Abstract

We theoretically examine the bending loss of organic molecular-crystal nanofibers for which the light propagation is carried out by optically anisotropic exciton polaritons. Previous experimental studies showed that the leakage of light for bent thiacyanine nanofibers was negligibly small even for the radius of curvature of several microns. We formulate a finite-difference frequency-domain method stabilized by a conformal transformation to calculate the bending loss as a function of the radius of curvature and the propagation frequency. The present method is applied to the thiacyanine nanofiber and numerical results that support the previous experimental observation are obtained. The present study clearly shows that the polariton nanofiber gives a novel possibility for bent waveguides to fabricate optical microcircuits and interconnection that cannot be attained by the conventional waveguides based on the index guiding.

© 2013 Optical Society of America

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References

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  1. D. J. Lockwood and L. Pavesi, Silicon Photonics II: Components and Integration (Springer, 2011).
    [Crossref]
  2. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
    [Crossref]
  3. K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
    [Crossref] [PubMed]
  4. K. Takazawa, “Waveguiding properties of fiber-shaped aggregates self-assembled from thiacyanine dye molecules,” J. Chem. Phys. 111, 8671–8676 (2007).
  5. K. Takazawa, “Flexibility and bending loss of waveguiding molecular fibers self-assembled from thiacyanine dye,” Chem. Phys. Lett. 452, 168–172 (2008).
    [Crossref]
  6. K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
    [Crossref]
  7. H. Takeda and K. Sakoda, “Exciton-polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
    [Crossref]
  8. R. G. Hunsperger, Integrated Optics: Theory and Technology, 6th ed. (Springer, 2009).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2013 (2)

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

Z. Han, P. Zhang, and S. I. Bozhevolnyi, “Calculation of bending losses for highly confined modes of optical waveguides with transformation optics,” Opt. Lett. 38, 1778–1780 (2013).
[Crossref] [PubMed]

2012 (2)

2010 (1)

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

2008 (3)

2007 (1)

K. Takazawa, “Waveguiding properties of fiber-shaped aggregates self-assembled from thiacyanine dye molecules,” J. Chem. Phys. 111, 8671–8676 (2007).

2006 (1)

2004 (1)

2001 (1)

1997 (1)

F. L. Teixeira and W. C. Chew, “PML-FDTD in Cylindrical and Spherical Grids,” IEEE Microw. Guid. Wave Lett. 7, 285–287 (1997).
[Crossref]

1971 (1)

D. Marcuse, “Bending losses of the asymmetric slab waveguide,” Bell Syst. Tech. J. 50, 2551–2563 (1971).
[Crossref]

1958 (1)

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Bozhevolnyi, S. I.

Carniel, F.

Chao, S.

Chew, W. C.

F. L. Teixeira and W. C. Chew, “PML-FDTD in Cylindrical and Spherical Grids,” IEEE Microw. Guid. Wave Lett. 7, 285–287 (1997).
[Crossref]

Costa, R.

Dai, D.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Han, Z.

He, S.

Hopfield, J. J.

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology, 6th ed. (Springer, 2009).
[Crossref]

Inoue, J.

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

Kakihara, K.

Kono, N.

Koshiba, M.

Kuroda, T.

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

Lockwood, D. J.

D. J. Lockwood and L. Pavesi, Silicon Photonics II: Components and Integration (Springer, 2011).
[Crossref]

Marcuse, D.

D. Marcuse, “Bending losses of the asymmetric slab waveguide,” Bell Syst. Tech. J. 50, 2551–2563 (1971).
[Crossref]

Martinelli, M.

Melloni, A.

Mitsuishi, K.

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

Ni, H.

Pavesi, L.

D. J. Lockwood and L. Pavesi, Silicon Photonics II: Components and Integration (Springer, 2011).
[Crossref]

Saitoh, K.

Sakoda, K.

H. Takeda and K. Sakoda, “Exciton-polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

Shih, C. T.

Sun, X.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Takamasu, T.

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

Takazawa, K.

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

K. Takazawa, “Flexibility and bending loss of waveguiding molecular fibers self-assembled from thiacyanine dye,” Chem. Phys. Lett. 452, 168–172 (2008).
[Crossref]

K. Takazawa, “Waveguiding properties of fiber-shaped aggregates self-assembled from thiacyanine dye molecules,” J. Chem. Phys. 111, 8671–8676 (2007).

Takeda, H.

H. Takeda and K. Sakoda, “Exciton-polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

Teixeira, F. L.

F. L. Teixeira and W. C. Chew, “PML-FDTD in Cylindrical and Spherical Grids,” IEEE Microw. Guid. Wave Lett. 7, 285–287 (1997).
[Crossref]

Xiao, J.

Zhang, P.

Adv. Func. Mater. (1)

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Kuroda, “Ultracompact asymmetric Mach-Zehnder interferometers with high visibility constructed from exciton polariton waveguides of organic dye nanofibers,” Adv. Func. Mater. 23, 839–845 (2013).
[Crossref]

Bell Syst. Tech. J. (1)

D. Marcuse, “Bending losses of the asymmetric slab waveguide,” Bell Syst. Tech. J. 50, 2551–2563 (1971).
[Crossref]

Chem. Phys. Lett. (1)

K. Takazawa, “Flexibility and bending loss of waveguiding molecular fibers self-assembled from thiacyanine dye,” Chem. Phys. Lett. 452, 168–172 (2008).
[Crossref]

IEEE Microw. Guid. Wave Lett. (1)

F. L. Teixeira and W. C. Chew, “PML-FDTD in Cylindrical and Spherical Grids,” IEEE Microw. Guid. Wave Lett. 7, 285–287 (1997).
[Crossref]

J. Chem. Phys. (1)

K. Takazawa, “Waveguiding properties of fiber-shaped aggregates self-assembled from thiacyanine dye molecules,” J. Chem. Phys. 111, 8671–8676 (2007).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958).
[Crossref]

Phys. Rev. B (1)

H. Takeda and K. Sakoda, “Exciton-polariton mediated light propagation in anisotropic waveguides,” Phys. Rev. B 86, 205319 (2012).
[Crossref]

Phys. Rev. Lett. (1)

K. Takazawa, J. Inoue, K. Mitsuishi, and T. Takamasu, “Fraction of a millimeter propagation of exciton polaritons in photoexcited nanofibers of organic dye,” Phys. Rev. Lett. 105, 067401 (2010).
[Crossref] [PubMed]

Other (3)

D. J. Lockwood and L. Pavesi, Silicon Photonics II: Components and Integration (Springer, 2011).
[Crossref]

R. G. Hunsperger, Integrated Optics: Theory and Technology, 6th ed. (Springer, 2009).
[Crossref]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (5)

Fig. 1
Fig. 1

(a) Top and (b) side views of a bent organic molecular-crystal nanofiber on a glass substrate in the cylindrical coordinate system. The nanofiber has w = 500 nm and h = 150 nm. The tilt angle of the transition dipole moment is α = 60°. R is the radius of curvature. (c) Configuration of the nanofiber on the glass substrate after the conformal transformation.

Fig. 2
Fig. 2

(a) Microscope image of a bent thiacyanine nanofiber, (b) the signal intensity of the scanning optical microscope along the nanofiber, and (c) experimental result of the group refractive index estimated from Fabry-Perot peaks in fluorescence emission spectra. Experimental data were provided by Takazawa [3, 5].

Fig. 3
Fig. 3

Dispersion curves of the straight organic molecular-crystal nanofiber on the glass substrate.

Fig. 4
Fig. 4

(a) Real and (b) imaginary parts of the wave number of the lowest dispersion curve as a function of the radius of curvature.

Fig. 5
Fig. 5

Leakage of light in bent organic molecular-crystal nanofibers for R = 1 μm. While Figs. (a) and (b) show |Hr(r, z)| and |Hz(r, z)| of the lowest dispersion curve, respectively, at h̄ω = 2.3 eV, Figs. (c) and (d) are for h̄ω = 2.5 eV.

Equations (22)

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ε ( ω ) = i j ε i j ( ω ) e i e j T ,
ε r r ( ω ) = ε [ 1 + 2 ω L 2 ω T 2 ω T 2 ω 2 sin 2 α ] ,
ε r ϕ ( ω ) = ε ϕ r ( ω ) = 2 ε ω L 2 ω T 2 ω T 2 ω 2 sin α cos α ,
ε ϕ ϕ ( ω ) = ε [ 1 + 2 ω L 2 ω T 2 ω T 2 ω 2 cos 2 α ] ,
ε z z ( ω ) = ε .
× [ ε 1 ( r ; ω ) × H ( r ) ] = ω 2 c 2 H ( r ) ,
H ( r ) H ( r , z ) exp ( i β R ϕ ) H r e r + H ϕ e ϕ + H z e z ,
ω 2 c 2 H r + ε z z 1 r 2 r [ r ( r H r ) r ] + z [ ε ϕ ϕ 1 H r z ] + ε z z 1 r 2 r [ r 2 H z z ] z [ ε ϕ ϕ 1 H z r ] + i β R r ( ε ϕ r 1 H z ) z z [ ε ϕ r 1 H ϕ z ] = β 2 ε z z 1 R 2 r 2 H r ,
ε r r 1 z [ ( r H r ) r r ] r r [ r ε ϕ ϕ 1 H r z ] + ω 2 c 2 H z + r r [ r ε ϕ ϕ 1 H z r ] + ε r r 1 2 H z z 2 + i β R r ε r ϕ 1 [ H r z H z r ] i β R r ( ε ϕ r 1 H z ) r + r r [ r ε ϕ r 1 H ϕ z ] = β 2 ε r r 1 R 2 r 2 H z ,
ω 2 c 2 H ϕ + r [ ε z z 1 ( r H ϕ ) r r ] + z [ ε r r 1 H ϕ z ] = z [ ε r ϕ 1 { H r z H z r } ] + i β R r [ ε z z 1 H r r ] + i β R z [ ε r r 1 H z r ] .
u = R ln ( r / R ) ,
e 2 u / R ε z z 1 ω 2 c 2 H ˜ r + 2 H ˜ r u 2 + e 2 u / R ε z z 1 z [ ε ϕ ϕ 1 H ˜ r z ] + u [ e 2 u / R H z z ] e 2 u / R ε z z 1 z [ ε ϕ ϕ 1 H z u ] + i β e 2 u / R ε z z 1 ( ε ϕ r 1 H z ) z e 2 u / R ε z z 1 z [ ε ϕ r 1 H ˜ ϕ z ] = β 2 H ˜ r ,
2 H ˜ r z u 1 ε r r 1 u [ ε ϕ ϕ 1 H ˜ r z ] + e 2 u / R ε r r 1 ω 2 c 2 H z + 1 ε r r 1 u [ ε ϕ ϕ 1 H z u ] + e 2 u / R 2 H z z 2 + i β ε r ϕ 1 ε r r 1 [ H ˜ r z H z u ] i β 1 ε r r 1 ( ε ϕ r 1 H z ) u + 1 ε r r 1 u [ ε ϕ r 1 H ˜ ϕ z ] = β 2 H z ,
ω 2 c 2 H ˜ ϕ + u [ ε z z 1 e 2 u / R H ˜ ϕ u ] + z [ ε r r 1 H ˜ ϕ z ] = z [ ε r ϕ 1 { H ˜ r z H z u } ] + i β u [ ε z z 1 e 2 u / R H ˜ r ] + i β ( ε r r 1 H z ) z ,
A r r H ˜ r + A r z H z + i β B r z H z + C r ϕ H ˜ ϕ = β 2 H ˜ r ,
A z r H ˜ r + A z z H z + i β B z r H ˜ r + i β B z z H z + C z ϕ H ˜ ϕ = β 2 H z ,
M ϕ ϕ H ˜ ϕ = D ϕ r H ˜ r + D ϕ z H z + i β G ϕ r H ˜ r + i β G ϕ z H z ,
[ A r r A r z A z r A z z ] [ H ˜ r H z ] = β 2 [ H ˜ r H z ] .
[ A r r A r z A z r A z z ] [ H ˜ r H z ] + i β [ B r r B r z B z r B z z ] [ H ˜ r H z ] = β 2 [ H ˜ r H z ] ,
[ B r r B r z A r r A r z B z r B z z A z r A z z 1 0 0 0 0 1 0 0 ] [ i β H ˜ r i β H z H ˜ r H z ] = i β [ i β H ˜ r i β H z H ˜ r H z ] .
d ξ { 1 + i σ ξ ( ξ ) ω } d ξ ,
u u + i u s u σ u ( u ) ω d u .

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