Abstract

A photonic nanojet is a highly focused optical beam with a subwavelength waist on the shadow side of the sphere. Successful far-field applications require long nanojets that extend afar. Using the exact Mie theory, we show that ultralong nanojets can be generated using a simple two-layer microsphere structure, using conventional optical materials that are readily available. In particular, we show that for a glass-based two-layer microsphere, the nanojet has an extension of 22 wavelengths. We also show that long nanojets can be formed using semiconductors at infrared frequencies in free space.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
    [CrossRef]
  2. X. Li, Z. Chen, A. Taflove, and V. Backman, Opt. Express 13, 526 (2005).
    [CrossRef]
  3. E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
    [CrossRef]
  4. W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).
  5. A. Kapitonov and V. Astratov, Opt. Lett. 32, 409 (2007).
    [CrossRef]
  6. S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
    [CrossRef]
  7. A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
    [CrossRef]
  8. E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).
  9. S. C. Kong, A. Taflove, and V. Backman, Opt. Express 17, 3722 (2009).
    [CrossRef]
  10. L. W. Hrubesh and J. F. Poco, “Method of producing optical quality glass having a selected refractive index,” U.S. patent6,158,244 (12December2000).
  11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).
  12. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).
  13. Schott optical glass data sheet–catalog, http://refractiveindex.info/download/data/2012/schott_optical_glass_collection_datasheets_dec_2012_us.pdf

2009 (2)

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
[CrossRef]

S. C. Kong, A. Taflove, and V. Backman, Opt. Express 17, 3722 (2009).
[CrossRef]

2008 (2)

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

2007 (3)

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).

A. Kapitonov and V. Astratov, Opt. Lett. 32, 409 (2007).
[CrossRef]

2005 (1)

2004 (1)

Arnold, C. B.

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Astratov, V.

Astratov, V. N.

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

Backman, V.

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Chen, Z.

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Heifetz, A.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
[CrossRef]

Hrubesh, L. W.

L. W. Hrubesh and J. F. Poco, “Method of producing optical quality glass having a selected refractive index,” U.S. patent6,158,244 (12December2000).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Kapitonov, A.

Katsnelson, A.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

Kim, J. K.

E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).

Kong, S. C.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
[CrossRef]

S. C. Kong, A. Taflove, and V. Backman, Opt. Express 17, 3722 (2009).
[CrossRef]

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Li, X.

MacDonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Mcleod, E.

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Memis, O. G.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

Mohseni, H.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

Poco, J. F.

L. W. Hrubesh and J. F. Poco, “Method of producing optical quality glass having a selected refractive index,” U.S. patent6,158,244 (12December2000).

Sahakian, A. V.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
[CrossRef]

Schubert, E. F.

E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).

Stryland, E. V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Taflove, A.

Wu, W.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

Xi, J. Q.

E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).

Yang, S.

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comput. Theor. Nanosci. 6, 1979 (2009).
[CrossRef]

Nanotechnology (1)

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, Nanotechnology 18, 485302 (2007).

Nat. Nanotechnol. (1)

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Status Solidi B (1)

E. F. Schubert, J. K. Kim, and J. Q. Xi, Phys. Status Solidi B 244, 3002 (2007).

Other (4)

L. W. Hrubesh and J. F. Poco, “Method of producing optical quality glass having a selected refractive index,” U.S. patent6,158,244 (12December2000).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (McGraw-Hill Professional, 2009).

Schott optical glass data sheet–catalog, http://refractiveindex.info/download/data/2012/schott_optical_glass_collection_datasheets_dec_2012_us.pdf

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Power flow plots for microspheres. (a) Single microsphere. (b) Two-layer microsphere. “L” and “H” denote the low index core and high index shell, respectively. The arrows denote the Poynting vector at each grid point. The two continuous red lines in each figure are the streamlines for the Poynting vector fields, assuming the same two fixed starting points on the incident side for each case.

Fig. 2.
Fig. 2.

Schematics of the two-layer microsphere. The sphere consists of an inner core of radius Rc and with a refractive index nc, and of a shell with outer radius Rs and with an index ns. The directions of the incident plane wave and the polarization are also denoted.

Fig. 3.
Fig. 3.

Intensity plots of the nanojets. (a) Single microsphere with R=5λ, n=1.377 (MgF2 [12]). (b) A two-layer microsphere with Rc=2.5λ, nc=1.6028 (BaF [13]), and Rs=5λ, ns=1.8445 (LaSF [13]). In each case, the upper panel plots the intensity for the y-z plane; and the lower panel plots the intensity profile along the z direction. In the intensity profile, the origin of the coordinate system corresponds to the center of the sphere, and the locations of the focal points are denoted by the dashed lines. The transverse profiles at the focal point are also shown in the insets. To clearly show the details of the nanojets, the maximum value of the colormap is chosen to be the value at the focal point. The focal lengths for the two cases are approximately 1.25λ and 2.8λ, respectively.

Fig. 4.
Fig. 4.

Long nanojet formed by a two-layer microsphere with high refractive index materials (nc=2, ns=3.85, Rc=2.5λ, and Rs=5λ). Silicon nitride has a refractive index around 2 at the near-infrared frequency range, while many doped semiconductors can have an index range covering 3.85.

Equations (3)

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

E={n=1(ianNe1n(3)bnMo1n(3))En,ifRs<rn=1(fnMo1n(1)ignNe1n(1)+vnMo1n(2)iwnNe1n(2))En,ifRc<r<Rsn=1(cnMo1n(1)idnNe1n(1))En,ifr<Rc,
an=ψn(y)[ψn(m2y)Anχn(m2y)]m2ψn(y)[ψn(m2y)Anχn(m2y)]ξn(y)[ψn(m2y)Anχn(m2y)]m2ξn(y)[ψn(m2y)Anχn(m2y)],bn=m2ψn(y)[ψn(m2y)Bnχn(m2y)]ψn(y)[ψn(m2y)Bnχn(m2y)]m2ξn(y)[ψn(m2y)Bnχn(m2y)]ξn(y)[ψn(m2y)Bnχn(m2y)],
An=m2ψn(m2x)ψn(m1x)m1ψn(m2x)ψn(m1x)m2χn(m2x)ψn(m1x)m1χn(m2x)ψn(m1x),Bn=m1ψn(m2x)ψn(m1x)m2ψn(m2x)ψn(m1x)m1χn(m2x)ψn(m1x)m2χn(m2x)ψn(m1x).

Metrics