Abstract

Nonlinear optical interactions play a crucial role in modern technology and lead to important applications such as optical switching, optical harmonic generation, and the characterization of ultrafast material processes. Nonlinear interactions are enhanced by using a tightly focused laser beam, but nonetheless they are typically excited by a loosely focused (that is, paraxial) laser beam. Here we investigate a specific process, third-harmonic generation, excited by a highly nonparaxial beam that illuminates an interaction region from a nearly full solid angle. We elucidate the influence of the focal volume and the pump intensity on the number of frequency-tripled photons by varying the solid angle from which the pump light is focused, and we find good agreement between the experiments and numerical calculations. As the pump light is focused to a spot size much smaller than the laser wavelength, the Gouy phase does not limit the yield of frequency-converted photons, in stark contrast to the paraxial regime. We believe that our findings are generic and apply to many other nonlinear optical processes when the pump light is focused from a full solid angle.

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

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References

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  5. P. Reichenbach, A. Horneber, D. A. Gollmer, A. Hille, J. Mihaljevic, C. Schäfer, D. P. Kern, A. J. Meixner, D. Zhang, M. Fleischer, and L. M. Eng, “Nonlinear optical point light sources through field enhancement at metallic nanocones,” Opt. Express 22, 15484–15501 (2014).
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  9. V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
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    [Crossref]
  22. R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
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    [Crossref]
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    [Crossref]
  28. G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
    [Crossref]
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    [Crossref]
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    [Crossref]
  32. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
    [Crossref]
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    [Crossref]

2016 (1)

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

2015 (1)

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

2014 (1)

2013 (1)

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

2012 (4)

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

T. Tyc, “Gouy phase for full-aperture spherical and cylindrical waves,” Opt. Lett. 37, 924–926 (2012).
[Crossref]

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

2009 (1)

V. Vaičaitis, V. Jarutis, and D. Pentaris, “Conical third-harmonic generation in normally dispersive media,” Phys. Rev. Lett. 103, 103901 (2009).
[Crossref]

2008 (2)

2007 (3)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

2006 (1)

2005 (1)

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

2003 (2)

D. P. Biss and T. G. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28, 923–925 (2003).
[Crossref]

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

2002 (1)

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88, 163901 (2002).
[Crossref]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

1999 (1)

1998 (1)

J. Kutzner and H. Zacharias, “VUV generation by frequency tripling the third harmonic of a picosecond kHz Nd:YLF laser in xenon and mercury vapour,” Appl. Phys. B 66, 571–577 (1998).
[Crossref]

1990 (1)

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

1989 (1)

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

1988 (1)

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

1986 (2)

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

I. M. Basset, “Limit to concentration by focusing,” J. Mod. Opt. 33, 279–286 (1986).

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

1931 (1)

M. Göppert-Mayer, “Über elementarakte mit zwei quantensprüngen,” Ann. Phys. 401, 273–294 (1931).

Aiello, A.

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

Baba, M.

Bader, M.

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

Barrett, D.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Basset, I. M.

I. M. Basset, “Limit to concentration by focusing,” J. Mod. Opt. 33, 279–286 (1986).

Berger, A.

Biss, D. P.

Bokor, N.

N. Bokor and N. Davidson, “4π focusing with single paraboloid mirror,” Opt. Commun. 281, 5499–5503 (2008).
[Crossref]

Boyd, R. W.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Braun, K.

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

Brown, T. G.

Chalopin, B.

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley, 1989).

Collett, E.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Davidson, N.

N. Bokor and N. Davidson, “4π focusing with single paraboloid mirror,” Opt. Commun. 281, 5499–5503 (2008).
[Crossref]

Davis, W. V.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley, 1989).

Dyba, M.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88, 163901 (2002).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Eng, L. M.

Ferray, M.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Fischer, M.

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

Fleischer, M.

Fraher, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Ganeev, R.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

Ganeev, R. A.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Golla, A.

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

Gollmer, D. A.

Gonoskov, I.

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

Göppert-Mayer, M.

M. Göppert-Mayer, “Über elementarakte mit zwei quantensprüngen,” Ann. Phys. 401, 273–294 (1931).

Gorbushin, V.

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley, 1989).

Harder, I.

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

Hell, S. W.

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88, 163901 (2002).
[Crossref]

Henis, Z.

Heugel, S.

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Hille, A.

Horneber, A.

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

P. Reichenbach, A. Horneber, D. A. Gollmer, A. Hille, J. Mihaljevic, C. Schäfer, D. P. Kern, A. J. Meixner, D. Zhang, M. Fleischer, and L. M. Eng, “Nonlinear optical point light sources through field enhancement at metallic nanocones,” Opt. Express 22, 15484–15501 (2014).
[Crossref]

Jarutis, V.

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

V. Vaičaitis, V. Jarutis, and D. Pentaris, “Conical third-harmonic generation in normally dispersive media,” Phys. Rev. Lett. 103, 103901 (2009).
[Crossref]

Kamalov, S. R.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Kern, D. P.

Kodirov, M.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Konermann, H.

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

Kulagin, I.

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

Kulagin, I. A.

Kuroda, H.

Kutzner, J.

J. Kutzner and H. Zacharias, “VUV generation by frequency tripling the third harmonic of a picosecond kHz Nd:YLF laser in xenon and mercury vapour,” Appl. Phys. B 66, 571–577 (1998).
[Crossref]

L’Huillier, A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Leiderer, P.

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

Leuchs, G.

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

M. Sondermann, N. Lindlein, and G. Leuchs, “Maximizing the electric field strength in the foci of high numerical aperture optics,” arXiv:0811.2098 (2008).

Li, X.

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Li, X. F.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

Li, Y.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Lindlein, N.

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

M. Sondermann, N. Lindlein, and G. Leuchs, “Maximizing the electric field strength in the foci of high numerical aperture optics,” arXiv:0811.2098 (2008).

Lompre, L.

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Lompré, L. A.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

Mainfray, G.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Maiwald, R.

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

Malcuit, M. S.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

Malikov, M.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Mantel, K.

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

Manus, C.

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

Marcus, G.

Meixner, A. J.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

P. Reichenbach, A. Horneber, D. A. Gollmer, A. Hille, J. Mihaljevic, C. Schäfer, D. P. Kern, A. J. Meixner, D. Zhang, M. Fleischer, and L. M. Eng, “Nonlinear optical point light sources through field enhancement at metallic nanocones,” Opt. Express 22, 15484–15501 (2014).
[Crossref]

Mihaljevic, J.

Pan, A.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Pentaris, D.

V. Vaičaitis, V. Jarutis, and D. Pentaris, “Conical third-harmonic generation in normally dispersive media,” Phys. Rev. Lett. 103, 103901 (2009).
[Crossref]

Peschel, U.

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Reichenbach, P.

Rogalski, J.

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

Ryasnyansky, A.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Rzaewski, K.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

Schaefer, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Schäfer, C.

Schwider, J.

Sheppard, C.

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

Smyth, R.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Sondermann, M.

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

G. Leuchs, K. Mantel, A. Berger, H. Konermann, M. Sondermann, U. Peschel, N. Lindlein, and J. Schwider, “Interferometric null test of a deep parabolic reflector generating a Hertzian dipole field,” Appl. Opt. 47, 5570–5584 (2008).
[Crossref]

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

M. Sondermann, N. Lindlein, and G. Leuchs, “Maximizing the electric field strength in the foci of high numerical aperture optics,” arXiv:0811.2098 (2008).

Stabinis, A.

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

Steponkevicius, K.

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

Suzuki, M.

Tugushev, R.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Tyc, T.

Umidullaev, S. U.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

Usmanov, T.

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

Vaicaitis, V.

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

V. Vaičaitis, V. Jarutis, and D. Pentaris, “Conical third-harmonic generation in normally dispersive media,” Phys. Rev. Lett. 103, 103901 (2009).
[Crossref]

Wackenhut, F.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Wang, X.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Webb, W. W.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Westphal, V.

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

Williams, R. M.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

Yew, E.

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

Zacharias, H.

J. Kutzner and H. Zacharias, “VUV generation by frequency tripling the third harmonic of a picosecond kHz Nd:YLF laser in xenon and mercury vapour,” Appl. Phys. B 66, 571–577 (1998).
[Crossref]

Zhang, D.

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

P. Reichenbach, A. Horneber, D. A. Gollmer, A. Hille, J. Mihaljevic, C. Schäfer, D. P. Kern, A. J. Meixner, D. Zhang, M. Fleischer, and L. M. Eng, “Nonlinear optical point light sources through field enhancement at metallic nanocones,” Opt. Express 22, 15484–15501 (2014).
[Crossref]

Zhuang, X.

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Zigler, A.

Zipfel, W. R.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

Am. J. Phys. (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Ann. Phys. (1)

M. Göppert-Mayer, “Über elementarakte mit zwei quantensprüngen,” Ann. Phys. 401, 273–294 (1931).

Appl. Opt. (2)

Appl. Phys. B (2)

R. Ganeev, V. Gorbushin, I. Kulagin, and T. Usmanov, “Optical harmonic generation in media with positive dispersion,” Appl. Phys. B 41, 69–71 (1986).
[Crossref]

J. Kutzner and H. Zacharias, “VUV generation by frequency tripling the third harmonic of a picosecond kHz Nd:YLF laser in xenon and mercury vapour,” Appl. Phys. B 66, 571–577 (1998).
[Crossref]

Eur. Phys. J. D (1)

A. Golla, B. Chalopin, M. Bader, I. Harder, K. Mantel, R. Maiwald, N. Lindlein, M. Sondermann, and G. Leuchs, “Generation of a wave packet tailored to efficient free space excitation of a single atom,” Eur. Phys. J. D 66, 190 (2012).
[Crossref]

Europhys. Lett. (1)

A. L’Huillier, L. Lompre, M. Ferray, X. Li, G. Mainfray, and C. Manus, “Third-harmonic generation in xenon in a pulsed jet and a gas cell,” Europhys. Lett. 5, 601 (1988).
[Crossref]

J. Mod. Opt. (1)

I. M. Basset, “Limit to concentration by focusing,” J. Mod. Opt. 33, 279–286 (1986).

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

Laser Photon. Rev. (1)

X. Wang, X. Zhuang, F. Wackenhut, Y. Li, A. Pan, and A. J. Meixner, “Power-and polarization dependence of two photon luminescence of single CdSe nanowires with tightly focused cylindrical vector beams of ultrashort laser pulses,” Laser Photon. Rev. 10, 835–842 (2016).
[Crossref]

Laser Phys. (1)

N. Lindlein, R. Maiwald, H. Konermann, M. Sondermann, U. Peschel, and G. Leuchs, “A new 4π -geometry optimized for focusing onto an atom with a dipole-like radiation pattern,” Laser Phys. 17, 927–934 (2007).
[Crossref]

Nat. Biotechnol. (1)

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[Crossref]

Opt. Commun. (4)

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

N. Bokor and N. Davidson, “4π focusing with single paraboloid mirror,” Opt. Commun. 281, 5499–5503 (2008).
[Crossref]

R. Ganeev, S. R. Kamalov, M. Kodirov, M. Malikov, A. Ryasnyansky, R. Tugushev, S. U. Umidullaev, and T. Usmanov, “Harmonic generation in organic dye vapors,” Opt. Commun. 184, 305–308 (2000).
[Crossref]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Chem. Chem. Phys. (1)

A. Horneber, K. Braun, J. Rogalski, P. Leiderer, A. J. Meixner, and D. Zhang, “Nonlinear optical imaging of single plasmonic nanoparticles with 30 nm resolution,” Phys. Chem. Chem. Phys. 17, 21288–21293 (2015).
[Crossref]

Phys. Rev. A (5)

I. Gonoskov, A. Aiello, S. Heugel, and G. Leuchs, “Dipole pulse theory: maximizing the field amplitude from 4π focused laser pulses,” Phys. Rev. A 86, 053836 (2012).
[Crossref]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref]

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rząewski, “Anomalies in optical harmonic generation using high-intensity laser radiation,” Phys. Rev. A 41, 3822–3825 (1990).
[Crossref]

V. Vaičaitis, V. Jarutis, K. Steponkevičius, and A. Stabinis, “Noncollinear six-wave mixing of femtosecond laser pulses in air,” Phys. Rev. A 87, 063825 (2013).
[Crossref]

R. Maiwald, A. Golla, M. Fischer, M. Bader, S. Heugel, B. Chalopin, M. Sondermann, and G. Leuchs, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431 (2012).
[Crossref]

Phys. Rev. Lett. (4)

V. Vaičaitis, V. Jarutis, and D. Pentaris, “Conical third-harmonic generation in normally dispersive media,” Phys. Rev. Lett. 103, 103901 (2009).
[Crossref]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field florescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88, 163901 (2002).
[Crossref]

Other (3)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms (Wiley, 1989).

M. Sondermann, N. Lindlein, and G. Leuchs, “Maximizing the electric field strength in the foci of high numerical aperture optics,” arXiv:0811.2098 (2008).

Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Illustration of different focusing regimes. (a) Paraxial regime using low NA; (b) nonparaxial regime of focusing with high NA; (c) focusing from a full solid angle. Solid/dotted arrows represent the propagation direction of a wave propagating toward/out of the focus. In nonparaxial regimes (b) and (c), the vector properties of the field are important. The rosé ellipse in the center indicates the size of the focal spot. Note that in (c) the spot is not spherical, which is a result of the vector properties of the light, not shown in the diagrams.
Fig. 2.
Fig. 2. (a) Scheme of the experimental setup. HWP, half-wave plate; PBS, polarizing beam splitter; LCC, liquid-crystal polarization converter; M, mirror; CM, compensation mirror; DM, dichroic mirror; PD, photodiode; PM, parabolic mirror; G, grating; BB, beam block; ND, neutral density filter; F 355, 355 nm laser-line filter; PMT, photomultiplier tube. (b) Normalized intensity distribution (b1) and spatially resolved orientation angle ψ of the polarization vector (b2) of the pump beam. ψ=0 is pointing parallel to the optical table and perpendicular to the optical axis of the PM. (c) Simulated axial intensity distribution in the focal region of an aberration-free PM (black solid curve), the PM used in the experiments (orange dotted curve), and for this PM when the aberrations are partially corrected by use of the CM (blue dashed-dotted curve).
Fig. 3.
Fig. 3. Number of generated frequency-tripled photons versus the solid angle subtended by the pump beam. Red points show the experimental results for a pressure of 668 mbar and a fixed pump pulse energy of 114 μJ. The dashed-dotted blue line shows the result of a simulation when using the nonlinear susceptibility χ(5) as a fit parameter (see Section 2 of Supplement 1 for simulation details).
Fig. 4.
Fig. 4. Frequency-tripled photon generation versus power of the fundamental beam at a pressure of 657 mbar for two different solid angles: 55% (red stars) and 94% (blue circles) of full solid angle. The data are presented in double logarithmic scale (symbols). The error bars are obtained from the Poisson statistics of the detected photons. Lines denote the results of fitting a linear function to the respective data.
Fig. 5.
Fig. 5. Theoretical on-axis intensity (solid line) and phase distribution (dashed line) of the pump light on the optical axis of the PM when focusing with the complete PM covering 94% of the full solid angle without any aberrations.