Near-field focusing of the dielectric microsphere with wavelength scale radius

doi:10.1364/OE.21.002434

Near-field focusing of the dielectric microsphere with wavelength scale radius

Hanming Guo, Yunxuan Han, Xiaoyu Weng, Yanhui Zhao, Guorong Sui, Yang Wang, and Songlin Zhuang »View Author Affiliations

Optics Express, Vol. 21, Issue 2, pp. 2434-2443 (2013)
http://dx.doi.org/10.1364/OE.21.002434

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Abstract

We focus on physically analyzing the origins of the numerical aperture ( $N A$ ) and the spherical aberration of the microsphere with wavelength scale radius. We demonstrate that the microsphere naturally has negligible spherical aberration and high $N A$ when the refractive index contrast ( $R I C$ ) between the microsphere and its surrounding medium is about from 1.5 to 1.75. The reason is due to the spherical aberration compensation arising from the positive spherical aberration caused by the surface shape of the microsphere and the $R I C$ and the negative spherical aberration caused by the focal shifts due to the wavelength scale dimension of the microsphere. We show that, only within the approximate region of $1.5 \leq R I C \leq 1.75$ with the proper radius $r$ of microsphere, the microsphere can generate a near-field focal spot with lateral resolution slightly beyond $λ / 2 n_{s}$ , which is also the lateral resolution limit of the dielectric microsphere. The $r$ for each $R I C$ can be obtained by optimizing $r$ from $1.125 λ / n_{o}$ to $1.275 λ / n_{o}$ . Here $λ$ , $n_{s}$ , and $n_{o}$ are the wavelength in vacuum and the refractive indices of microsphere and its surrounding medium, respectively. For the case of the near-field focusing, we also develop a simple transform formula used to calculate the new radius from the known radius of microsphere corresponding to the original illumination wavelength when the illumination wavelength is changed.

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(350.3950) Other areas of optics : Micro-optics

ToC Category:
Physical Optics

History
Original Manuscript: November 21, 2012
Revised Manuscript: December 21, 2012
Manuscript Accepted: January 15, 2013
Published: January 24, 2013

Citation
Hanming Guo, Yunxuan Han, Xiaoyu Weng, Yanhui Zhao, Guorong Sui, Yang Wang, and Songlin Zhuang, "Near-field focusing of the dielectric microsphere with wavelength scale radius," Opt. Express 21, 2434-2443 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2434

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References

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, “Near-field focusing and magnification through self-ssembled nanoscale spherical lenses,” Nature460(7254), 498–501 (2009). [CrossRef]
J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol.5(2), 127–132 (2010). [CrossRef] [PubMed]
Z. Wang, W. Guo, L. Li, B. Luk'yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50nm lateral resolution with a white-light nanoscope,” Nat. Commun.2, 218 (2011). [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. Express12(7), 1214–1220 (2004). [CrossRef] [PubMed]
A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J Comput Theor Nanosci6(9), 1979–1992 (2009). [CrossRef] [PubMed]
Y. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic jets from resonantly excited transparent dielectric microspheres,” J. Opt. Soc. Am. B29(4), 758–762 (2012). [CrossRef]
X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express13(2), 526–533 (2005). [CrossRef] [PubMed]
A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A22(12), 2847–2858 (2005). [CrossRef] [PubMed]
P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express16(10), 6930–6940 (2008). [CrossRef] [PubMed]
A. Devilez, N. Bonod, J. Wenger, D. Gérard, B. Stout, H. Rigneault, and E. Popov, “Three-dimensional subwavelength confinement of light with dielectric microspheres,” Opt. Express17(4), 2089–2094 (2009). [CrossRef] [PubMed]
M. S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, “Engineering photonic nanojets,” Opt. Express19(11), 10206–10220 (2011). [CrossRef] [PubMed]
D. McCloskey, J. J. Wang, and J. F. Donegan, “Low divergence photonic nanojets from Si3N4 microdisks,” Opt. Express20(1), 128–140 (2012). [CrossRef] [PubMed]
Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012). [CrossRef]
E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol.3(7), 413–417 (2008). [CrossRef] [PubMed]
J. Kim, K. Cho, I. Kim, W. M. Kim, T. S. Lee, and K. S. Lee, “Fabrication of plasmonic nanodiscs by photonic nanojet lighography,” Appl. Phys. Express5(2), 025201 (2012). [CrossRef]
D. A. Fletcher, K. E. Goodson, and G. S. Kino, “Focusing in microlenses close to a wavelength in diameter,” Opt. Lett.26(7), 399–401 (2001). [CrossRef] [PubMed]
T. J. Gould, S. T. Hess, and J. Bewersdorf, “Optical nanoscopy: from acquisition to analysis,” Annu. Rev. Biomed. Eng.14(1), 231–254 (2012). [CrossRef] [PubMed]
B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959). [CrossRef]
J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol.5(2), 127–132 (2010). [CrossRef] [PubMed]
Z. Wang, W. Guo, L. Li, B. Luk'yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50nm lateral resolution with a white-light nanoscope,” Nat. Commun.2, 1–6 (2011). [CrossRef]
M. S. Kim, T. Scharf, M. T. Haq, W. Nakagawa, and H. P. Herzig, “Subwavelength-size solid immersion lens,” Opt. Lett.36(19), 3930–3932 (2011). [CrossRef] [PubMed]
D. R. Mason, M. V. Jouravlev, and K. S. Kim, “Enhanced resolution beyond the Abbe diffraction limit with wavelength-scale solid immersion lenses,” Opt. Lett.35(12), 2007–2009 (2010). [CrossRef] [PubMed]
C. J. R. Sheppard and P. Török, “Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number,” J. Opt. Soc. Am. A20(11), 2156–2162 (2003). [CrossRef] [PubMed]
Y. Li, “Focal shifts in diffracted converging electromagnetic waves. I. Kirchhoff theory,” J. Opt. Soc. Am. A22(1), 68–76 (2005). [CrossRef] [PubMed]
S. Guo, H. Guo, and S. Zhuang, “Analysis of imaging properties of a microlens based on the method for a dyadic Green’s function,” Appl. Opt.48(2), 321–327 (2009). [CrossRef] [PubMed]
http://www.microspheres-nanospheres.com/
J. M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett.109(2), 023901 (2012). [CrossRef] [PubMed]
J. J. Stamnes, Waves in Focal Regions (Taylor & Francis Group, 1986), p456.

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[1] J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, “Near-field focusing and magnification through self-ssembled nanoscale spherical lenses,” Nature460(7254), 498–501 (2009). [CrossRef]

[2] J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol.5(2), 127–132 (2010). [CrossRef] [PubMed]

[3] Z. Wang, W. Guo, L. Li, B. Luk'yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50nm lateral resolution with a white-light nanoscope,” Nat. Commun.2, 218 (2011). [CrossRef]

[4] Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express12(7), 1214–1220 (2004). [CrossRef] [PubMed]

[5] A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic Nanojets,” J Comput Theor Nanosci6(9), 1979–1992 (2009). [CrossRef] [PubMed]

[6] Y. E. Geints, A. A. Zemlyanov, and E. K. Panina, “Photonic jets from resonantly excited transparent dielectric microspheres,” J. Opt. Soc. Am. B29(4), 758–762 (2012). [CrossRef]

[7] X. Li, Z. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express13(2), 526–533 (2005). [CrossRef] [PubMed]

[8] A. V. Itagi and W. A. Challener, “Optics of photonic nanojets,” J. Opt. Soc. Am. A22(12), 2847–2858 (2005). [CrossRef] [PubMed]

[9] P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express16(10), 6930–6940 (2008). [CrossRef] [PubMed]

[10] A. Devilez, N. Bonod, J. Wenger, D. Gérard, B. Stout, H. Rigneault, and E. Popov, “Three-dimensional subwavelength confinement of light with dielectric microspheres,” Opt. Express17(4), 2089–2094 (2009). [CrossRef] [PubMed]

[11] M. S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, “Engineering photonic nanojets,” Opt. Express19(11), 10206–10220 (2011). [CrossRef] [PubMed]

[12] D. McCloskey, J. J. Wang, and J. F. Donegan, “Low divergence photonic nanojets from Si3N4 microdisks,” Opt. Express20(1), 128–140 (2012). [CrossRef] [PubMed]

[13] Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012). [CrossRef]

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

[15] J. Kim, K. Cho, I. Kim, W. M. Kim, T. S. Lee, and K. S. Lee, “Fabrication of plasmonic nanodiscs by photonic nanojet lighography,” Appl. Phys. Express5(2), 025201 (2012). [CrossRef]

[16] D. A. Fletcher, K. E. Goodson, and G. S. Kino, “Focusing in microlenses close to a wavelength in diameter,” Opt. Lett.26(7), 399–401 (2001). [CrossRef] [PubMed]

[17] T. J. Gould, S. T. Hess, and J. Bewersdorf, “Optical nanoscopy: from acquisition to analysis,” Annu. Rev. Biomed. Eng.14(1), 231–254 (2012). [CrossRef] [PubMed]

[18] B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959). [CrossRef]

[19] J. J. Schwartz, S. Stavrakis, and S. R. Quake, “Colloidal lenses allow high-temperature single-molecule imaging and improve fluorophore photostability,” Nat. Nanotechnol.5(2), 127–132 (2010). [CrossRef] [PubMed]

[20] Z. Wang, W. Guo, L. Li, B. Luk'yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50nm lateral resolution with a white-light nanoscope,” Nat. Commun.2, 1–6 (2011). [CrossRef]

[21] M. S. Kim, T. Scharf, M. T. Haq, W. Nakagawa, and H. P. Herzig, “Subwavelength-size solid immersion lens,” Opt. Lett.36(19), 3930–3932 (2011). [CrossRef] [PubMed]

[22] D. R. Mason, M. V. Jouravlev, and K. S. Kim, “Enhanced resolution beyond the Abbe diffraction limit with wavelength-scale solid immersion lenses,” Opt. Lett.35(12), 2007–2009 (2010). [CrossRef] [PubMed]

[23] C. J. R. Sheppard and P. Török, “Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number,” J. Opt. Soc. Am. A20(11), 2156–2162 (2003). [CrossRef] [PubMed]

[24] Y. Li, “Focal shifts in diffracted converging electromagnetic waves. I. Kirchhoff theory,” J. Opt. Soc. Am. A22(1), 68–76 (2005). [CrossRef] [PubMed]

[25] S. Guo, H. Guo, and S. Zhuang, “Analysis of imaging properties of a microlens based on the method for a dyadic Green’s function,” Appl. Opt.48(2), 321–327 (2009). [CrossRef] [PubMed]

[26] http://www.microspheres-nanospheres.com/

[27] J. M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett.109(2), 023901 (2012). [CrossRef] [PubMed]

[28] J. J. Stamnes, Waves in Focal Regions (Taylor & Francis Group, 1986), p456.

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Near-field focusing of the dielectric microsphere with wavelength scale radius

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