) 26999-27008 (2016)

References

  • View by:
  • |
  • |
  • |

  1. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [Crossref]
  2. Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon-the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
    [Crossref]
  3. C. McKell and K. D. Bonin, “Optical corral using a standing-wave Bessel beam,” J. Opt. Soc. Am. B 35, 1910–1920 (2018).
    [Crossref]
  4. J. C. Gutiérrez-Vega, R. Rodrguez-Masegosa, and S. Chávez-Cerda, “Bessel-Gauss resonator with spherical output mirror: geometrical-and wave-optics analysis,” J. Opt. Soc. Am. A 20, 2113–2122 (2003).
    [Crossref]
  5. O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
    [Crossref]
  6. D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
    [Crossref]
  7. J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
    [Crossref]
  8. N. D. C. Lozano-Rincón and J. C. Valencia-Estrada, “Paraboloid-aspheric lenses free of spherical aberration,” J. Mod. Opt. 64, 1146–1157 (2017).
    [Crossref]
  9. J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
    [Crossref]
  10. J. C. V. Estrada, Á. H. B. Calle, and D. M. Hernández, “Explicit representations of all refractive optical interfaces without spherical aberration,” J. Opt. Soc. Am. A 30, 1814–1824 (2013).
    [Crossref]
  11. J. C. Valencia-Estrada, J. García-Marquez, L. Chassagne, and S. Topsu, “Catadioptric interfaces for designing VLC antennae,” Appl. Opt. 56, 7559–7566 (2017).
    [Crossref]
  12. J. Sochacki, S. Bara, Z. Jaroszewicz, and A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17, 7–9 (1992).
    [Crossref]
  13. I. Golub, B. Chebbi, D. Shaw, and D. Nowacki, “Characterization of a refractive logarithmic axicon,” Opt. Lett. 35, 2828–2830 (2010).
    [Crossref]
  14. I. Golub and T. Mirtchev, “Absorption-free beam generated by a phase-engineered optical element,” Opt. Lett. 34, 1528–1530 (2009).
    [Crossref]
  15. 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]
  16. B. Chebbi and I. Golub, “Development of spot size and lateral intensity distribution generated by exponential, logarithmic, and linear axicons,” J. Opt. Soc. Am. A 31, 2447–2452 (2014).
    [Crossref]
  17. A. Thaning, A. T. Friberg, S. Y. Popov, and Z. Jaroszewicz, “Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination,” J. Opt. Soc. Am. A 19, 491–496 (2002).
    [Crossref]

2018 (1)

2017 (3)

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

N. D. C. Lozano-Rincón and J. C. Valencia-Estrada, “Paraboloid-aspheric lenses free of spherical aberration,” J. Mod. Opt. 64, 1146–1157 (2017).
[Crossref]

J. C. Valencia-Estrada, J. García-Marquez, L. Chassagne, and S. Topsu, “Catadioptric interfaces for designing VLC antennae,” Appl. Opt. 56, 7559–7566 (2017).
[Crossref]

2015 (1)

J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

2010 (1)

2009 (1)

2008 (1)

2005 (1)

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

2003 (2)

2002 (1)

1992 (1)

1954 (1)

Bara, S.

Bonin, K. D.

Brzobohatý, O.

Burvall, A.

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

Calle, Á. H. B.

Chaparro-Romo, H. A.

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

Chassagne, L.

Chávez-Cerda, S.

Chebbi, B.

Cižmár, T.

Dholakia, K.

Estrada, J. C. V.

Flores-Hernández, R. B.

J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
[Crossref]

Friberg, A. T.

Garcés-Chávez, V.

García-Marquez, J.

Golub, I.

Gutiérrez-Vega, J. C.

Hernández, D. M.

Jaroszewicz, Z.

Kolodziejczyk, A.

Lozano-Rincón, N. D. C.

N. D. C. Lozano-Rincón and J. C. Valencia-Estrada, “Paraboloid-aspheric lenses free of spherical aberration,” J. Mod. Opt. 64, 1146–1157 (2017).
[Crossref]

Malacara-Hernández, D.

J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
[Crossref]

Malacara-Hernández, Z.

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

McGloin, D.

McKell, C.

McLeod, J. H.

Mirtchev, T.

Nowacki, D.

Nuttall, J.

Pereira-Ghirghi, M. V.

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

Popov, S. Y.

Rodrguez-Masegosa, R.

Shaw, D.

Sochacki, J.

Thaning, A.

Topsu, S.

Valencia-Estrada, J. C.

J. C. Valencia-Estrada, J. García-Marquez, L. Chassagne, and S. Topsu, “Catadioptric interfaces for designing VLC antennae,” Appl. Opt. 56, 7559–7566 (2017).
[Crossref]

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

N. D. C. Lozano-Rincón and J. C. Valencia-Estrada, “Paraboloid-aspheric lenses free of spherical aberration,” J. Mod. Opt. 64, 1146–1157 (2017).
[Crossref]

J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
[Crossref]

Zemánek, P.

Appl. Opt. (1)

J. Mod. Opt. (1)

N. D. C. Lozano-Rincón and J. C. Valencia-Estrada, “Paraboloid-aspheric lenses free of spherical aberration,” J. Mod. Opt. 64, 1146–1157 (2017).
[Crossref]

J. Opt. (1)

J. C. Valencia-Estrada, M. V. Pereira-Ghirghi, Z. Malacara-Hernández, and H. A. Chaparro-Romo, “Aspheric coefficients of deformation for a Cartesian oval surface,” J. Opt. 46, 100–107 (2017).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

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

Opt. Express (1)

Opt. Lett. (5)

Opt. Photon. News (1)

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

Proc. R. Soc. A (1)

J. C. Valencia-Estrada, R. B. Flores-Hernández, and D. Malacara-Hernández, “Singlet lenses free of all orders of spherical aberration,” Proc. R. Soc. A 471, 20140608 (2015).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. An axicon converts a normally incident plane wave into a converging conical wave. This is a traditional method to generate nondiffracting beams within the interfering biconical region.
Fig. 2.
Fig. 2. (a) Meridional half-plane of the gaxicon, illustrating the deviation of the incoming rays by the surfaces and their optical paths traversed. (b) Notation for the unit vectors of the incoming and emerging rays. (c) Auxiliary source and image points used in the derivation of Eqs. (7) and (8).
Fig. 3.
Fig. 3. Convergent and divergent gaxicons with a concave parabolic input surface with fa=20  cm, refraction index n=1.5, thickness T=5  cm.
Fig. 4.
Fig. 4. Convergent and divergent gaxicons with an exotic input surface Eq. (12) and slope parameters w=tanβ=0.15, i.e., β=8.53°. Refraction index n=1.5, thickness T=5  cm.
Fig. 5.
Fig. 5. Convergent gaxicons with cosinusoidal and Gaussian input functions and slope parameters w=tanβ=0.15, i.e., β=8.53°. Refraction index n=1.5, thickness T=5  cm.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

n=sinθ1sinθ2=1cos2θ11cos2θ2=1(v^1·n^a)21(v^2·n^a)2,
v^1=[0,1],
v^2=[rbra,zbza](rbra)2+(zbza)2,
n^a=[za,1]1+(za)2,
n=|za|(rarb)2+(zazb)2|rbra+(zbza)za|.
ra2+(zaa)2+n(rbra)2+(zbza)2+(rbh)2+(zbTb)2=a+nT+b2+h2.
n=1T(rbra)2+(zbza)2×[a+ra2+(zaa)2b2+h2+(rbh)2+(zbTb)2].
n=rbwTzaw2+1+zbw2+1((rarb)2+(zazb)2T),
rb=ra+ρ(zbza)ζ,
zb=(sζ+wρns)za+(1ns)ζTwζraζ+wρns,
ρzaK(1nKza2),
ζ1K(za2+nKza2),
Kn(za2+1),
s1+w2=secβ.
rb=raandzb(ra)=T(sin|β|ncos|β|)ra,
za(ra)=ra2/4fa,
za(ra)=c1ra2c2ra3,
za(ra)=0.2[cos(2πra/0.1)1].
za(ra)=0.05[exp((ra/0.05)2)1]