Abstract

Nanojet has been emerging as an interesting topic in variety photonics applications. In this paper, inspired by the properties of generalized Luneburg lens (GLLs), a two-dimensional photonic nanojet system has been developed, which focal distance can be tuned by engineering the refractive index profile of GLLs. Simulation and analysis results show that the maximum light intensity, transverse and longitudinal dimensions of the photonic nanojet are dependent on the focal distance of the GLLs, thereby, by simply varying the focal distance, it is possible to obtain localized photon fluxes with different power characteristics and spatial dimensions. This can be of interest for many promising applications, such as high-resolution optical detection, optical manipulation, technology of direct-write nano-patterning and nano-lithography.

© 2015 Optical Society of America

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References

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2015 (3)

2014 (4)

2013 (1)

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

2011 (3)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Y. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet effect in multilayer micrometre-sized spherical particles,” Quantum Electron. 41(6), 520–525 (2011).
[Crossref]

Y. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet calculations in layered radially inhomogennous micrometer-sized spherical particles,” J. Opt. Soc. Am. B 28(8), 1825–1830 (2011).
[Crossref]

2010 (1)

2009 (2)

S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17(5), 3722–3731 (2009).
[Crossref] [PubMed]

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

2008 (6)

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92(26), 261111 (2008).
[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(21), 211102 (2008).
[Crossref]

S.-C. Kong, A. Sahakian, A. Taflove, and V. Backman, “Photonic nanojet-enabled optical data storage,” Opt. Express 16(18), 13713–13719 (2008).
[Crossref] [PubMed]

X. Cui, D. Erni, and C. Hafner, “Optical forces on metallic nanoparticles induced by a photonic nanojet,” Opt. Express 16(18), 13560–13568 (2008).
[Crossref] [PubMed]

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[Crossref] [PubMed]

J. A. Lock, “Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory,” J. Opt. Soc. Am. A 25(12), 2971–2979 (2008).
[Crossref] [PubMed]

2007 (3)

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007).
[Crossref]

A. M. Kapitonov and V. N. Astratov, “Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities,” Opt. Lett. 32(4), 409–411 (2007).
[Crossref] [PubMed]

E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244(8), 3002–3008 (2007).
[Crossref]

2005 (3)

2004 (1)

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

1984 (1)

Arnold, C. B.

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[Crossref] [PubMed]

Astratov, V. N.

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92(26), 261111 (2008).
[Crossref]

A. M. Kapitonov and V. N. Astratov, “Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities,” Opt. Lett. 32(4), 409–411 (2007).
[Crossref] [PubMed]

Backman, V.

Beruete, M.

Cai, G.

Cai, Z.

Challener, W. A.

Chen, Z.

Cui, X.

Erni, D.

Feldman, A.

Geints, Y. E.

Gouesbet, G.

Gréhan, G.

Gu, G.

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(5644), 419–422 (2003).
[Crossref] [PubMed]

Han, L.

Han, Y.

Hao, Y.

Heifetz, A.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

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(21), 211102 (2008).
[Crossref]

Hong, M.

Horsley, S. A. R.

Itagi, A. V.

Jiang, Y.

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

Ju, D.

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

Kapitonov, A. M.

Katsnelson, A.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007).
[Crossref]

Kim, J. K.

E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244(8), 3002–3008 (2007).
[Crossref]

Kong, S.-C.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

S.-C. Kong, A. Taflove, and V. Backman, “Quasi one-dimensional light beam generated by a graded-index microsphere,” Opt. Express 17(5), 3722–3731 (2009).
[Crossref] [PubMed]

S.-C. Kong, A. Sahakian, A. Taflove, and V. Backman, “Photonic nanojet-enabled optical data storage,” Opt. Express 16(18), 13713–13719 (2008).
[Crossref] [PubMed]

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(21), 211102 (2008).
[Crossref]

Kotlyar, V. V.

Lecler, S.

Li, X.

Liu, Y.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Lock, J. A.

Mcleod, E.

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[Crossref] [PubMed]

McManus, T. M.

Memis, O. G.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007).
[Crossref]

Meyrueis, P.

Mikkelsen, M. H.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Minin, I. V.

Minin, O. V.

Mitchell-Thomas, R. C.

Mohseni, H.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 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(5644), 419–422 (2003).
[Crossref] [PubMed]

Pacheco-Peña, V.

Panina, E. K.

Pei, H.

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Quevedo-Teruel, O.

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Ruiz, C. M.

Sahakian, A.

Sahakian, A. V.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

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(21), 211102 (2008).
[Crossref]

Schubert, E. F.

E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244(8), 3002–3008 (2007).
[Crossref]

Shen, J.-T.

Shen, Y.

Simpson, J. J.

Sochacki, J.

Stafeev, S. S.

Sun, X.

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

Taflove, A.

Takakura, Y.

Valentine, J.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Wang, J.

Wang, L. V.

Wu, W.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007).
[Crossref]

Xi, J.-Q.

E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244(8), 3002–3008 (2007).
[Crossref]

Xu, H.

Yang, S.

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92(26), 261111 (2008).
[Crossref]

Zemlyanov, A. A.

Zentgraf, T.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Zhang, X.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

Zhou, R.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

D. Ju, H. Pei, Y. Jiang, and X. Sun, “Controllable and enhanced nanojet effects excited by surface plasmon polariton,” Appl. Phys. Lett. 102(17), 171109 (2013).
[Crossref]

S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92(26), 261111 (2008).
[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(21), 211102 (2008).
[Crossref]

J. Comput. Theor. Nanosci. (1)

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (3)

Nanotechnology (1)

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18(48), 485302 (2007).
[Crossref]

Nat. Nanotechnol. (2)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011).
[Crossref] [PubMed]

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (6)

Phys. Status Solidi B (1)

E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Status Solidi B 244(8), 3002–3008 (2007).
[Crossref]

Quantum Electron. (1)

Y. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic nanojet effect in multilayer micrometre-sized spherical particles,” Quantum Electron. 41(6), 520–525 (2011).
[Crossref]

Science (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Other (3)

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

O. V. Mazurin, M. V. Streltsina, and T. P. Shvaiko-Shavaikovskaya, Handbook of Glass Data (Elsevier, 1993).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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Figures (7)

Fig. 1
Fig. 1 The refractive index distributions of single-focus GLLs with various normalized focal length for (a) f = 1.0, (b) f = 1.25, (c) f = 1.5, (d) f = 1.75. The refractive index distributions of double-focus GLLs for (e) f2 = 1.7, (f) f2 = 2.2, (g) f2 = 2.7, (h) f2 = 3.2 when the first focal length f1 is set as 1.2. Insets in each subfigures show the ray tracing results.
Fig. 2
Fig. 2 Intensity distributions of single-focus GLLs with various normalized focal length for (a) f = 1.0, (b) f = 1.25, (c) f = 1.5, and (d) f = 1.75 for a 400 nm incident wavelength.
Fig. 3
Fig. 3 Intensity distributions of single-focus GLLs (a) along the x axis passing through center of GLLs, and (b) along the y axis at maximum intensity spots. The insets of the right upper corner each figure correspond to the concrete value of L and FWHM with different normalized focal length f.
Fig. 4
Fig. 4 Intensity distributions of double-focus GLLs with various normalized focal length for (a) f2 = 1.7, (b) f2 = 2.2, (c) f2 = 2.7, and (d) f2 = 3.2 when the first focal length f1 is set as 1.2 for a 400 nm incident wavelength. Intensity distributions of double-focus GLLs (e) along the x axis passing through center of GLLs, and (f) along the y axis at maximum intensity spots. The insets of the right upper corner each figure correspond to the concrete value of L and FWHM with different normalized focal length f2.
Fig. 5
Fig. 5 Intensity distributions of double-focus GLLs with various normalized focal length for (a) f1 = 1.0, (b) f1 = 1.2, (c) f1 = 1.5 when the second focal length f2 is set as 2.7 for a 400 nm incident wavelength. The corresponding L and FWHM of double-focus GLLs (d).
Fig. 6
Fig. 6 The longitudinal waist L and the corresponding FWHM of double-focus GLLs with various normalized first focal length f1 when the second focal length f2 is fixed as 1.7, 2.2, 2.7, 3.2 respectively for a 400 nm incident wavelength.
Fig. 7
Fig. 7 Arrow-plot of the energy power flow in the x-y plane. Single-focus GLLs for (a) f = 1.0 and (b) f = 1.75. Double-focus GLLs for (c) f2 = 1.7 and (d) f2 = 3.2. For double-focus GLLs, the first focal length f1 is set as 1.2.

Equations (4)

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n(r)= n 0 [ 1+ f 2 ( r R ) 2 ] 1/2 /f
n( ρ )={ exp[ ω 1 ( ρ, f 2 ) ], P a ρ1 exp[ ω 1 ( ρ, f 2 )+ ω 2 ( ρ, f 1 , P a )+ ω 2 ( ρ, f 2 , P a ) ],0ρ P a
ω 1 (ρ, f 2 )= 1 π ρ 1 arcsin( k/ f 2 )dk ( k 2 ρ 2 ) 1/2
ω 2 ( ρ,i, P a )= 1 π ρ P a arcsin( k/i )dk ( k 2 ρ 2 ) 1/2

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