Abstract

Optical needles produced by means of diffractive technology might display limited quality and uniformity. It has been suggested that the bulky optical elements present on these setups can be responsible of such behavior. In particular, issues such as the lack of flatness of the optical components, modulation errors in the holographic displays, and optical aberrations might degrade the quality of the needle. In this paper, we model how these variables affect the uniformity of the irradiance of the needle on the propagation axis. A comparison between experimental and computationally estimated results is provided.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

L. Turquet, X. Zang, J.-P. Kakko, H. Lipsanen, G. Bautista, and M. Kauranen, “Demonstration of longitudinally polarized optical needles,” Opt. Express 26(21), 27572–27584 (2018).
[Crossref]

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, “Diffractive optics for axial intensity shaping of Bessel beams,” J. Opt. 20(8), 085606 (2018).
[Crossref]

R. Martínez-Herrero, D. Maluenda, I. Juvells, and A. Carnicer, “Synthesis of light needles with tunable length and nearly constant irradiance,” Sci. Rep. 8(1), 2657 (2018).
[Crossref]

2017 (2)

M. Veysi, C. Guclu, O. Boyraz, and F. Capolino, “Reflective metasurface lens with an elongated needle-shaped focus,” J. Opt. Soc. Am. B 34(2), 374–382 (2017).
[Crossref]

Y. Yu, H. Huang, M. Zhou, and Q. Zhan, “Creation of a multi-segmented optical needle with prescribed length and spacing using the radiation pattern from a sectional-uniform line source,” Sci. Rep. 7(1), 10708 (2017).
[Crossref]

2016 (1)

2015 (3)

2014 (1)

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2014).
[Crossref]

2013 (3)

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

D. Maluenda, I. Juvells, R. Martínez-Herrero, and A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21(5), 5432–5439 (2013).
[Crossref]

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(1), 2061 (2013).
[Crossref]

2012 (4)

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
[Crossref]

C. J. Sheppard and S. Mehta, “Three-level filter for increased depth of focus and bessel beam generation,” Opt. Express 20(25), 27212–27221 (2012).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2005 (2)

2003 (1)

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E 67(4), 046611 (2003).
[Crossref]

1985 (1)

K. Perlin, “An image synthesizer,” ACM Siggraph Comput. Graph. 19(3), 287–296 (1985).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959).
[Crossref]

1954 (1)

Adamo, G.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2014).
[Crossref]

Anbarasan, P.

April, A.

Arrizón, V.

Bateman, D.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave version 4.2.1 manual: a high-level interactive language for numerical computations (2017).

Bautista, G.

Bhattacharya, S.

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, “Diffractive optics for axial intensity shaping of Bessel beams,” J. Opt. 20(8), 085606 (2018).
[Crossref]

Boyraz, O.

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(1), 2061 (2013).
[Crossref]

Capolino, F.

Carnicer, A.

Chad, J. E.

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Cižmár, T.

Courjon, D.

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E 67(4), 046611 (2003).
[Crossref]

Dehez, H.

Dennis, M. R.

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Dharmavarapu, R.

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, “Diffractive optics for axial intensity shaping of Bessel beams,” J. Opt. 20(8), 085606 (2018).
[Crossref]

Dholakia, K.

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
[Crossref]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

Eaton, J. W.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave version 4.2.1 manual: a high-level interactive language for numerical computations (2017).

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(1), 2061 (2013).
[Crossref]

Fourmaux, S.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Gan, F.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(1), 2061 (2013).
[Crossref]

González, L. A.

Grosjean, T.

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E 67(4), 046611 (2003).
[Crossref]

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(1), 2061 (2013).
[Crossref]

Guclu, C.

Hauberg, S.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave version 4.2.1 manual: a high-level interactive language for numerical computations (2017).

Hecht, B.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University Press, 2012).

Hong, M.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

Huang, H.

Y. Yu, H. Huang, M. Zhou, and Q. Zhan, “Creation of a multi-segmented optical needle with prescribed length and spacing using the radiation pattern from a sectional-uniform line source,” Sci. Rep. 7(1), 10708 (2017).
[Crossref]

Huang, K.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

Jaroszewicz, Z.

Javidi, B.

Jiao, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

Juodkazis, S.

R. Dharmavarapu, S. Bhattacharya, and S. Juodkazis, “Diffractive optics for axial intensity shaping of Bessel beams,” J. Opt. 20(8), 085606 (2018).
[Crossref]

Juvells, I.

Kakko, J.-P.

Kauranen, M.

Kieffer, J.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Kim, J.

Kitamura, K.

Kozawa, Y.

Y. Kozawa and S. Sato, “Long depth-of-focus imaging by a non-diffracting optical needle under strong aberration,” in Lasers and Electro-Optics (CLEO), 2017 Conference on, (IEEE, 2017) pp. 1–2.

Légaré, F.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Li, Y.

Lin, J.

Lindberg, J.

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Lipsanen, H.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Luo, X.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

MacLean, J.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Maluenda, D.

Martínez-Herrero, R.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

McLeod, J. H.

Mehta, S.

Noda, S.

Novotny, L.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University Press, 2012).

Payeur, S.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Perlin, K.

K. Perlin, “An image synthesizer,” ACM Siggraph Comput. Graph. 19(3), 287–296 (1985).
[Crossref]

Piché, M.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express 20(14), 14891–14905 (2012).
[Crossref]

Ponce, R.

Qin, F.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

Qiu, C.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref]

Rajesh, K.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253(1274), 358–379 (1959).
[Crossref]

Rogers, E. T.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2014).
[Crossref]

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Roy, T.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2014).
[Crossref]

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Sakai, K.

Sato, S.

Y. Kozawa and S. Sato, “Long depth-of-focus imaging by a non-diffracting optical needle under strong aberration,” in Lasers and Electro-Optics (CLEO), 2017 Conference on, (IEEE, 2017) pp. 1–2.

Savo, S.

E. T. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref]

Schmidt, B.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Serrano-Heredia, A.

Shen, Z.

G. Yuan, E. T. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2014).
[Crossref]

Sheppard, C.

C. Sheppard, “Optimization of pupil filters for maximal signal concentration factor,” Opt. Lett. 40(4), 550–553 (2015).
[Crossref]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Sheppard, C. J.

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Tan, J.

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. Schmidt, J. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J. Kieffer, “Generation of a beam of fast electrons by tightly focusing a radially polarized ultrashort laser pulse,” Appl. Phys. Lett. 101(4), 041105 (2012).
[Crossref]

Turquet, L.

Veysi, M.

Wang, H.

Y. Zha, J. Wei, H. Wang, and F. Gan, “Creation of an ultra-long depth of focus super-resolution longitudinally polarized beam with a ternary optical element,” J. Opt. 15(7), 075703 (2013).
[Crossref]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wehbring, R.

J. W. Eaton, D. Bateman, S. Hauberg, and R. Wehbring, GNU Octave version 4.2.1 manual: a high-level interactive language for numerical computations (2017).

Wei, J.

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Supplementary Material (1)

NameDescription
» Code 1       A numerical tool to evaluate highly focused holographic optical needles

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Figures (5)

Fig. 1.
Fig. 1. Coordinate systems and geometrical variables.
Fig. 2.
Fig. 2. Optical setup: LP: linear polarizer, $\lambda /2$: half-wave plate, $\lambda /4$: quarter-wave plate, SLM: spatial light modulator, L$_1$ ($f_1$= 100 mm) and L$_2$ ($f_2$ = 50 mm), SF: spatial filter, TL: tube lens ($f_{\textrm {TL}}$= 400), ML: microscope lens (NA=0.65), CCD1 and CCD2: cameras.
Fig. 3.
Fig. 3. Modulation function $h(\theta )$ for $N=10$ and $N=50$. The inset shows the 2D-profile of the modulation function $h(\theta )$ for $N=10$.
Fig. 4.
Fig. 4. Experimental results. Left column: HON for $N=$4, 6 and 10. Right column: Irradiance of the HON on the optical axis. Blue, green and red curves display experimental, estimated and theoretical data
Fig. 5.
Fig. 5. Point spread function across the $z-$ axis

Equations (7)

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E 0 = cos θ ( ( E s e 1 ) e 1 + ( E s e 2 ) e 2 ) .
e 1 = ( sin φ , cos φ , 0 )
e 2 = ( cos θ cos φ , cos θ sin φ , sin θ )
e 2 = ( cos φ , sin φ , 0 ) .
E ( r , ϕ , z ) 0 θ 0 0 2 π E 0 ( θ , φ ) e i k r sin θ cos ( ϕ φ ) e i k z cos θ sin θ d θ d φ
E s ( θ , φ ) = exp ( sin 2 θ f 0 2 sin 2 θ 0 ) h ( θ ) e x ,
h ( θ ) = N sinc ( 2 π N cos θ ( 1 + cos θ 0 ) / 2 1 cos θ 0 ) sin θ ;

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