Abstract

Maxwell’s vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell’s equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (1)

S. Bartkiewicz and A. Miniewicz, “Whirl-enhanced continuous wave laser trapping of particles,” Phys. Chem. Chem. Phys. 17(2), 1077–1083 (2015).
[Crossref] [PubMed]

2014 (2)

N. Ghazyani, M. Hossein, M. Ara, F. Tajabadi, A. Dabirian, R. Mohammadpour, and N. Taghavinia, “Dielectric core-shells with enhanced scattering efficiency as back-reflectors in dye sensitized solar cells,” Royal Soc Chem. 4, 3621–3626 (2014).

G. Burlak, M. N. Villeda, and R. S. Salgado, “The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems,” Prog. Electromag. Res. Lett. 48, 1–6 (2014).
[Crossref]

2013 (1)

R. Gauthier and M. Alzahrani, “Cylindrical space Fourier Bessel mode solver for Maxwell’s wave equation,” Adv. Mater. 2(3), 32–35 (2013).

2011 (2)

S. Newman and R. Gauthier, “Representation of photonic crystals and their localized modes through the use of Fourier–Bessel expansions,” IEEE Photonics J. 3(6), 1133–1141 (2011).
[Crossref]

M. C. Gather and S. H. Yun, “Single-cell biological lasers,” Nat. Photonics 5(7), 406–410 (2011).
[Crossref]

2010 (5)

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82(3), 033801 (2010).
[Crossref]

K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
[Crossref] [PubMed]

A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
[Crossref]

G. Burlak, A. Díaz-de-Anda, R. S. Salgado, and J. P. Ortega, “Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left handed stack,” Opt. Commun. 283(19), 3569–3577 (2010).
[Crossref]

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: The concept and design,” Opt. Express 18(1), 123–133 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (3)

A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
[Crossref]

G. N. Burlak and A. Dı’az-de-Anda, “Optical fields in a multilayered microsphere with a quasiperiodic spherical stack,” Opt. Commun. 281(1), 181–189 (2008).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

2007 (1)

J. Breeze, J. Krupka, and N. M. N. Alford, “Enhanced quality factors in aperiodic reflector resonators,” Appl. Phys. Lett. 91(15), 152902 (2007).
[Crossref]

2006 (3)

I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
[Crossref]

A. Matsko and V. Ilchenko, “Optical resonators with whispering gallery modes I: Basic,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).

I. Teraoka and S. Arnold, “Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer,” J. Opt. Soc. Am. B 23(7), 1434–1441 (2006).
[Crossref]

2005 (3)

R. Gauthier and K. Mnaymneh, “Photonic band gap properties of 12-fold quasi-crystal determined through FDTD analysis,” Opt. Express 13(6), 1985–1998 (2005).
[Crossref] [PubMed]

C. Vandenbem and J. P. Vigneron, “Mie resonances of dielectric spheres in face-centered cubic photonic crystals,” J. Opt. Soc. Am. A 22(6), 1042–1047 (2005).
[Crossref] [PubMed]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[Crossref] [PubMed]

2001 (1)

G. Burlak, S. Koshevaya, J. Sanchez-Mondragon, and V. Grimalsky, “Electromagnetic eigenoscillations and felds in a dielectric microsphere with multilayer spherical stack,” Opt. Commun. 187(1–3), 91–105 (2001).
[Crossref]

1999 (1)

1998 (3)

B. E. Little, S. T. Chu, and H. A. Haus, “Second-order filtering and sensing with partially coupled traveling waves in a single resonator,” Opt. Lett. 23(20), 1570–1572 (1998).
[Crossref] [PubMed]

Z. Q. Wen and G. J. Thomas., “UV resonance Raman spectroscopy of DNA and protein constituents of viruses: assignments and cross sections for excitations at 257, 244, 238, and 229 nm,” Biopolymers 45(3), 247–256 (1998).
[Crossref] [PubMed]

C. Chen, “Electromagnetic resonance of immersed dielectric spheres,” IEEE Trans. Antenn. Propag. 46(7), 1074–1083 (1998).
[Crossref]

1997 (3)

J. C. Ï. Tyrokyâ, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29(2), 301–311 (1997).
[Crossref]

E. M. Ganapolskii and A. V. Golik, “A sapphire sphere resonator for the measurement of low dielectric losses in the millimetrewave range in liquids,” Meas. Sci. Technol. 8(9), 1016–1022 (1997).
[Crossref]

D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S. T. Ho, and R. C. Tiberio, “Waveguide-coupled AlGaAs / GaAs microcavity ring and disk resonators with high f inesse and 21.6-nm f ree spectral range,” Opt. Lett. 22(16), 1244–1246 (1997).
[Crossref] [PubMed]

1996 (2)

V. Klimov, M. Ducloy, and V. Letokhov, “Spontaneous emission rate and level shift of an atom inside a dielectric microsphere,” J. Mod. Opt. 43(3), 549–563 (1996).
[Crossref]

R. Heim and R. Y. Tsien, “Engineering green fluorescent protein for improved brightness, longer wavelengths and fluorescence resonance energy transfer,” Curr. Biol. 6(2), 178–182 (1996).
[Crossref] [PubMed]

1992 (1)

K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46(9), 6104–6107 (1992).
[Crossref] [PubMed]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

1986 (1)

1985 (2)

1981 (1)

1977 (1)

S. Ezekiel and S. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478 (1977).
[Crossref]

1975 (1)

R. L. Panton and J. M. Miller, “Resonant frequencies of cylindrical Helmholtz resonators,” J. Acoust. Soc. Am. 57(6), 1533 (1975).
[Crossref]

1967 (1)

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microw. Theory Tech. 15(12), 694–700 (1967).
[Crossref]

1966 (1)

Ahmadi, A.

Alford, N. M. N.

J. Breeze, J. Krupka, and N. M. N. Alford, “Enhanced quality factors in aperiodic reflector resonators,” Appl. Phys. Lett. 91(15), 152902 (2007).
[Crossref]

Alteheld, A.

I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
[Crossref]

Alzahrani, M.

R. Gauthier and M. Alzahrani, “Cylindrical space Fourier Bessel mode solver for Maxwell’s wave equation,” Adv. Mater. 2(3), 32–35 (2013).

Ara, M.

N. Ghazyani, M. Hossein, M. Ara, F. Tajabadi, A. Dabirian, R. Mohammadpour, and N. Taghavinia, “Dielectric core-shells with enhanced scattering efficiency as back-reflectors in dye sensitized solar cells,” Royal Soc Chem. 4, 3621–3626 (2014).

Arakawa, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[Crossref] [PubMed]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

I. Teraoka and S. Arnold, “Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer,” J. Opt. Soc. Am. B 23(7), 1434–1441 (2006).
[Crossref]

Ashkin, A.

Ayaz, U.

Balsamo, S.

S. Ezekiel and S. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478 (1977).
[Crossref]

Bartkiewicz, S.

S. Bartkiewicz and A. Miniewicz, “Whirl-enhanced continuous wave laser trapping of particles,” Phys. Chem. Chem. Phys. 17(2), 1077–1083 (2015).
[Crossref] [PubMed]

Breeze, J.

J. Breeze, J. Krupka, and N. M. N. Alford, “Enhanced quality factors in aperiodic reflector resonators,” Appl. Phys. Lett. 91(15), 152902 (2007).
[Crossref]

Burlak, G.

G. Burlak, M. N. Villeda, and R. S. Salgado, “The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems,” Prog. Electromag. Res. Lett. 48, 1–6 (2014).
[Crossref]

G. Burlak, A. Díaz-de-Anda, R. S. Salgado, and J. P. Ortega, “Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left handed stack,” Opt. Commun. 283(19), 3569–3577 (2010).
[Crossref]

G. Burlak, S. Koshevaya, J. Sanchez-Mondragon, and V. Grimalsky, “Electromagnetic eigenoscillations and felds in a dielectric microsphere with multilayer spherical stack,” Opt. Commun. 187(1–3), 91–105 (2001).
[Crossref]

Burlak, G. N.

G. N. Burlak and A. Dı’az-de-Anda, “Optical fields in a multilayered microsphere with a quasiperiodic spherical stack,” Opt. Commun. 281(1), 181–189 (2008).
[Crossref]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Chembo, Y. K.

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82(3), 033801 (2010).
[Crossref]

Chen, C.

C. Chen, “Electromagnetic resonance of immersed dielectric spheres,” IEEE Trans. Antenn. Propag. 46(7), 1074–1083 (1998).
[Crossref]

Chu, S. T.

Courtois, L.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microw. Theory Tech. 15(12), 694–700 (1967).
[Crossref]

Dabirian, A.

N. Ghazyani, M. Hossein, M. Ara, F. Tajabadi, A. Dabirian, R. Mohammadpour, and N. Taghavinia, “Dielectric core-shells with enhanced scattering efficiency as back-reflectors in dye sensitized solar cells,” Royal Soc Chem. 4, 3621–3626 (2014).

Di’az-de-Anda, A.

G. N. Burlak and A. Dı’az-de-Anda, “Optical fields in a multilayered microsphere with a quasiperiodic spherical stack,” Opt. Commun. 281(1), 181–189 (2008).
[Crossref]

Díaz-de-Anda, A.

G. Burlak, A. Díaz-de-Anda, R. S. Salgado, and J. P. Ortega, “Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left handed stack,” Opt. Commun. 283(19), 3569–3577 (2010).
[Crossref]

Dietrich, K.

K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
[Crossref] [PubMed]

Dormann, J. L.

M. Gastine, L. Courtois, and J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microw. Theory Tech. 15(12), 694–700 (1967).
[Crossref]

Ducloy, M.

V. Klimov, M. Ducloy, and V. Letokhov, “Spontaneous emission rate and level shift of an atom inside a dielectric microsphere,” J. Mod. Opt. 43(3), 549–563 (1996).
[Crossref]

Dziedzic, J. M.

Englund, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
[Crossref] [PubMed]

Ezekiel, S.

S. Ezekiel and S. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478 (1977).
[Crossref]

Fattal, D.

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Kiefer, W.

Kipp, T.

K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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A. Matsko and V. Ilchenko, “Optical resonators with whispering gallery modes I: Basic,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).

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K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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Mohammadpour, R.

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Mosallaei, H.

Nair, S. V.

A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
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A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
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Ruda, H. E.

A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
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G. Burlak, M. N. Villeda, and R. S. Salgado, “The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems,” Prog. Electromag. Res. Lett. 48, 1–6 (2014).
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G. Burlak, A. Díaz-de-Anda, R. S. Salgado, and J. P. Ortega, “Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left handed stack,” Opt. Commun. 283(19), 3569–3577 (2010).
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Sanchez-Mondragon, J.

G. Burlak, S. Koshevaya, J. Sanchez-Mondragon, and V. Grimalsky, “Electromagnetic eigenoscillations and felds in a dielectric microsphere with multilayer spherical stack,” Opt. Commun. 187(1–3), 91–105 (2001).
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K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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Shik, A.

A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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Sipe, J. E.

I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
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J. C. Ï. Tyrokyâ, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29(2), 301–311 (1997).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
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Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
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Stemmann, A.

K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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Taghavinia, N.

N. Ghazyani, M. Hossein, M. Ara, F. Tajabadi, A. Dabirian, R. Mohammadpour, and N. Taghavinia, “Dielectric core-shells with enhanced scattering efficiency as back-reflectors in dye sensitized solar cells,” Royal Soc Chem. 4, 3621–3626 (2014).

Tajabadi, F.

N. Ghazyani, M. Hossein, M. Ara, F. Tajabadi, A. Dabirian, R. Mohammadpour, and N. Taghavinia, “Dielectric core-shells with enhanced scattering efficiency as back-reflectors in dye sensitized solar cells,” Royal Soc Chem. 4, 3621–3626 (2014).

Teraoka, I.

Thomas, G. J.

Z. Q. Wen and G. J. Thomas., “UV resonance Raman spectroscopy of DNA and protein constituents of viruses: assignments and cross sections for excitations at 257, 244, 238, and 229 nm,” Biopolymers 45(3), 247–256 (1998).
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Thurn, R.

Tiberio, R. C.

Tsien, R. Y.

R. Heim and R. Y. Tsien, “Engineering green fluorescent protein for improved brightness, longer wavelengths and fluorescence resonance energy transfer,” Curr. Biol. 6(2), 178–182 (1996).
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J. C. Ï. Tyrokyâ, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29(2), 301–311 (1997).
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Vigneron, J. P.

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G. Burlak, M. N. Villeda, and R. S. Salgado, “The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems,” Prog. Electromag. Res. Lett. 48, 1–6 (2014).
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A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
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I. Gourevich, L. M. Field, Z. Wei, C. Paquet, A. Petukhova, A. Alteheld, E. Kumacheva, J. J. Saarinen, and J. E. Sipe, “Polymer multilayer particles: a route to spherical dielectric resonators,” Macromolecules 39(4), 1449–1454 (2006).
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K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical Modes Excited by Evanescent-Wave-Coupled PbS Nanocrystals in Semiconductor Microtube Bottle Resonators,” Nano Lett. 10(2), 627–631 (2010).
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Z. Q. Wen and G. J. Thomas., “UV resonance Raman spectroscopy of DNA and protein constituents of viruses: assignments and cross sections for excitations at 257, 244, 238, and 229 nm,” Biopolymers 45(3), 247–256 (1998).
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Yamamoto, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
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Yun, S. H.

M. C. Gather and S. H. Yun, “Single-cell biological lasers,” Nat. Photonics 5(7), 406–410 (2011).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 95(1), 013904 (2005).
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Zhang, J. P.

Adv. Funct. Mater. (1)

A. Petukhova, A. S. Paton, Z. Wei, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Polymer Multilayer Microspheres Loaded with Semiconductor Quantum Dots,” Adv. Funct. Mater. 18(13), 1961–1968 (2008).
[Crossref]

Adv. Mater. (1)

R. Gauthier and M. Alzahrani, “Cylindrical space Fourier Bessel mode solver for Maxwell’s wave equation,” Adv. Mater. 2(3), 32–35 (2013).

Appl. Opt. (3)

Appl. Phys. Lett. (2)

J. Breeze, J. Krupka, and N. M. N. Alford, “Enhanced quality factors in aperiodic reflector resonators,” Appl. Phys. Lett. 91(15), 152902 (2007).
[Crossref]

S. Ezekiel and S. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30(9), 478 (1977).
[Crossref]

Biopolymers (1)

Z. Q. Wen and G. J. Thomas., “UV resonance Raman spectroscopy of DNA and protein constituents of viruses: assignments and cross sections for excitations at 257, 244, 238, and 229 nm,” Biopolymers 45(3), 247–256 (1998).
[Crossref] [PubMed]

Can. J. Chem. (1)

A. Petukhova, A. S. Paton, I. Gourevich, S. V. Nair, H. E. Ruda, A. Shik, and E. Kumacheva, “Hybrid microspheres with alternating layers of a polymer and metal nanoparticles,” Can. J. Chem. 88(3), 298–304 (2010).
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Figures (15)

Fig. 1
Fig. 1 (a) – Geometry of the solid-uniform, ε r = 9 , dielectric sphere, radius a, in the spherical computation domain of radius R = 2a. (b) – Real part of the dielectric series expansion coefficients plotted versus spherical Bessel basis function index. Imaginary parts all zero.
Fig. 2
Fig. 2 The (x, y) plane normalized intensity profile E φ field component (Left), and the (y, z) plane normalized intensity profile E φ field component (Right), for the R1Θ1Ψ0 localized state listed in Table 1, computed using BLF, k a = 1.0604 . The field profile and corresponding eigenvalue match those of [24, 25].
Fig. 3
Fig. 3 The (x, y) plane normalized intensity profile E φ field component (Left), and the (y, z) plane normalized intensity profile E φ field component (Right), for the R1Θ5Ψ0 localized state listed in Table 1, computed using BLF,   k a = 2.7040 . The field profile and corresponding eigenvalue match those of [24, 25].
Fig. 4
Fig. 4 The (x, y) plane normalized intensity profile E θ field component (Left), and the (y, z) plane normalized intensity profile E θ field component (Right), for R2Θ1Ψ0 localized state listed in Table 2, computed using BLF, k a = 2.4954 .
Fig. 5
Fig. 5 The (x, y) plane normalized intensity profile E θ field component (Left), and the (y, z) plane normalized intensity profile E θ field component (Right), for R2Θ5Ψ0 localized state listed in Table 2, computed using BLF,   k a = 4.2850 .
Fig. 6
Fig. 6 The (y, z) plane normalized intensity profile E r field component for R2Θ1Ψ0 localized state listed in Table 2, computed using BLF,   k a = 2.4954 . (Left). The (y, z) plane normalized intensity profile E r field component for R2Θ5Ψ0 localized state listed in Table 2, computed using BLF,   k a = 4.2850 (Right). The (x, y) plane have zero E r field values.
Fig. 7
Fig. 7 Intensity profile for the E θ field component of the FBL computed whispering-gallery-modes of the solid sphere in air. (a) Top pair – Azimuthal mode order 20 with field R1Θ1Ψ20 and k a = 8.3280 . (b) Bottom pair – Azimuthal mode order 40 with field R1Θ1Ψ40 and k a = 15.4701 . Left – (x, y) plane. Right – (y, z) plane.
Fig. 8
Fig. 8 The normalized intensity profile   E φ field component for R1Θ1Ψ0 with, k a = 4.4935 . Left – (x, y) plane. Right – (y, z) plane.
Fig. 9
Fig. 9 The normalized intensity profile for   E φ field component for R2Θ3Ψ0 for k a = 10.4181 . Left – (x, y) plane. Right – (y, z) plane.
Fig. 10
Fig. 10 A dielectric sphere coated by spherical shells dielectric. The shells structure acts as quarter wave Bragg reflector, the relative dielectric constant has real values only. First 100 radial dielectric expansion coefficients for the spherical shell structure.
Fig. 11
Fig. 11 The normalized intensity profile   H φ field component for R1Θ1Ψ0, computed using BLF. The field profile and corresponding eigenvalue match those of [27]. Left – (x, y) plane. Right – (y, z) plane.
Fig. 12
Fig. 12 The normalized intensity profile E θ field component for R1Θ1Ψ30, computed using BLF, f = 134.12 THz ( k a = 2.8089 ). Left – (x, y) plane. Right – (y, z) plane.
Fig. 13
Fig. 13 The normalized intensity profile E θ field component for R1Θ3Ψ30, computed using BLF, f = 142.09 THz ( k a = 2.9760 ). Left – (x, y) plane. Right – (y, z) plane.
Fig. 14
Fig. 14 A sphere of air coated by aperiodic spherical shells, the dielectric has real and imaginary values. Real radial dielectric expansion coefficients for the aperiodic shell structure (Left). Imaginary radial dielectric expansion coefficients for the aperiodic shell structure (Right).
Fig. 15
Fig. 15 The normalized intensity profile E φ field component for R1Θ1Ψ0, computed using BLF. The field profile and corresponding eigenvalue match those of [42]. f r e a l = 10.06 GHz, f i m a g i n a r y = 1.0 × 10 3 Hz. Left – (x, y) plane. Right – (y, z) plane.

Tables (3)

Tables Icon

Table 1 Scaled resonance wavenumbers determined using BLF and from [24, 25] for the E φ , TE polarization. Bold entries have field profiles plotted in Figs. 2 and 3.

Tables Icon

Table 2 Scaled resonance wavenumbers determined using BLF and from [24, 25] for the E r ,   E θ , TM polarization. Bold entries have field profiles plotted in Figs. 4 to 6 (TM)

Tables Icon

Table 3 Comparison of the scaled resonance wavenumber obtained using BLF and from [38, 39]. Bold-field profiles plotted in Figs. 8 and 9 computed using the BLF technique with eigenvector dominated by the E φ field component.

Equations (17)

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× 1 ε r × H = ( ω c ) 2 H 1 ε r × × E = ( ω c ) 2 E
Ω = 1 ε r = p Ω ,     n Ω , q Ω   κ Ω   j 0 ( ρ m Ω r R ) P n Ω ( cos ( θ ) ) e j q Ω φ
[ H f E f ] = p f ,     n f , q f   κ f   j 0 ( ρ p f r R ) P n f ( cos ( θ ) ) e j q f φ
[ R r               Θ r               Φ r R θ               Θ θ               Φ θ R φ               Θ φ               Φ φ ] [ κ r κ θ κ φ ] = ( ω c ) 2 [ κ r κ θ κ φ ]
0 2 π e j ( q + q Ω q * ) φ d φ = δ q + q Ω ,     q *
[ R r               Θ r             0 R θ             Θ θ             0 0               0                   Φ φ ] [ κ r κ θ κ φ ] = ( ω c ) 2 [ κ r κ θ κ φ ]
Q = R e a l ( ω ) 2 * I m a g i n a r y ( ω )
( ω c ) 2 [ H E ] = 1 ε r × [ H E ] + 1 ε r × × [ H 0 ]
R r   [ H E ] = C 1 Ω κ Ω { [ ( n 2 + n )   P c 0 s 1   00 + q 2   P c 0 s 1   00 ] ξ 000 } [ H E ] + C 1 Ω κ Ω { [ ( n   n Ω ) ( P c 1 s 1   01 + P c 1 s 1   10 P c 2 s 1   00 P c 0 s 1   11 ) + ( q   q Ω ) P c 0 s 1   00 ] ξ 000 } [ H 0 ]
R θ   [ H E ] = C 1 Ω κ Ω { ρ p [ n   P c 0 s 0   01 ( n + 1 ) P c 1 s 0   00 ] ξ 011 + [ ( n + 1 ) P c 1 s 0   00 n   P c 0 s 0   01 ] ξ 000 } [ H E ] + C 1 Ω κ Ω { ρ p   n Ω [ P c 0 s 0   10 P c 1 s 0   00 ] ξ 101 + n Ω [ ( P c 1 s 0   00 P c 0 s 0   10 ) ] ξ 000 } [ H 0 ]
R φ   [ H E ] = j C 1 Ω κ Ω   q   P c 0 s 0   00   { ξ 000 ρ p ξ 011 } [ H E ] + j C 1 Ω κ Ω   q Ω   P c 0 s 0   00   { ξ 000 + ρ p ξ 011 } [ H 0 ]
Θ r   [ H E ] = C 1 Ω κ Ω { n   ρ p [   P c 0 s 0   01 P c 1 s 0   00 ] ξ 011 } [ H E ] + C 1 Ω κ Ω { n   ρ p Ω [   P c 0 s 0   01 P c 1 s 0   00 ] ξ 101 } [ H 0 ]
Θ θ   [ H E ] = C 1 Ω κ Ω     { q 2   P c 0 s 1   00   ξ 000 + ρ p 2   P c 0 s 1   00   ξ 002 } [ H E ] + C 1 Ω κ Ω     { q   q Ω   P c 0 s 1   00   ξ 000 + ρ p Ω   P c 0 s 1   00 [ ξ 101 ρ p ξ 112 ] } [ H 0 ]
Θ φ   [ H E ] = j C 1 Ω κ Ω q   { [   ( n + 1 ) P c 1 s 1   00 n P c 0 s 1   01 ] ξ 000 } [ H E ] + j C 1 Ω κ Ω q Ω   { [   ( n + 1 ) P c 1 s 1   00 n P c 0 s 1   01 ] ξ 000 } [ H 0 ]
Φ r   [ H E ] = j C 1 Ω κ Ω   { ρ p   q   P c 0 s 0   00   ξ 011 } [ H E ] j C 1 Ω κ Ω   { ρ p Ω   q   P c 0 s 0   00   ξ 101 } [ H 0 ]
Φ θ   [ H E ] = j C 1 Ω κ Ω   q { [ ( n 1 )   P c 1 s 1   00 n P c 0 s 1   01 ] ξ 000 } [ H E ] + j C 1 Ω κ Ω   q   n Ω { [   P c 1 s 1   00 P c 0 s 1   10 ] ξ 000 } [ H 0 ]
Φ φ   [ H E ] = C 1 Ω κ Ω   { [ ( n 2 + n + 1 )   P c 0 s 1   00 + P c 2 s 1   00 ] ξ 000 + ρ p 2   P c 0 s 1   00   ξ 002 } [ H E ] + C 1 Ω κ Ω { n Ω [ n   P c 1 s 1   01 n P c 0 s 1   11 + ( n + 1 )   P c 1 s 1   10 ( n + 1 ) P c 2 s 1   00 ] ξ 000 + ρ p Ω   P c 0 s 1   00 [ ξ 101 ρ p   ξ 112 ] [ H 0 ]

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