Abstract

An approach to yield a planar light sheet with thickness below the Abbe’s diffraction limit over ultra-long propagation distances is presented. Such features emerge by an induced interference of the fields associated to the caustic branches of a cusp-type curved beam. The optical sheet width and length are dynamically tuned by just varying one parameter of the signal encoded in a spatial light modulator within a standard setup for curved beam generation. This light sheet possesses the following characteristics: a high length-to-width ratio, a width below the Abbe’s diffraction limit, reduced sidelobes, and very low spreading along the sheet length. These planar light sheets could be useful in light-sheet microscopy and applications to surface and interface physics. In addition, these sheets can be easily transformed in an optical needle having rectangular symmetry by using a two-dimensional cusp beam instead of an one-dimensional beam.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (2)

2019 (4)

2018 (4)

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

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (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]

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

2017 (5)

2016 (1)

2015 (4)

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Caustics, catastrophes and symmetries in curved beams,” Phys. Rev. A 92(3), 033850 (2015).
[Crossref]

D. Panneton, G. St-Onge, M. Piché, and S. Thibault, “Needles of light produced with a spherical mirror,” Opt. Lett. 40(3), 419–422 (2015).
[Crossref]

G. Yuan, E. T. F. 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 (2015).
[Crossref]

2014 (4)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
[Crossref]

M. N. Zhu, Q. Cao, and Q. H. Gao, “Creation of a 50,000λ long needle-like field with 0.36λ width,” J. Opt. Soc. Am. A 31(3), 500–504 (2014).
[Crossref]

2013 (6)

P. Suresh, C. Mariyal, K. B. Rajesh, T. V. S. Pillai, and Z. Jaroszewicz, “Generation of a strong uniform transversely polarized nondiffracting beam using a high-numerical-aperture lens axicon with a binary phase mask,” Appl. Opt. 52(4), 849–853 (2013).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21(11), 13425–13435 (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]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

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]

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38(8), 1331–1333 (2013).
[Crossref]

2012 (2)

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. F. 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]

2009 (1)

Focus issue: super-resolution imaging, “Beyond the diffraction limit,” Nat. Photonics 3(7), 361 (2009).
[Crossref]

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]

2007 (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Adamo, G.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

Admon, T.

Amaya, D.

Andilla, J.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Arie, A.

N. Shapira, Z. Deng, R. Remez, D. Singh, E. Katzav, and A. Arie, “Multi-lobe superoscillation and its application to structured illumination microscopy,” Opt. Express 27(24), 34530–34541 (2019).
[Crossref]

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Banerji, S.

Bautista, G.

Bekenstein, R.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

Berry, M. V.

M. V. Berry, Catastrophe optics: morphologies of caustics and their diffraction patterns, in Progress in Optics XVII, E. Wolf, ed. (North Holland, 1989).

Bock, M.

R. Grunwald and M. Bock, “Needle beams: a review,” Adv. Phys.: X 5(1), 1736950 (2020).
[Crossref]

Bongiovanni, D.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Boyraz, O.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Cao, Q.

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.

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]

Chad, J. E.

E. T. F. 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]

Chen, G.

Chen, H.

Chen, Z.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[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]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Dai, L.

Deng, Z.

Dennis, M. R.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Du, L.

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]

Eyal, A.

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]

Goldman, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts & Company, 2005) Chap.III-IV, pp. 55–85.

Greenfield, E.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21(11), 13425–13435 (2013).
[Crossref]

Grunwald, R.

R. Grunwald and M. Bock, “Needle beams: a review,” Adv. Phys.: X 5(1), 1736950 (2020).
[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]

Gualda, E. J.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Guclu, C.

H. Gao, Q.

Hu, Y.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Hurwitz, I.

Jaroszewicz, Z.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref]

Juvells, I.

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]

Kakko, J.

Kaminer, I.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

Katzav, E.

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]

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]

Lencina, A.

Li, H.

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

Li, M.

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

Li, W.

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

Li, Y.

Lindberg, J.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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.

Loza-Alvarez, P.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

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]

Lumer, Y.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[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]

Majumder, A.

Makris, K.

Maluenda, D.

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]

Man, Z.

Mariyal, C.

Martínez-Herrero, R.

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]

Martínez-Matos, Ó.

D. Amaya, Ó. Martínez-Matos, and P. Vaveliuk, “Abruptly autofocusing beams from phase perturbations having forced symmetry,” Opt. Lett. 44(15), 3733–3736 (2019).
[Crossref]

P. Vaveliuk, A. Lencina, and Ó. Martínez-Matos, “Caustic beams from unusual powers of the spectral phase,” Opt. Lett. 42(19), 4008–4011 (2017).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Caustics, catastrophes and symmetries in curved beams,” Phys. Rev. A 92(3), 033850 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
[Crossref]

E. Neyra, Ó. Martínez-Matos, and P. Vaveliuk, “Numerical simulations of the propagation properties of the Optical Razor Blade (ORB),” figshare (2020), https://doi.org/10.6084/m9.figshare.12597140.

Marti-Panameño, E. A.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Meem, M.

Mendoza González, G.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Menon, R.

Min, C.

Morandotti, R.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Nagar, H.

H. Nagar, T. Admon, D. Goldman, A. Eyal, and Y. Roichman, “Optical trapping below the diffraction limit with a tunable beam waist using super-oscillating beams,” Opt. Lett. 44(10), 2430–2433 (2019).
[Crossref]

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Nemirovsky, J.

Neyra, E.

E. Neyra, Ó. Martínez-Matos, and P. Vaveliuk, “Numerical simulations of the propagation properties of the Optical Razor Blade (ORB),” figshare (2020), https://doi.org/10.6084/m9.figshare.12597140.

Olarte, O. E.

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Panneton, D.

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]

Piché, M.

D. Panneton, G. St-Onge, M. Piché, and S. Thibault, “Needles of light produced with a spherical mirror,” Opt. Lett. 40(3), 419–422 (2015).
[Crossref]

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]

Pillai, T. V. S.

Qiu, C.

G. Chen, Z. Wen, and C. Qiu, “Superoscillation: from physics to optical applications,” Light: Sci. Appl. 8(1), 56 (2019).
[Crossref]

Rajesh, K. B.

Remez, R.

Robles, R. A.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Rodrigo, J. A.

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Caustics, catastrophes and symmetries in curved beams,” Phys. Rev. A 92(3), 033850 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
[Crossref]

Rogers, E. T. F.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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]

Roichman, Y.

H. Nagar, T. Admon, D. Goldman, A. Eyal, and Y. Roichman, “Optical trapping below the diffraction limit with a tunable beam waist using super-oscillating beams,” Opt. Lett. 44(10), 2430–2433 (2019).
[Crossref]

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Roy, T.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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]

Savo, S.

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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]

Schley, R.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21(11), 13425–13435 (2013).
[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]

Segev, M.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. Makris, and M. Segev, “Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams,” Opt. Express 21(11), 13425–13435 (2013).
[Crossref]

Sensale-Rodriguez, B.

Shapira, N.

Shen, Z.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

Sheppard, C.

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]

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]

Singh, B. K.

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Singh, D.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

St-Onge, G.

Suresh, P.

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]

Thibault, S.

Turquet, L.

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref]

Vaveliuk, P.

D. Amaya, Ó. Martínez-Matos, and P. Vaveliuk, “Abruptly autofocusing beams from phase perturbations having forced symmetry,” Opt. Lett. 44(15), 3733–3736 (2019).
[Crossref]

P. Vaveliuk, A. Lencina, and Ó. Martínez-Matos, “Caustic beams from unusual powers of the spectral phase,” Opt. Lett. 42(19), 4008–4011 (2017).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Caustics, catastrophes and symmetries in curved beams,” Phys. Rev. A 92(3), 033850 (2015).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
[Crossref]

E. Neyra, Ó. Martínez-Matos, and P. Vaveliuk, “Numerical simulations of the propagation properties of the Optical Razor Blade (ORB),” figshare (2020), https://doi.org/10.6084/m9.figshare.12597140.

Veysi, M.

Wang, A.

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]

Wang, S.

Wei, J.

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]

Wen, Z.

Wetzel, B.

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Wu, Z.

Xie, X.

Yang, L.

Yu, Y.

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

Yuan, G.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

Yuan, W.

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

Yuan, X.

Zang, X.

Zha, Y.

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]

Zhang, K.

Zhang, S.

Zhang, Y.

Zhang, Z.

Zheludev, N. I.

G. Yuan, E. T. F. 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 (2015).
[Crossref]

E. T. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

E. T. F. 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]

Zhou, J.

Zhu, M. N.

Zhu, S.

Zhu, Y.

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref]

Adv. Opt. Photonics (1)

O. E. Olarte, J. Andilla, E. J. Gualda, and P. Loza-Alvarez, “Light-sheet microscopy: a tutorial,” Adv. Opt. Photonics 10(1), 111–179 (2018).
[Crossref]

Adv. Phys.: X (1)

R. Grunwald and M. Bock, “Needle beams: a review,” Adv. Phys.: X 5(1), 1736950 (2020).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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. F. Rogers, S. Savo, J. Lindberg, T. Roy, M. R. Dennis, and N. I. Zheludev, “Super-oscillatory optical needle,” Appl. Phys. Lett. 102(3), 031108 (2013).
[Crossref]

J. Opt. (1)

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]

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

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

Light: Sci. Appl. (2)

G. Chen, Z. Wen, and C. Qiu, “Superoscillation: from physics to optical applications,” Light: Sci. Appl. 8(1), 56 (2019).
[Crossref]

B. K. Singh, H. Nagar, Y. Roichman, and A. Arie, “Particle manipulation beyond the diffraction limit using structured super-oscillating light beams,” Light: Sci. Appl. 6(9), e17050 (2017).
[Crossref]

Nanomaterials (1)

Y. Yu, W. Li, H. Li, M. Li, and W. Yuan, “An investigation of influencing factors on practical sub-diffraction limit focusing of planar super-oscillation lenses,” Nanomaterials 8(4), 185 (2018).
[Crossref]

Nat. Commun. (2)

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]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5(1), 5189 (2014).
[Crossref]

Nat. Mater. (1)

E. T. F. 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]

Nat. Photonics (3)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref]

Focus issue: super-resolution imaging, “Beyond the diffraction limit,” Nat. Photonics 3(7), 361 (2009).
[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]

Opt. Express (5)

Opt. Lett. (6)

Optica (1)

Phys. Rev. A (1)

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and Ó. Martínez-Matos, “Caustics, catastrophes and symmetries in curved beams,” Phys. Rev. A 92(3), 033850 (2015).
[Crossref]

Phys. Rev. Lett. (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Sci. Rep. (4)

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]

G. Yuan, E. T. F. 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 (2015).
[Crossref]

M. Li, W. Li, H. Li, Y. Zhu, and Y. Yu, “Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci,” Sci. Rep. 7(1), 1335 (2017).
[Crossref]

D. Bongiovanni, Y. Hu, B. Wetzel, R. A. Robles, G. Mendoza González, E. A. Marti-Panameño, Z. Chen, and R. Morandotti, “Efficient optical energy harvesting in self-accelerating beams,” Sci. Rep. 5(1), 13197 (2015).
[Crossref]

Other (3)

J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts & Company, 2005) Chap.III-IV, pp. 55–85.

E. Neyra, Ó. Martínez-Matos, and P. Vaveliuk, “Numerical simulations of the propagation properties of the Optical Razor Blade (ORB),” figshare (2020), https://doi.org/10.6084/m9.figshare.12597140.

M. V. Berry, Catastrophe optics: morphologies of caustics and their diffraction patterns, in Progress in Optics XVII, E. Wolf, ed. (North Holland, 1989).

Supplementary Material (1)

NameDescription
» Code 1       This Code (in Mathematica language) performs a numerical integration of the field intensity as a function of the longitudinal (z) and transversal (x) coordinates from Eqs. (2-3) considering the set of experimental parameters defining the beam propaga

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Figures (4)

Fig. 1.
Fig. 1. Representation of the ORB generated from the SAB (shown in the $xz$-plane). The LS occurs in the $yz$-plane. The cusp caustic tied to the SAB (dashed line) becomes a caustic with laterally displaced branches (continuum line) when an even linear phase is superposed to the SAB phase. The phase perturbation strength $\alpha$ fixes the branch displacement. The ORB emerges along $z$-axis, in the closeness of $z_{in}/z_0$. Top inset: SAB phase mask, scale: 0 (black), $2\pi$ (white) and intensity map, scale: maximum intensity (bright), zero intensity (dark). Bottom inset: ORB phase mask and intensity map.
Fig. 2.
Fig. 2. FWHM of the ORB intensity: (a) along the $x$-axis at its waist ($z=z_w$) and (b) along the $z$-axis (at $x=0)$ vs. $\alpha$. The inset depicts the ORB length-to-width ratio against $\alpha$.
Fig. 3.
Fig. 3. (a) Intensity distribution of the ORB for $\alpha =11$ in the $xz$-plane. Light-blue dashed curves are the caustic branches intersecting at $z_{in}$. A zoom of the framed box of (a) is shown on (b) numerical and (c) experimental. The different scales for $x$ and $z$ axes remark the ultra-long feature of the ORB.
Fig. 4.
Fig. 4. (a) ORB sidelobe-to-main lobe intensity ratio and (b) thickness $\Delta x$ against $z-z_{in}$. Vertical lines in (a)-(b) indicate the $\Delta z$ extension. The gray curve in (b) is the on-axis intensity profile. (c) Transverse intensity profile along $x$ for the ORB (red) and the sinc-squared pattern (black). Dots and stars are experimental values while lines are the numerical simulations.

Equations (4)

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

x c ( K c ) = x 0 [ K ( d 2 ψ / d K 2 ) ( d ψ / d K ) ] K = K c ,
z c ( K c ) = z 0 ( d 2 ψ / d K 2 ) K = K c .
u K + ( K ) ( x , z ) = e i ( 2 π / λ ) z 0 ( ) ( 0 ) A ( K ) e i ψ ( K ) e i K 2 z 2 z 0 e i K x x 0 d K ,
I = | u K + + u K | 2 = I K + + I K + I c r ,