Abstract

We employ a genetic algorithm coupled with Mie theory to optimize the magnetic field intensity profile of photonic nanojets (PNJs) generated by multilayer microcylinders at visible wavelengths in free space. We first optimize five-layer microcylinders to elongate the PNJs. We show that a properly designed five-layer microcylinder structure can generate an ultra-long PNJ with a beam length ~ 107.5 times the illumination wavelength λ0. We then optimize five-layer microcylinders to narrow the waist of PNJs. We show that a PNJ with a full-width at half maximum waist of ~ 0.22λ0 can be obtained outside the surface of the optimized microcylinder. In addition, curved PNJs with subwavelength waist are also obtained. We finally optimize the five-layer structures for refractive index sensing based on the beam length of PNJs. The estimated minimum detectable refractive index variation when using this sensing method is ultra-small. Our results could potentially contribute to the development of a new generation of devices for optical nanoscopy and biophotonics, and greatly promote the practical applications of PNJs.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  38. P. Tobiska, O. Hugon, A. Trouillet, and H. Gagnaire, “An integrated optic hydrogen sensor based on SPR on palladium,” Sensors Actuators B: Chem. 74, 168–172 (2001).
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    [Crossref]
  42. R. Remez and A. Arie, “Super-narrow frequency conversion,” Optica 2, 472–475 (2015).
    [Crossref]
  43. Y. Ogura, M. Aino, and J. Tanida, “Design and demonstration of fan-out elements generating an array of subdiffraction spots,” Opt. Express 22, 25196–25207 (2014).
    [Crossref]
  44. H. Nagel, A. Aberle, and R. Hezel, “Optimised antireflection coatings for planar silicon solar cells using remote PECVD silicon nitride and porous silicon dioxide,” Prog. Photovoltaics Res. Appl. 7, 245–260 (1999).
    [Crossref]
  45. D. Aspnes, S. Kelso, R. Logan, and R. Bhat, “Optical properties of Alx Ga1−x As,” J. Appl. Phys. 60, 754–767 (1986).
    [Crossref]
  46. K. Sato and S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
    [Crossref]
  47. G. Gu, J. Song, M. Chen, X. Peng, H. Liang, and J. Qu, “Single nanoparticle detection using a photonic nanojet,” Nanoscale 10, 14182–14189 (2018).
    [Crossref]
  48. Y. Huang, C. Min, P. Dastmalchi, and G. Veronis, “Slow-light enhanced subwavelength plasmonic waveguide refractive index sensors,” Opt. Express 23, 14922–14936 (2015).
    [Crossref]
  49. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
    [Crossref]
  50. F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
    [Crossref] [PubMed]
  51. R. Hillenbrand and F. Keilmann, “Material-specific mapping of metal/semiconductor/dielectric nanosystems at 10 nm resolution by backscattering near-field optical microscopy,” Appl. Phys. Lett. 80, 25–27 (2002).
    [Crossref]
  52. S. Tanemura, L. Miao, P. Jin, K. Kaneko, A. Terai, and N. Gabain, “Optical properties of polycrystalline and epitaxial anatase and rutile TiO2 thin films by rf magnetron sputtering,” Appl. Surf. Sci. 212, 654–660 (2003).
    [Crossref]
  53. S. Ozaki and S. Adachi, “Optical constants of cubic ZnS,” Jpn. J. Appl. Phys. 32, 5008–5013 (1993).
    [Crossref]
  54. X. Fan, I. White, S. Shopova, H. Zhu, J. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chimica Acta 620, 8–26 (2008).
    [Crossref]
  55. L. Zhang, R. Tu, and H. Dai, “Parallel core-shell metal-dielectric-semiconductor germanium nanowires for high-current surround-gate field-effect transistors,” Nano Lett. 6, 2785–2789 (2006).
    [Crossref] [PubMed]
  56. C. Guan, X. Wang, Q. Zhang, Z. Fan, H. Zhang, and H. Fan, “Highly stable and reversible lithium storage in SnO2 nanowires surface coated with a uniform hollow shell by atomic layer deposition,” Nano Lett. 14, 4852–4858 (2014).
    [Crossref]

2018 (8)

C. Liu, T. Yen, O. Minin, and I. Minin, “Engineering photonic nanojet by a graded-index micro-cuboid,” Phys. E 98, 105–110 (2018).
[Crossref]

L. Yue, B. Yan, J. Monks, R. Dhama, Z. Wang, O. Minin, and I. Minin, “Intensity-enhanced apodization effect on an axially illuminated circular-column particle-lens,” Ann. Phys. 530, 1700384 (2018).
[Crossref]

J. Yang, P. Twardowski, P. Gerard, Y. Duo, J. Fontaine, and S. Lecler, “Ultra-narrow photonic nanojets through a glass cuboid embedded in a dielectric cylinder,” Opt. Express 26, 3723–3731 (2018).
[Crossref] [PubMed]

S. Zanjani, S. Inampudi, and H. Mosallaei, “Adaptive genetic algorithm for optical metasurfaces design,” Sci. Reports 8, 11040 (2018).
[Crossref]

L. Yue, O. Minin, Z. Wang, J. Monks, A. Shalin, and I. Minin, “Photonic hook: a new curved light beam,” Opt. Lett. 43, 771–774 (2018).
[Crossref] [PubMed]

Y. Geints, A. Zemlyanov, O. Minin, and I. Minin, “Systematic study and comparison of photonic nanojets produced by dielectric microparticles in 2D-and 3D-spatial configurations,” J. Opt. 20, 065606 (2018).
[Crossref]

Y. Huang, Y. Shen, C. Min, and G. Veronis, “Switching photonic nanostructures between cloaking and superscattering regimes using phase-change materials,” Opt. Mater. Express 8, 1672–1685 (2018).
[Crossref]

G. Gu, J. Song, M. Chen, X. Peng, H. Liang, and J. Qu, “Single nanoparticle detection using a photonic nanojet,” Nanoscale 10, 14182–14189 (2018).
[Crossref]

2017 (2)

G. Gu, J. Song, H. Liang, M. Zhao, Y. Chen, and J. Qu, “Overstepping the upper refractive index limit to form ultra-narrow photonic nanojets,” Sci. Reports 7, 5635 (2017).
[Crossref]

B. Lukyanchuk, R. Dominguez, I. Minin, O. Minin, and Z. Wang, “Refractive index less than two: photonic nanojets yesterday, today and tomorrow,” Opt. Mater. Express 7, 1820–1847 (2017).
[Crossref]

2016 (2)

H. Yang, R. Trouillon, G. Huszka, and M. Gijs, “Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet,” Nano Lett. 16, 4862–4870 (2016).
[Crossref] [PubMed]

L. Yue, B. Yan, and Z. Wang, “Photonic nanojet of cylindrical metalens assembled by hexagonally arranged nanofibers for breaking the diffraction limit,” Opt. Lett. 41, 1336–1339 (2016).
[Crossref] [PubMed]

2015 (5)

Y. Huang, C. Min, P. Dastmalchi, and G. Veronis, “Slow-light enhanced subwavelength plasmonic waveguide refractive index sensors,” Opt. Express 23, 14922–14936 (2015).
[Crossref]

G. Gu, R. Zhou, Z. Chen, H. Xu, G. Cai, Z. Cai, and M. Hong, “Super-long photonic nanojet generated from liquid-filled hollow microcylinder,” Opt. Lett. 40, 625–628 (2015).
[Crossref] [PubMed]

B. Born, J. Krupa, S. Gagnon, and J. Holzman, “Integration of photonic nanojets and semiconductor nanoparticles for enhanced all-optical switching,” Nat. Commun. 6, 8097 (2015).
[Crossref] [PubMed]

M. Wu, B. Huang, R. Chen, Y. Yang, J. Wu, R. Ji, X. Chen, and M. Hong, “Modulation of photonic nanojets generated by microspheres decorated with concentric rings,” Opt. Express 25, 20096–20103 (2015).
[Crossref]

R. Remez and A. Arie, “Super-narrow frequency conversion,” Optica 2, 472–475 (2015).
[Crossref]

2014 (5)

Y. Ogura, M. Aino, and J. Tanida, “Design and demonstration of fan-out elements generating an array of subdiffraction spots,” Opt. Express 22, 25196–25207 (2014).
[Crossref]

T. Pickering, J. Hamm, A. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5, 4972 (2014).
[Crossref]

A. Mirzaei, A. Miroshnichenko, I. Shadrivov, and Y. Kivshar, “Superscattering of light optimized by a genetic algorithm,” Appl. Phys. Lett. 105, 011109 (2014).
[Crossref]

Y. Shen, L. Wang, and J. Shen, “Ultralong photonic nanojet formed by a two-layer dielectric microsphere,” Opt. Lett. 39, 4120–4123 (2014).
[Crossref] [PubMed]

C. Guan, X. Wang, Q. Zhang, Z. Fan, H. Zhang, and H. Fan, “Highly stable and reversible lithium storage in SnO2 nanowires surface coated with a uniform hollow shell by atomic layer deposition,” Nano Lett. 14, 4852–4858 (2014).
[Crossref]

2012 (5)

N. Horiuchi, “Photonic nanojets,” Nat. Photonics 6, 138–139 (2012).

C. Forestiere, A. Pasquale, A. Capretti, G. Miano, A. Tamburrino, and S. Lee, B. einhard, and L. Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012).
[Crossref] [PubMed]

Y. Huang, C. Min, and G. Veronis, “Compact slit-based couplers for metal-dielectric-metal plasmonic waveguides,” Opt. Express 25, 22233–22244 (2012).
[Crossref]

P. Chen, J, Soric, and A. Alu, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater. 24, OP281–OP304 (2012).
[PubMed]

D. Tahir and S. Tougaard, “Electronic and optical properties of Cu, CuO and Cu2O studied by electron spectroscopy,” J. Physics: Condens. Matter 24, 175002 (2012).

2011 (1)

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

2010 (1)

2009 (2)

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

R. Reddy, K. Gopal, K. Narasimhulu, L. Reddy, K. Kumar, G. Balakrishnaiah, and M. Kumar, “Interrelationship between structural, optical, electronic and elastic properties of materials,” J. Alloy. Compd. 473, 28–35 (2009).
[Crossref]

2008 (4)

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

S. Yang and V. 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, 261111 (2008).
[Crossref]

X. Fan, I. White, S. Shopova, H. Zhu, J. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chimica Acta 620, 8–26 (2008).
[Crossref]

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[Crossref]

2007 (1)

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

2006 (1)

L. Zhang, R. Tu, and H. Dai, “Parallel core-shell metal-dielectric-semiconductor germanium nanowires for high-current surround-gate field-effect transistors,” Nano Lett. 6, 2785–2789 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

S. Tanemura, L. Miao, P. Jin, K. Kaneko, A. Terai, and N. Gabain, “Optical properties of polycrystalline and epitaxial anatase and rutile TiO2 thin films by rf magnetron sputtering,” Appl. Surf. Sci. 212, 654–660 (2003).
[Crossref]

2002 (1)

R. Hillenbrand and F. Keilmann, “Material-specific mapping of metal/semiconductor/dielectric nanosystems at 10 nm resolution by backscattering near-field optical microscopy,” Appl. Phys. Lett. 80, 25–27 (2002).
[Crossref]

2001 (1)

P. Tobiska, O. Hugon, A. Trouillet, and H. Gagnaire, “An integrated optic hydrogen sensor based on SPR on palladium,” Sensors Actuators B: Chem. 74, 168–172 (2001).
[Crossref]

2000 (1)

R. Goldhahn, J. Scheiner, S. Shokhovets, T. Frey, U. Koler, D. As, and K. Lischka, “Refractive index and gap energy of cubic Inx Ga1−x N,” Appl. Phys. Lett. 76, 291–293 (2000).
[Crossref]

1999 (1)

H. Nagel, A. Aberle, and R. Hezel, “Optimised antireflection coatings for planar silicon solar cells using remote PECVD silicon nitride and porous silicon dioxide,” Prog. Photovoltaics Res. Appl. 7, 245–260 (1999).
[Crossref]

1995 (1)

F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
[Crossref] [PubMed]

1993 (2)

K. Sato and S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[Crossref]

S. Ozaki and S. Adachi, “Optical constants of cubic ZnS,” Jpn. J. Appl. Phys. 32, 5008–5013 (1993).
[Crossref]

1987 (2)

A. Rakhshani and J. Varghese, “Optical absorption coefficient and thickness measurement of electrodeposited films of Cu2O,” Phys. Status Solidi (a) 101, 479–486 (1987).
[Crossref]

D. Benincasa, P. Barber, J. Zhang, W. Hsieh, and R. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
[Crossref] [PubMed]

1986 (1)

D. Aspnes, S. Kelso, R. Logan, and R. Bhat, “Optical properties of Alx Ga1−x As,” J. Appl. Phys. 60, 754–767 (1986).
[Crossref]

Aberle, A.

H. Nagel, A. Aberle, and R. Hezel, “Optimised antireflection coatings for planar silicon solar cells using remote PECVD silicon nitride and porous silicon dioxide,” Prog. Photovoltaics Res. Appl. 7, 245–260 (1999).
[Crossref]

Adachi, S.

K. Sato and S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[Crossref]

S. Ozaki and S. Adachi, “Optical constants of cubic ZnS,” Jpn. J. Appl. Phys. 32, 5008–5013 (1993).
[Crossref]

Aino, M.

Arie, A.

As, D.

R. Goldhahn, J. Scheiner, S. Shokhovets, T. Frey, U. Koler, D. As, and K. Lischka, “Refractive index and gap energy of cubic Inx Ga1−x N,” Appl. Phys. Lett. 76, 291–293 (2000).
[Crossref]

Aspnes, D.

D. Aspnes, S. Kelso, R. Logan, and R. Bhat, “Optical properties of Alx Ga1−x As,” J. Appl. Phys. 60, 754–767 (1986).
[Crossref]

Astratov, V.

S. Yang and V. 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, 261111 (2008).
[Crossref]

Backman, V.

Balakrishnaiah, G.

R. Reddy, K. Gopal, K. Narasimhulu, L. Reddy, K. Kumar, G. Balakrishnaiah, and M. Kumar, “Interrelationship between structural, optical, electronic and elastic properties of materials,” J. Alloy. Compd. 473, 28–35 (2009).
[Crossref]

Barber, P.

Benincasa, D.

Berini, P.

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[Crossref]

Bhat, R.

D. Aspnes, S. Kelso, R. Logan, and R. Bhat, “Optical properties of Alx Ga1−x As,” J. Appl. Phys. 60, 754–767 (1986).
[Crossref]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles(Wiley, 1998).
[Crossref]

Born, B.

B. Born, J. Krupa, S. Gagnon, and J. Holzman, “Integration of photonic nanojets and semiconductor nanoparticles for enhanced all-optical switching,” Nat. Commun. 6, 8097 (2015).
[Crossref] [PubMed]

Cai, G.

Cai, Z.

Capretti, A.

C. Forestiere, A. Pasquale, A. Capretti, G. Miano, A. Tamburrino, and S. Lee, B. einhard, and L. Negro, “Genetically engineered plasmonic nanoarrays,” Nano Lett. 12, 2037–2044 (2012).
[Crossref] [PubMed]

Chang, R.

Chen, M.

G. Gu, J. Song, M. Chen, X. Peng, H. Liang, and J. Qu, “Single nanoparticle detection using a photonic nanojet,” Nanoscale 10, 14182–14189 (2018).
[Crossref]

Chen, P.

P. Chen, J, Soric, and A. Alu, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater. 24, OP281–OP304 (2012).
[PubMed]

Chen, R.

M. Wu, B. Huang, R. Chen, Y. Yang, J. Wu, R. Ji, X. Chen, and M. Hong, “Modulation of photonic nanojets generated by microspheres decorated with concentric rings,” Opt. Express 25, 20096–20103 (2015).
[Crossref]

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[Crossref]

Tanida, J.

Terai, A.

S. Tanemura, L. Miao, P. Jin, K. Kaneko, A. Terai, and N. Gabain, “Optical properties of polycrystalline and epitaxial anatase and rutile TiO2 thin films by rf magnetron sputtering,” Appl. Surf. Sci. 212, 654–660 (2003).
[Crossref]

Tobiska, P.

P. Tobiska, O. Hugon, A. Trouillet, and H. Gagnaire, “An integrated optic hydrogen sensor based on SPR on palladium,” Sensors Actuators B: Chem. 74, 168–172 (2001).
[Crossref]

Tougaard, S.

D. Tahir and S. Tougaard, “Electronic and optical properties of Cu, CuO and Cu2O studied by electron spectroscopy,” J. Physics: Condens. Matter 24, 175002 (2012).

Trouillet, A.

P. Tobiska, O. Hugon, A. Trouillet, and H. Gagnaire, “An integrated optic hydrogen sensor based on SPR on palladium,” Sensors Actuators B: Chem. 74, 168–172 (2001).
[Crossref]

Trouillon, R.

H. Yang, R. Trouillon, G. Huszka, and M. Gijs, “Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet,” Nano Lett. 16, 4862–4870 (2016).
[Crossref] [PubMed]

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L. Zhang, R. Tu, and H. Dai, “Parallel core-shell metal-dielectric-semiconductor germanium nanowires for high-current surround-gate field-effect transistors,” Nano Lett. 6, 2785–2789 (2006).
[Crossref] [PubMed]

Twardowski, P.

Varghese, J.

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[Crossref]

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[Crossref]

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X. Fan, I. White, S. Shopova, H. Zhu, J. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chimica Acta 620, 8–26 (2008).
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[Crossref]

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M. Wu, B. Huang, R. Chen, Y. Yang, J. Wu, R. Ji, X. Chen, and M. Hong, “Modulation of photonic nanojets generated by microspheres decorated with concentric rings,” Opt. Express 25, 20096–20103 (2015).
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Y. Li, H. Xin, X. Liu, Y. Zhang, H. Lei, and B. Li, “Trapping and detection of nanoparticles and cells using a parallel photonic nanojet array,” ACS Nano10, 5800–5808 (2016).
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H. Yang, R. Trouillon, G. Huszka, and M. Gijs, “Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet,” Nano Lett. 16, 4862–4870 (2016).
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Yang, S.

S. Yang and V. 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, 261111 (2008).
[Crossref]

Yang, Y.

M. Wu, B. Huang, R. Chen, Y. Yang, J. Wu, R. Ji, X. Chen, and M. Hong, “Modulation of photonic nanojets generated by microspheres decorated with concentric rings,” Opt. Express 25, 20096–20103 (2015).
[Crossref]

Yen, T.

C. Liu, T. Yen, O. Minin, and I. Minin, “Engineering photonic nanojet by a graded-index micro-cuboid,” Phys. E 98, 105–110 (2018).
[Crossref]

Yue, L.

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S. Zanjani, S. Inampudi, and H. Mosallaei, “Adaptive genetic algorithm for optical metasurfaces design,” Sci. Reports 8, 11040 (2018).
[Crossref]

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Y. Geints, A. Zemlyanov, O. Minin, and I. Minin, “Systematic study and comparison of photonic nanojets produced by dielectric microparticles in 2D-and 3D-spatial configurations,” J. Opt. 20, 065606 (2018).
[Crossref]

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F. Zenhausern, Y. Martin, and H. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269, 1083–1085 (1995).
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C. Guan, X. Wang, Q. Zhang, Z. Fan, H. Zhang, and H. Fan, “Highly stable and reversible lithium storage in SnO2 nanowires surface coated with a uniform hollow shell by atomic layer deposition,” Nano Lett. 14, 4852–4858 (2014).
[Crossref]

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Zhang, L.

L. Zhang, R. Tu, and H. Dai, “Parallel core-shell metal-dielectric-semiconductor germanium nanowires for high-current surround-gate field-effect transistors,” Nano Lett. 6, 2785–2789 (2006).
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Zhang, Q.

C. Guan, X. Wang, Q. Zhang, Z. Fan, H. Zhang, and H. Fan, “Highly stable and reversible lithium storage in SnO2 nanowires surface coated with a uniform hollow shell by atomic layer deposition,” Nano Lett. 14, 4852–4858 (2014).
[Crossref]

Zhang, Y.

Y. Li, H. Xin, X. Liu, Y. Zhang, H. Lei, and B. Li, “Trapping and detection of nanoparticles and cells using a parallel photonic nanojet array,” ACS Nano10, 5800–5808 (2016).
[Crossref] [PubMed]

Zhao, M.

G. Gu, J. Song, H. Liang, M. Zhao, Y. Chen, and J. Qu, “Overstepping the upper refractive index limit to form ultra-narrow photonic nanojets,” Sci. Reports 7, 5635 (2017).
[Crossref]

Zhou, R.

Zhu, H.

X. Fan, I. White, S. Shopova, H. Zhu, J. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chimica Acta 620, 8–26 (2008).
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C. Guan, X. Wang, Q. Zhang, Z. Fan, H. Zhang, and H. Fan, “Highly stable and reversible lithium storage in SnO2 nanowires surface coated with a uniform hollow shell by atomic layer deposition,” Nano Lett. 14, 4852–4858 (2014).
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[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Schematic of a five-layer core-shell cylindrical structure.
Fig. 2
Fig. 2 (a) General flow of a genetic algorithm. (b) A coded chromosome section corresponding to a variable γ within a bounded range [γmin, γmax]. (c) Crossover process applied to a pair of chromosomes (d1, d2, d3, d4) and (D1, D2, D3, D4). Chromosomes of parents are split into two parts which are then exchanged to produce offspring with a randomly chosen crossover point. Gn and Gn+1 represent generations n and n + 1, respectively. (d) Mutation process applied to a chromosome (b1, b2, b3, b4). Some genes of the chromosome change. The mutated genes are randomly chosen.
Fig. 3
Fig. 3 (a) Magnetic field intensity profile and magnetic field intensity distribution along the x-axis at y = 0 for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave with unit intensity is normally incident from the left. The inset shows the magnetic field intensity profile inside the microstructure. Results are shown for ρ1 = 2.05λ0, ρ2 = 2.92λ0, ρ3 = 4.90λ0, ρ4 = 4.98λ0, ρ5 = 5λ0, n1 = 1.47, n2 = 1.55, n3 = 2.85, n4 = 1.55, and n5 = 2.37. The horizontal red dashed line corresponds to |Hz|2 = 2. The two vertical red dashed lines indicate the beam length of the optimized PNJ. (b) Streamlines of the Poynting vector for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when the plane wave is normally incident from the left. The vertical red dashed line corresponds to the focal plane of the optimized PNJ. All other parameters are as in Fig. 3(a).
Fig. 4
Fig. 4 (a) Magnetic field intensity profile for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave with unit intensity is normally incident from the left. Results are shown for n1 = 3.17, n2 = 1.60, n3 = 1.86, n4 = 1.62, n5 = 3.07, ρ1 = 1.29λ0, ρ2 = 3.96λ0, ρ3 = 4.57λ0, and ρ4 = 4.80λ0. (b) Magnetic field intensity distribution on the focal plane for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a uniform plane wave is normally incident from the left. All other parameters are as in Fig. 4(a).(c) The magnetic field intensity distribution along the x-axis at y = 0 for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a uniform plane wave with unit intensity is normally incident from the left. The two vertical red dashed lines indicate the beam length of the optimized PNJ. All other parameters are as in Fig. 4(a).
Fig. 5
Fig. 5 Streamlines of the Poynting vector for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave is normally incident from the left. All other parameters are as in Fig. 4(a).
Fig. 6
Fig. 6 Beam length variation ΔL for the optimized structure of Fig. 1 as a function of the refractive index variation in the core region Δn1 at the wavelength of λ0 = 632.8 nm, when the plane wave with unit intensity is normally incident from the left. The inset shows the beam length variation ΔL for the optimized structure of Fig. 1 for a variation in the refractive index of the core region n1 from 1.333 to 1.3331 at the wavelength of λ0 = 632.8 nm. Results are shown for ρ1 = 3.55λ0, ρ2 = 4.40λ0, ρ3 = 4.63λ0, ρ4 = 4.64λ0, ρ5 = 5λ0, n2 = 3.14, n3 = 2.50, n4 = 2.33, and n5 = 1.86.
Fig. 7
Fig. 7 Magnetic field intensity profiles for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave with unit intensity is normally incident from the left. Results are shown for refractive index in the core region n1 = 1.333 and n1 = 1.343. Also shown are magnetic field intensity distributions along the x-axis at y = 0 for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave with unit intensity is normally incident from the left, for refractive index in the core region n1 = 1.333 (blue) and n1 = 1.343 (green). The inset shows the magnetic field intensity profile inside the microstructure for refractive index in the core region n1 = 1.333 at the wavelength of λ0 = 632.8 nm. Results are shown for ρ1 = 3.55λ0, ρ2 = 4.40λ0, ρ3 = 4.63λ0, ρ4 = 4.64λ0, ρ5 = 5λ0, n2 = 3.14, n3 = 2.50, n4 = 2.33, and n5 = 1.86. The horizontal red dashed line corresponds to |Hz|2 = 2. The two vertical red dashed lines indicate the difference between the beam length for refractive index in the core region n1 = 1.333 and n1 = 1.343.
Fig. 8
Fig. 8 (a) Streamlines of the Poynting vector for the optimized structure of Fig. 1 at the wavelength of λ0 = 632.8 nm, when a plane wave is normally incident from the left for refractive index in the core regionn1 = 1.333. The vertical red dashed line indicates the focal plane of the PNJ. All other parameters are as in Fig. 6. (b) Same as in (a) except that n1 = 1.343.

Equations (19)

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

H i n = n = H n N n ( 1 ) ,
E i n = i k 0 ω ϵ 0 n = H n M n ( 1 ) ,
H 1 = n = H n [ i c n M n ( 1 ) + d n N n ( 1 ) ] ,
E 1 = i k 1 ω ϵ 1 n = H n [ i c n N n ( 1 ) + d n M n ( 1 ) ] ,
H m = n = H n [ i g m , n M n ( 1 ) + f m , n N n ( 1 ) + i p m , n M n ( 2 ) + q m , n N n ( 2 ) ] ,
E m = i k m ω ϵ m n = H n [ i g m , n N n ( 1 ) + f m , n M n ( 1 ) + i p m , n N n ( 2 ) + q m , n M n ( 2 ) ] ,
H s = n = H n [ i b n N n ( 3 ) + a n M n ( 3 ) ] ,
E s = i k 0 ω ϵ 0 n = H n [ i b n M n ( 3 ) + a n N n ( 3 ) ] .
a n = 0 ,
b n = U n T M U n T M + i V n T M .
U n T M = | M 1 M 2 M 3 M 4 | ,
M 1 = [ J n ( k 1 ρ 1 ) J n ( k 2 ρ 1 ) Y n ( k 2 ρ 1 ) 0 0 J n ( k 1 ρ 1 ) η 1 J n ( k 2 ρ 1 ) η 2 Y n ( k 2 ρ 1 ) η 2 0 0 0 J n ( k 2 ρ 2 ) Y n ( k 2 ρ 2 ) J n ( k 3 ρ 2 ) Y n ( k 3 ρ 2 ) 0 J n ( k 2 ρ 2 ) η 2 Y n ( k 2 ρ 2 ) η 2 J n ( k 3 ρ 2 ) η 3 Y n ( k 3 ρ 2 ) η 3 0 0 0 J n ( k 3 ρ 3 ) Y n ( k 3 ρ 3 ) ] ,
M 2 = [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 J n ( k 4 ρ 4 ) Y n ( k 4 ρ 4 ) 0 0 0 ] ,
M 3 = [ 0 0 0 J n ( k 3 ρ 3 ) η 3 Y n ( k 3 ρ 3 ) η 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] ,
M 4 = [ J n ( k 4 ρ 4 ) η 4 Y n ( k 4 ρ 4 ) η 4 0 0 0 J n ( k 4 ρ 4 ) Y n ( k 4 ρ 4 ) J n ( k 5 ρ 5 ) Y n ( k 5 ρ 5 ) 0 J n ( k 4 ρ 4 ) η 4 Y n ( k 4 ρ 4 ) η 4 J n ( k 5 ρ 5 ) η 5 Y n ( k 5 ρ 5 ) η 5 0 0 0 J n ( k 5 ρ 5 ) Y n ( k 5 ρ 5 ) J n ( k 0 ρ 5 ) 0 0 J n ( k 5 ρ 5 ) η 5 Y n ( k 5 ρ 5 ) η 5 J n ( k 0 ρ 5 ) η 0 ] ,
V n T M = | M 1 M 2 M 3 M 4 | ,
M 4 = [ J n ( k 4 ρ 4 ) η 4 Y n ( k 4 ρ 4 ) η 4 0 0 0 J n ( k 4 ρ 4 ) Y n ( k 4 ρ 4 ) J n ( k 5 ρ 5 ) Y n ( k 5 ρ 5 ) 0 J n ( k 4 ρ 4 ) η 4 Y n ( k 4 ρ 4 ) η 4 J n ( k 5 ρ 5 ) η 5 Y n ( k 5 ρ 5 ) η 5 0 0 0 J n ( k 5 ρ 5 ) Y n ( k 5 ρ 5 ) Y n ( k 0 ρ 5 ) 0 0 J n ( k 5 ρ 5 ) η 5 Y n ( k 5 ρ 5 ) η 5 Y n ( k 0 ρ 5 ) η 0 ] .
F O M = | d L ( n ) d n | ,
| Δ n min | = | Δ L min F O M | .

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