Abstract

A photonic nanojet (PNJ) corresponds to the specific highly localized spatial region of electromagnetic near-field distribution in the vicinity of a transparent micrometer-sized particle illuminated by a light wave. Here we consider dielectric spherical composite particles consisting of a core and several concentric shells having different refractive indices. The longitudinal and latitudinal sizes of a PNJ and its peak intensity depending on the optical contrast variation of shells are numerically investigated. We show that by properly changing the refractive indices of neighboring shells, it is possible to manipulate the PNJ shape and, in particular, extend its longitudinal size or increase its peak intensity.

© 2011 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, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992, doi:10.1166/jctn.2009.1254 (2009).
    [CrossRef]
  3. U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
    [CrossRef]
  4. 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]
  5. 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, doi:10.1117/2.1201002.002578 (2010).
    [CrossRef]
  6. X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express 16, 13560–13568 (2008).
    [CrossRef]
  7. 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]
  8. 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,” Nanotechnology 18, 485302(2007).
    [CrossRef]
  9. A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A 22, 2847–2858 (2005).
    [CrossRef]
  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. A. Devilez, B. Stout, N. Bonod, and E. Popov, “Spectral analysis of three-dimensional photonic jets,” Opt. Express 16, 14200–14212 (2008).
    [CrossRef]
  12. A. Devilez, N. Bonod, B. Stout, D. Gerard, J. Wenger, H. Rigneault, and E. Popov, “Three-dimensional subwavelength confinement of light with dielectric microspheres,” Opt. Express 17, 2089–2094 (2009).
    [CrossRef]
  13. S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17, 3722–3731 (2009).
    [CrossRef]
  14. C. M. Ruiz and J. J. Simpson, “Detection of embedded ultra subwavelength-thin dielectric features using elongated photonic nanojets,” Opt. Express 18, 16805–16812 (2010).
    [CrossRef]
  15. 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]
  16. H. Xu, “Multilayered metal core-shell nanostructures for inducing a large and tunable local optical field,” Phys. Rev. B. 72, 073405 (2005).
    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  18. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
    [CrossRef]
  19. J. F. Poco and L. W. Hrubesh, “Method of producing optical quality glass having a selected refractive index,” U.S. patent 6,158,244 (12 December 2008).

2010

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]

C. M. Ruiz and J. J. Simpson, “Detection of embedded ultra subwavelength-thin dielectric features using elongated photonic nanojets,” Opt. Express 18, 16805–16812 (2010).
[CrossRef]

2009

2008

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]

A. Devilez, B. Stout, N. Bonod, and E. Popov, “Spectral analysis of three-dimensional photonic jets,” Opt. Express 16, 14200–14212 (2008).
[CrossRef]

2007

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,” Nanotechnology 18, 485302(2007).
[CrossRef]

2005

2004

2003

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef]

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

Backman, V.

Bohren, C. F.

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

Bonod, N.

Challener, W. A.

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

Devilez, A.

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

Geints, Yu. E.

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]

Gerard, D.

Hafner, C.

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Heifetz, A.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992, doi:10.1166/jctn.2009.1254 (2009).
[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]

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]

Hrubesh, L. W.

J. F. Poco and L. W. Hrubesh, “Method of producing optical quality glass having a selected refractive index,” U.S. patent 6,158,244 (12 December 2008).

Huffman, D. R.

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

Itagi, A. V.

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,” Nanotechnology 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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

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, doi:10.1166/jctn.2009.1254 (2009).
[CrossRef]

S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17, 3722–3731 (2009).
[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]

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.

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,” Nanotechnology 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,” Nanotechnology 18, 485302(2007).
[CrossRef]

Nordlander, P.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Panina, E. K.

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]

Poco, J. F.

J. F. Poco and L. W. Hrubesh, “Method of producing optical quality glass having a selected refractive index,” U.S. patent 6,158,244 (12 December 2008).

Popov, E.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Richards-Kortum, R. R.

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef]

Rigneault, H.

Ruiz, C. M.

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]

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, doi:10.1166/jctn.2009.1254 (2009).
[CrossRef]

Simpson, J. J.

Stout, B.

Taflove, A.

Utzinger, U.

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef]

Wenger, J.

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,” Nanotechnology 18, 485302(2007).
[CrossRef]

Xu, H.

H. Xu, “Multilayered metal core-shell nanostructures for inducing a large and tunable local optical field,” Phys. Rev. B. 72, 073405 (2005).
[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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

Zemlyanov, A. A.

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. Phys. Lett.

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. Biomed. Opt.

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef]

J. Comput. Theor. Nanosci.

A. Heifetz, S.-C. Kong, A. V. Sahakiana, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6, 1979–1992, doi:10.1166/jctn.2009.1254 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Nanotechnology

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,” Nanotechnology 18, 485302(2007).
[CrossRef]

Opt. Commun.

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

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]

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

A. Devilez, B. Stout, N. Bonod, and E. Popov, “Spectral analysis of three-dimensional photonic jets,” Opt. Express 16, 14200–14212 (2008).
[CrossRef]

A. Devilez, N. Bonod, B. Stout, D. Gerard, J. Wenger, H. Rigneault, and E. Popov, “Three-dimensional subwavelength confinement of light with dielectric microspheres,” Opt. Express 17, 2089–2094 (2009).
[CrossRef]

S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17, 3722–3731 (2009).
[CrossRef]

C. M. Ruiz and J. J. Simpson, “Detection of embedded ultra subwavelength-thin dielectric features using elongated photonic nanojets,” Opt. Express 18, 16805–16812 (2010).
[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]

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]

Phys. Rev. B.

H. Xu, “Multilayered metal core-shell nanostructures for inducing a large and tunable local optical field,” Phys. Rev. B. 72, 073405 (2005).
[CrossRef]

Science

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Other

J. F. Poco and L. W. Hrubesh, “Method of producing optical quality glass having a selected refractive index,” U.S. patent 6,158,244 (12 December 2008).

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

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, doi:10.1117/2.1201002.002578 (2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Model of a multilayer spherical particle.

Fig. 2
Fig. 2

Different types of (a) refractive index n s and (b) optical contrast γ s variation between consequent layers in a multilayered particle depending on the g parameter.

Fig. 3
Fig. 3

Spatial distributions of the PNJ relative intensity formed in the vicinity of layered spheres with a = 2 μm and different internal structure exposed to the radiation at λ = 0.532 μm (incident from the left): (b)–(d) five-layer particle with (b)  g = 0.2 , (c) 1, (d) 2; (a), (e) homogeneous particles with (a)  n = 1.1 and (e) 1.5. Transverse PNJ profiles at the maximum F are shown in the insets.

Fig. 4
Fig. 4

PNJ parameters for five-layered spherical particles with different radii located in air ( λ = 0.532 μm ). (a)  L Σ is the total length of combined photonic jet structure (see text for details). The data points are connected by cubic spline curves as a guide for the eyes.

Fig. 5
Fig. 5

Normalized quality criterion of PNJ calculated for five-layered sphere with a = 2 μm and a different shell refractive index grading. The data points are connected by cubic spline curves as a guide for the eyes. The insets show symbolically the type of layer-to-layer grading.

Equations (6)

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

E s ( r ) = n = 1 E n [ i ( a n s N e 1 n ( 3 ) ( r ) d n s N e 1 n ( 1 ) ( r ) ) ( b n s M o 1 n ( 3 ) ( r ) c n s M o 1 n ( 1 ) ( r ) ) ] ,
H s ( r ) = k s ω n = 1 E n [ i ( b n s N o 1 n ( 3 ) ( r ) c n s N o 1 n ( 1 ) ( r ) ) + ( a n s M e 1 n ( 3 ) ( r ) d n s M e 1 n ( 1 ) ( r ) ) ] ,
a n s = A n s ; b n s = B n s ; c n s = D n s + 2 B n s ; d n s = C n s + 2 A n s ,
A n s = U n s 1 C n s ; B n s = V n s 1 D n s ; C n s = t = s N P n t ; D n s = t = s N Q n t ,
n s / n 0 = ( n N / n 0 ) ( s / N ) g .
γ s = ( n 0 / n N ) ( s + 1 ) g s g N g .

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