Abstract

We report on the theoretical investigations of the near-field diffraction patterns from micrometer-sized spherical dielectric particles illuminated by a light wave upon the excitation of morphology-dependent resonances in the internal field. The specific spatial area, which constitutes the so-called photonic jet (PJ), is studied. The longitudinal and transverse dimensions of the PJ are calculated along with its peak intensity as a function of the distance from a particle. The numerical calculations show that at a resonance depending on its quality factor, the PJ can “stick” to the particle; its intensity can increase to a several orders of magnitude, and its width can decrease but mostly near the microsphere surface. The average length of the PJ remains nearly unchanged.

© 2012 Optical Society of America

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References

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  1. Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
    [CrossRef]
  2. A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
    [CrossRef]
  3. X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
    [CrossRef]
  4. V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.
  5. X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express 16, 13560–13568 (2008).
    [CrossRef]
  6. S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
    [CrossRef]
  7. W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
    [CrossRef]
  8. A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).
  9. P. W. Barber and S. C. Hill, Light Scattering by Particles (World Scientific, 1990).
  10. A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
    [CrossRef]
  11. Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
    [CrossRef]
  12. Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet calculations in layered radially inhomogeneous micrometer-sized spherical particles,” J. Opt. Soc. Am. B 28, 1825–1830 (2011).
    [CrossRef]
  13. L. A. Weinstein, Open Resonators and Open Waveguides (Golem Press, 1969).
  14. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Willey, 1983).
  15. N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55–74 (2005).
    [CrossRef]
  16. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286–3296 (1996).
    [CrossRef]

2011 (1)

2010 (2)

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
[CrossRef]

2009 (1)

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

2008 (2)

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express 16, 13560–13568 (2008).
[CrossRef]

2007 (2)

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
[CrossRef]

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

2006 (1)

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

2005 (2)

N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55–74 (2005).
[CrossRef]

X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
[CrossRef]

2004 (1)

1996 (1)

Allen, K. W.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Antoszyk, A. N.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Astratov, V. N.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Athanasiadis, C.

N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55–74 (2005).
[CrossRef]

Backman, V.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
[CrossRef]

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[CrossRef]

Barber, P. W.

P. W. Barber and S. C. Hill, Light Scattering by Particles (World Scientific, 1990).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Willey, 1983).

Chen, Z.

Cui, X.

Darafsheh, A.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Erni, D.

Fried, N. M.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Geints, Yu. E.

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet calculations in layered radially inhomogeneous micrometer-sized spherical particles,” J. Opt. Soc. Am. B 28, 1825–1830 (2011).
[CrossRef]

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
[CrossRef]

Hafner, C.

Heifetz, A.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
[CrossRef]

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles (World Scientific, 1990).

Huang, K.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Willey, 1983).

Johnson, B. R.

Katsnelson, A.

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

Kerr, M. D.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Kong, S.-C.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
[CrossRef]

Li, X.

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
[CrossRef]

Memis, O.

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

Mohseni, H.

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

Panina, E. K.

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet calculations in layered radially inhomogeneous micrometer-sized spherical particles,” J. Opt. Soc. Am. B 28, 1825–1830 (2011).
[CrossRef]

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
[CrossRef]

Sahakian, A. V.

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

Sahakiana, A. V.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

Simpson, J. J.

Taflove, A.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

A. Heifetz, J. J. Simpson, S.-C. Kong, A. Taflove, and V. Backman, “Subdiffraction optical resolution of a gold nanosphere located within the nanojet of a Mie-resonant dielectric microsphere,” Opt. Express 15, 17334–17342 (2007).
[CrossRef]

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[CrossRef]

Tsitsas, N. L.

N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55–74 (2005).
[CrossRef]

Weinstein, L. A.

L. A. Weinstein, Open Resonators and Open Waveguides (Golem Press, 1969).

Wu, W.

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

Ying, H. S.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Zemlyanov, A. A.

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet calculations in layered radially inhomogeneous micrometer-sized spherical particles,” J. Opt. Soc. Am. B 28, 1825–1830 (2011).
[CrossRef]

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Heifetz, K. Huang, A. V. Sahakian, X. Li, A. Taflove, and V. Backman, “Experimental confirmation of backscattering enhancement induced by a photonic jet,” Appl. Phys. Lett. 89, 221118 (2006).
[CrossRef]

S.-C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992. (2009).

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

Nanotech. (1)

W. Wu, A. Katsnelson, O. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotech. 18, 485302 (2007).
[CrossRef]

Opt. Commun. (1)

Yu. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Control over parameters of photon nanojets of dielectric microspheres,” Opt. Commun. 283, 4775–4781 (2010).
[CrossRef]

Opt. Express (4)

Q. J. Mech. Appl. Math. (1)

N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55–74 (2005).
[CrossRef]

SPIE Newsroom (1)

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom, (2010), http://spie.org/x39280.xml.

Other (3)

P. W. Barber and S. C. Hill, Light Scattering by Particles (World Scientific, 1990).

L. A. Weinstein, Open Resonators and Open Waveguides (Golem Press, 1969).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Willey, 1983).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Squared absolute value of the Mie coefficient d30, and (b) the maximal relative intensity of the internal field Bmax as functions of particle size parameter with na=1.5 located in air. Digits indicate the orders of excited resonances, the dashed curve shows the intensity of nonresonant field. Open and closed symbols in (b) are for TE and TM resonances correspondingly.

Fig. 2.
Fig. 2.

Transverse distribution of the relative optical intensity B near a spherical particle at (a) resonance WGM excitation and (b) off-resonance. The plane light wave is incident from the top.

Fig. 3.
Fig. 3.

Spatial parameters of PJ from particles with different radii: (a) mean jet half-width in meridional (xz) and sagittal (yz) planes; (b) jet length. Solid curves correspond to off-resonance conditions, and symbols are for WGMs excitation.

Fig. 4.
Fig. 4.

(a) Radial intensity profile of the near-field zone of spherical particle, and (b) PJ half-width in the yz plane on- and off-resonance for TM401 and TM402 modes. The dashed curve marks the particle boundary.

Fig. 5.
Fig. 5.

Averaged PJ intensity BPJ and the maximal (relative) internal intensity Bmax as functions of particle radius.

Equations (6)

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

Esc(r)=n=1En(ian(γ,xa)Ne1n(3)(r)bn(γ,xa)Mo1n(3)(r)),
Ea(r)=n=1En(cn(γ,xa)Mo1n(1)(r)idn(γ,xa)Ne1n(1)(r)),
Ei(r)=n=1En(Mo1n(1)(r)iNe1n(1)(r)).
an=ψn(γxa)ψn(xa)γψn(xa)ψn(γxa)ψn(γxa)ξn(xa)γξn(xa)ψn(γxa);bn=γψn(γxa)ψn(xa)ψn(xa)ψn(γxa)γψn(γxa)ξn(xa)ξn(xa)ψn(γxa)
cn=γγψn(γxa)ξn(xa)ξn(xa)ψn(γxa);dn=γψn(γxa)ξn(xa)γξn(xa)ψn(γxa).
BPJ=VPJ102πdφπθcπsinθdθa0a0+LB(r,θ,φ)r2dr.

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