Abstract

We have investigated low frequency guiding polariton modes in finite linear chains of closely packed dielectric spherical particles of different optical materials. These guiding (chain bound) modes cannot decay radiatively, because photon emission cannot take place with simultaneous conservation of energy and momentum. For extending previous work on infinite chains of spherical particles[1] and infinite rods[2, 3], we were able to apply the multisphere Mie scattering formalism to finite chains of dielectric particles to calculate quality factors of most bound modes originating from the first two Mie resonances depending on the number of particles N and the material’s refractive index n r. We found that, in agreement with the earlier work [4], guiding modes exist for n r>2 and the quality factor of the most bound mode scales by N 3. We interpreted this behavior as the property of “frozen” modes near the edges of guiding bands with group velocity vanishing as N increases. In contrast with circular arrays, longitudinal guiding modes in particle chains possess a higher quality factor compared to the transverse ones.

© 2007 Optical Society of America

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    [CrossRef]
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2007 (1)

2006 (2)

2005 (4)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef] [PubMed]

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433,811812 (2005).
[CrossRef]

Z. Y. Tang and N. A. Kotov, "One-dimensional assemblies of nanoparticles: Preparation, properties, and promise," Adv. Mater. 17,951-962 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, "Traveling electromagnetic waves on linear periodic arrays of lossless spheres," Electron. Lett. 41,578-580 (2005).
[CrossRef]

2004 (4)

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85,5508 (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

A. L. Burin, G. C. Schatz, H. Cao, and M. A. Ratner, "High quality optical modes in low-dimensional arrays of nanoparticles. Application to random lasers," J. Opt. Soc. Am. B 21,121-131 (2004).
[CrossRef]

E. I. Smotrova and A. I. Nosich, "Mathematical study of the two-dimensional lasing problem for the whisperinggallery modes in a circular dielectric microcavity," Opt. Quantum Electron. 36,213-221 (2004).
[CrossRef]

2003 (4)

Y. L. Xu, "Scattering Mueller matrix of an ensemble of variously shaped small particles," J. Opt. Soc. Am. A 20,2093-2105 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301,200202 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

1997 (1)

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite one-dimensional, photonic band-gap structures," Phys. Rev. B 53,4107-4121 (1996).
[CrossRef]

1995 (1)

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band-edge laser a new approach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

1959 (1)

H. W. Ehrespeck and H. Poehler, "A new method for obtaining maximum gain from Yagi antennas," IEEE Trans. Antennas Propag. AP- 7,379-386 (1959).

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85,5508 (2004).
[CrossRef]

Astratov, V. N.

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

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85,5508 (2004).
[CrossRef]

Atwater, H. A.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite one-dimensional, photonic band-gap structures," Phys. Rev. B 53,4107-4121 (1996).
[CrossRef]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301,200202 (2003).
[CrossRef]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band-edge laser a new approach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

Boriskina, S. V.

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band-edge laser a new approach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

Boyd, R. W.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301,200202 (2003).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

Brongersma, M. L.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

Burin, A. L.

Cao, H.

Chang, S.-W.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Chang-Hasnain, C. J.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Chen, J. C.

Chuang, S.-L.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Devenyi, A.

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite one-dimensional, photonic band-gap structures," Phys. Rev. B 53,4107-4121 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band-edge laser a new approach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

Eggleton, B. J.

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433,811812 (2005).
[CrossRef]

Ehrespeck, H. W.

H. W. Ehrespeck and H. Poehler, "A new method for obtaining maximum gain from Yagi antennas," IEEE Trans. Antennas Propag. AP- 7,379-386 (1959).

Fan, S.

Franchak, J. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, "Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder," Appl. Phys. Lett. 85,5508 (2004).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef] [PubMed]

Harel, E.

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

Joannopoulos, J. D.

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade and J. D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12,1267-72 (1995).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

Kapitonov, A.M.

Kik, P. G.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

Koel, B. E.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

Kotov, N. A.

Z. Y. Tang and N. A. Kotov, "One-dimensional assemblies of nanoparticles: Preparation, properties, and promise," Adv. Mater. 17,951-962 (2005).
[CrossRef]

Ku, P. C.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301,200202 (2003).
[CrossRef]

Li, T.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Mayer, S. A.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef] [PubMed]

Meade, R. D.

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade and J. D. Joannopoulos, "Guided and defect modes in periodic dielectric waveguides," J. Opt. Soc. Am. B 12,1267-72 (1995).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

Meltzer, S.

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

Mok, J. T.

J. T. Mok and B. J. Eggleton, "Expect more delays," Nature 433,811812 (2005).
[CrossRef]

Nosich, A. I.

E. I. Smotrova and A. I. Nosich, "Mathematical study of the two-dimensional lasing problem for the whisperinggallery modes in a circular dielectric microcavity," Opt. Quantum Electron. 36,213-221 (2004).
[CrossRef]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
[CrossRef] [PubMed]

Palinginis, P.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Poehler, H.

H. W. Ehrespeck and H. Poehler, "A new method for obtaining maximum gain from Yagi antennas," IEEE Trans. Antennas Propag. AP- 7,379-386 (1959).

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48,8434 (1993).
[CrossRef]

Ratner, M. A.

Requicha, A. A. G.

S. A. Mayer, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, B. E. Koel, and H. A. Atwater, "Plasmonics A route to nanoscale optical devices," Adv. Mater. 15,562-562 (2003).
[CrossRef]

S. A. Mayer, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2,229-232 (2003).
[CrossRef]

Scalora, M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite one-dimensional, photonic band-gap structures," Phys. Rev. B 53,4107-4121 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band-edge laser a new approach to gain enhancement," J. Appl. Phys. 75,1896-1899 (1994).
[CrossRef]

Schatz, G. C.

Sedgwick, F.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
[CrossRef]

Shore, R. A.

R. A. Shore and A. D. Yaghjian, "Traveling electromagnetic waves on linear periodic arrays of lossless spheres," Electron. Lett. 41,578-580 (2005).
[CrossRef]

Smotrova, E. I.

E. I. Smotrova and A. I. Nosich, "Mathematical study of the two-dimensional lasing problem for the whisperinggallery modes in a circular dielectric microcavity," Opt. Quantum Electron. 36,213-221 (2004).
[CrossRef]

Tang, Z. Y.

Z. Y. Tang and N. A. Kotov, "One-dimensional assemblies of nanoparticles: Preparation, properties, and promise," Adv. Mater. 17,951-962 (2005).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438,65-69 (2005).
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P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S.-W. Chang, and S.-L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29,22912293 (2004).
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Figures (4)

Fig. 1.
Fig. 1.

(a) Linear chain of scattering particles; (b) Possible values of the quasi-wavevector of propagating polariton modes with domain of guiding modes indicated. All notations are described within the text.

Fig. 2.
Fig. 2.

Quality factor of a transverse b-mode for the chain of GaAs particles versus number of particles N, calculated in various approaches. The results for the approximation (F) corresponding to n max =4 are not shown because they will be not distinguishable with the approximation (E) different from it by less than 1%.

Fig. 3.
Fig. 3.

Quality factor of transverse and longitudinal b-modes for the chain of GaAs and TiO2 particles versus number of particles N, calculated for n max =3.

Fig. 4.
Fig. 4.

Quality factor of transverse and longitudinal b-modes for the chain of ZnO particles versus number of particles N, calculated for n max =2.

Tables (1)

Tables Icon

Table 1. Guiding parameter for low frequency modes.

Equations (17)

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( π a < k < ω c ) , ( ω c < q < π a ) ,
a < λ 2 .
a mn l a ¯ n + j = 1 ( l ) N n = 1 n max m = n n A mn μ ν jl a μ ν j + j = 1 ( l ) N n = 1 n max m = n n B mn μ ν jl b μ ν j = p mn l ;
b mn l b ¯ n + j = 1 ( l ) N n = 1 n max m = n n A mn μ ν jl b μ ν j + j = 1 ( l ) N n = 1 n max m = n n B mn μ ν jl a μ ν j = q mn l .
a mn l a ¯ n + j = 1 ( l ) N n = 1 n max m = n n A mn μ ν jl a μ ν j + j = 1 ( l ) N n = 1 n max m = n n B mn μ ν jl b μ ν j = 0 ;
b mn l b ¯ n + j = 1 ( l ) N n = 1 n max m = n n A mn μ ν jl b μ ν j + j = 1 ( l ) N n = 1 n max m = n n B mn μ ν jl a μ ν j = 0 ,
Q a = ω a 2 γ a ,
M ̂ ( z ) x = 0 ,
z n + 1 = z n f ( z n ) ( d f ( z n ) dz ) .
Q ( N ) N 3
C 0 cos ( E U L ) = C 1 e i E L ,
C 0 E U sin ( E U L ) = i E C 1 e i E L .
1 E U tan ( E U L ) = i E
E U = a , aL = π 2 δ , δ 1
ImE = i π 2 4 L 3 U
ReE = U + π 2 4 L 2 U
Q = ReE 2 ImE = L 3 π 2 U 3 2 ,

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