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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 16 — Aug. 7, 2006
  • pp: 6993–6998
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Dispersion shifts in optical nanowires with thin dielectric coatings

Jingyi Lou, Limin Tong, and Zhizhen Ye  »View Author Affiliations


Optics Express, Vol. 14, Issue 16, pp. 6993-6998 (2006)
http://dx.doi.org/10.1364/OE.14.006993


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Abstract

Based on exact solutions of Maxwell’s equations of a 3-layer-structured cylindrical waveguide, we calculated dispersion shifts in thin-dielectric-coated optical nanowires. Typical parameters of silica and silicon nanowires are used for numerical simulations. It shows that, the dispersion of a nanowire waveguide can be made highly sensitive to the thickness and index of the coating layer, and a thin coat may lead to considerable dispersion shift of the guided light. For example, in a 300-nm-diameter silicon nanowire, a 1% decrease in diameter of the silicon core by oxidation of silicon into silica shell leads to a 34% decrease in dispersion at 1450-nm wavelength. Results presented in this work suggest the possibility of tuning waveguide dispersions of optical nanowires by coating thin dielectric layers.

© 2006 Optical Society of America

1. Introduction

2. Mathematic model for dielectric coated nanowires

The mathematic model in our simulation is schematically illustrated in Fig. 1. A long straight nanowire with coat and air-clad is a cylindrical structure of translation symmetry involving three regions in the cross section (Fig. 1(a)): a circular dielectric core (e.g. silica or silicon nanowire) with radius ρ and a cylinder dielectric coat with thickness dc , is embedded in the infinite air cladding. Refractive indices of the core, coat and air is assumed to be ns , nc and na , respectively (Fig. 1(b)). Solving Maxwell’s equations in cylindrical coordinates (r, θ, z) leads to the following expressions for the components of the electromagnetic field for the mth mode [24

24. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

, 25

25. U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001). [CrossRef]

]:

Er=(iβkjZmj(kjr)amjmωkj2rZmj(kjr)bmj)Fm,Hr=(mnj2k02ωkj2rZmj(kjr)amj+iβkjZmj(kjr)bmj)Fm,
Eθ=(mβkj2rZmj(kjr)amjiωkjZmj(kjr)bmj)Fm,Hθ=(inj2k02ωkjZmj(kjr)amjmβkj2rZmj(kjr)bmj)Fm,
Ez=Zmj(kjr)amjFm,Hz=Zmj(kjr)bmjFm,
(1)

where the index j=s denotes the components inside the dielectric core ( r < ρ ), j=c, the cylinder coat (ρ < r < ρ + dc ), and j=a, the infinite air ( r > ρ+dc ), such that Zms (x) ≡ Jm (x), the Bessel function of order m, Zma (x) ≡ Hm(1)(x), the Hankel function of the first kind of order m, Zmc (x) ≡ c 1 jm (x) + c 2 Hm(1)(x), the linear combination of the Bessel function and the Hankel function, and the prime denotes differentiation with respect to the argument xkj∙r. β is the propagation constant and k 0 is the free space wave number: k 0=ω/c. amj and bmj are complex coefficients determined from the boundary conditions. Fm is the exponential factor,

Fm=exp(imθ+iβziωt),
(2)

and kj is the transverse wave number in the respective medium,

kj2=nj2k02β2.
(3)

By applying the boundary conditions, that the tangential components of the electromagnetic field E⃗ and H⃗ must be continuous at the inner and outer cylinder surfaces (r=ρ and r=ρ+dc ), a system of eight linear homogeneous equations is obtained that is satisfied by the eight coefficients. The system admits a nontrivial solution only in case its determinant is zero. The propagation constant β is determined by the condition that the determinant of the system of linear equations shall vanish:

det[M(β)]=0,
(4)

where M is the resulting matrix of the system of equations.

Fig. 1. Mathematic model of an optical nanowire with a cylinder coat. (a) Cross-section view and (b) refractive index profile of the nanowire.

Usually, subwavelength-diameter optical nanowires are designed and desired for working as single-mode waveguides [23

23. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

], therefore, here we consider the fundamental modes and thus set m=1 in Eqs.(1) and (2

2. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418–1432 (2000). [CrossRef]

).

With propagation constants (β) obtained by numerically solving Eq.(4), the group velocities (vg ) and waveguide dispersions (Dw ) can be obtained as [26

26. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991). [CrossRef]

]:

vg=dωdβ=2πcλ2dλdβ
(5)
Dw=d(vg1)dλ
(6)

where λ is the wavelength and c the light speed in vacuum.

For numerical simulations, we choose silica and silicon as typical moderate- and high-index materials under the following considerations: (1) silica and silicon are among the most important photonic materials within the visible and near-infrared ranges; (2) both silica and silicon nanowires have been successfully fabricated [6–8

6. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003). [CrossRef] [PubMed]

, 27–28

27. A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208–211 (1998). [CrossRef] [PubMed]

]; (3) they have typical values of moderate and high refractive indices (about 1.45 for silica and 3.4 for silicon). In addition, considering that material dispersion is usually orders of magnitude lower than waveguide dispersion in air-clad nanowire waveguides at their transparent (low-loss) spectral ranges [23

23. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

], we ignore the material dispersion of the core and coat for simplicity.

3. Dispersion shifts in silica nanowires with high-index coat

For silica nanowires with moderate refractive index around 1.45, the single-mode cut-off diameter is about 400 nm at the wavelength of 550 nm and larger thereafter [23

23. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

], therefore, we use a 400-nm-diameter silica nanowire (always single-mode when the wavelength exceeds 550 nm) as a typical situation for calculation.

Assuming the thickness (dc ) of the coat is 5 nm, calculated dispersion of a dielectric-coated 400-nm-diameter silica nanowire are shown in Fig. 2, in which 5-nm-thickness coats with indices (nc ) of 2.20 (e.g. of PbCl2) and 2.70 (e.g. of TiO2) are used. It shows that, starting from the short wavelength side, the waveguide dispersion goes through a maximum around 500-nm wavelength and a minimum around 900-nm wavelength, and then approaches zero at the IR edge. The dispersion increases with the increasing of the coat’s index before the minimum point (around 900 nm), and decreases with the increasing of the coat’s index afterward. Within the broad spectral range (e.g. from 500-nm to 1500-nm wavelength), considerable dispersion shift (compared to that of the bare nanowire) is produced by adding a thin high-index coat, and the shift increases with the index of the coating. For example, at 500-nm wavelength, dispersion of the fundamental modes of a bare 400-nm-diameter silica nanowire is about -480 ps∙nm-1∙km-1, well below the zero-dispersion level. When a 5-nm-thickness coating with index of 2.7 is added, a positive 485 ps∙nm-1∙km-1 shift is generated, which shifts the dispersion of the nanowires beyond the zero-dispersion point. Considerable dispersion shift of about 700 ps∙nm-1∙km-1 is observed within 560-800 wavelength range with a minimum (zero shift) at about 920-nm wavelength. For comparison, dispersion of a 410-nm-diameter silica nanowire (that is, a 5-nm-thickness silica coat with index of 1.45) is also provided.

Fig. 2. Modified dispersion of 400-nm-diameter silica wire with different coatings (dc =5nm). Dashed line: dispersion of 400-nm-diameter silica wire without coat.

We have also studied the dependence of dispersion shift with respect to the coat thickness. Calculated dispersions of a 400-nm-diameter silica nanowires is shown in Fig. 3(a), in which the wire is assumed to be coated with a high-index (nc =2.7) film with thickness of 2, 5, and 10 nm, respectively. It shows that, although the changes in wire diameters (due to the thin coat) are very small, the shifts in dispersion are considerably large. For example, a 2-nm-thickness coat on a 400-nm-diameter wire (that is, 1% increase in wire diameter) leads to a 415 ps∙nm-1∙km-1 shift in dispersion at 633-nm wavelength. Figure 3(b) shows the coat-thickness-dependant dispersion of a 400-nm-diameter wire at the wavelength of 633 nm. Refractive index of the coat is assumed to be 2.7. The dispersion increases continuously and smoothly with the increasing thickness of the coat, indicating the possibility for fine modification of the dispersion of a nanowire waveguide by the thickness of the coat. For comparison, dispersion shift caused by solely increasing the diameter of the same wire (that is, coating the 400-nm-diameter silica wire using silica layers with an index of 1.45) is also provided. It shows that, for dispersion modification, coating a high-index layer is much more efficient than increasing the wire diameter. For example, adding a 5-nm-thickness high-index coat leads to a dispersion shift of about 950 ps∙nm-1∙km-1, whereas increasing the diameter to the same thickness brings a dispersion shift of only 250 ps∙nm-1∙km-1.

Fig. 3. (a) Modified dispersion of a 400-nm-diameter silica wire with different coating thickness. (b) Coat-thickness-dependent dispersion of a 400-nm-diameter silica wire at the wavelength of 633 nm. Refractive indices of the coats are assumed to be 2.7 and 1.45, respectively.

4. Dispersion shifts in silicon nanowires with low-index silica coat

For silicon nanowires with short-wavelength absorption edge at 1200 nm and a notable high index of about 3.4, the single-mode cut-off diameter is about 350 nm at 1550-nm wavelength [23

23. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

]. Therefore, here we use a 300-nm-diameter silicon nanowire for the simulation.

Generally, silicon nanowires are likely to be oxidized in the synthesis or exposed in air afterwards [27

27. A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208–211 (1998). [CrossRef] [PubMed]

, 28

28. J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, “Study on thermal oxidation of Si nanowires,” Phys. Stat. Sol. A 168, 441–446 (1998). [CrossRef]

], resulting in silicon oxides shell with thickness up to tens of nanometers. For simplicity, here we use SiO2 (e.g. silica ), the dioxide (also the stable oxide) of silicon as a low-index (1.45 v.s. 3.4) coat.

When the oxidized coat is thin (compares with the thickness of the silicon core), the thickness of the SiO2 coat (dc ) can be obtained as

dc=dSiρSiMSiO2ρSiO2MSi
(7)

where dSi is the thickness reduction of the silicon core, ρSi =2.35g/cm3 and ρSiO2 = 2.2g/cm3 are densities of Si and SiO2 [27

27. A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208–211 (1998). [CrossRef] [PubMed]

], MSi =28.1 and MSiO2 =60.1 are molecular mass of Si and SiO2, respectively.

Calculated dispersions of SiO2-coated silicon nanowires are shown in Fig. 4. The nanowires, with different-thickness SiO2 layers, are assumed to be oxidized from the same pure silicon nanowire with a diameter of 300 nm. The simulation covers the overlapping area of transparent spectral ranges of silicon and silica (Fig. 4(a)). The thickness reduction of the silicon core is assumed to be 1, 2, 5 and 10 nm, corresponding to 2.3, 4.6, 11.4 and 22.8 nm thickness of SiO2 coat, respectively. As shown in Fig. 4(a), large dispersion shift is generated with a very thin layer of oxidation and the dispersion shift increases with the thickness of the coat (silica layer). For example, at 1450-nm wavelength, a 1% decrease in the diameter of silicon nanowire (by oxidization of silicon into SiO2 shell) lead to a 6849 ps∙nm-1∙km-1 dispersion shift (that is 34% decrease). Fig. 4(b) gives the oxidization-induced dispersion shift with respect to the reduction in silicon core at 1450-nm wavelength. The dispersion decreases smoothly and almost linearly with the thickness reduction of the silicon core. Practically, oxidization of silicon nanowires can be well controlled by environmental conditions such as temperature and reaction time [28

28. J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, “Study on thermal oxidation of Si nanowires,” Phys. Stat. Sol. A 168, 441–446 (1998). [CrossRef]

], therefore, shifting waveguide dispersion of a silicon nanowire by oxidization may be a feasible and efficient way.

Fig. 4. (a) Modified dispersion of 300-nm-diameter silicon wire with thickness reduction in silicon core by oxidization. (b) Thickness-reduction-dependent dispersion of a 300-nm-diameter silicon nanowire at the wavelength of 1450 nm.

5. Conclusion

In conclusion, using a 3-layer-structured cylindrical waveguide model, we’ve numerically investigated dispersion shifts in dielectric-coated silica and silicon nanowires. It shows that, with a thin dielectric coat, considerable dispersion shift of the guided light can be obtained. Since the thickness of the coat is much smaller than the diameter of the nanowires, the coat does not obviously change the geometric dimension and single-mode condition of the nanowire waveguide. In addition, the dielectric coat used in this work is non-dissipative and commonly available, making it simple for both theoretical modeling and experimental implementation.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 60425517, 60578061 and 60378036).

References and links

1.

P. P. Bishnu, Fundamentals of Fibre Optics in Telecommunication and Sensor Systems (John Wiley & Sons, New York, 1993).

2.

B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418–1432 (2000). [CrossRef]

3.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 2001).

4.

M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004). [CrossRef] [PubMed]

5.

J. N. Kutz, C. Lyngå, and B. J. Eggleton, “Enhanced Supercontinuum Generation through Dispersion-Management,” Opt. Express 13, 3989–3998 (2005). [CrossRef] [PubMed]

6.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003). [CrossRef] [PubMed]

7.

G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12, 2258–2263 (2004). [CrossRef] [PubMed]

8.

S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004). [CrossRef] [PubMed]

9.

Y. K. Lize, E. C. Magi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004). [CrossRef] [PubMed]

10.

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. Yang, “Nanoribbon waveguides for subwavelength photonics integration,” Science 305, 1269–1273 (2004). [CrossRef] [PubMed]

11.

J. Bures and R. Ghosh, “Power density of the evanescent field in the vicinity of a tapered fiber,” J. Opt. Soc. Am. A 16, 1992–1996 (1999). [CrossRef]

12.

M. Sumetsky, Y. Dulashko, and A. Hale, “Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer,” Opt. Express 12, 3521–3531 (2004). [CrossRef] [PubMed]

13.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004). [CrossRef]

14.

F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 063403 (2004). [CrossRef]

15.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, “Nanowire photonic circuit elements,” Nano Lett. 4, 1981–1985 (2004). [CrossRef]

16.

A. Zheltikov, “Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibers and photonic wires,” J. Opt. Soc. Am. B 22, 1100–1104 (2005). [CrossRef]

17.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, “Compound-glass optical nanowires,” Electron. Lett. 41, 400–402 (2005). [CrossRef]

18.

L. M. Tong, J. Y. Lou, R. R. Gattass, S. L. He, X. W. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5, 259–262 (2005). [CrossRef] [PubMed]

19.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86, 161108 (2005). [CrossRef]

20.

J. Y. Lou, L. M. Tong, and Z. Z. Ye, “Modeling of silica nanowires for optical sensing,” Opt. Express 13, 2135–2140 (2005). [CrossRef] [PubMed]

21.

P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, “Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels,” Opt. Lett. 30, 1273–1275 (2005). [CrossRef] [PubMed]

22.

J. Villatoro and D. Monzón-Hernández, “Fast detection of hydrogen with nano fiber tapers coated with ultra thin palladium layers,” Opt. Express 13, 5087–5092 (2005). [CrossRef] [PubMed]

23.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

24.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

25.

U. Schroter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B 64, 125420 (2001). [CrossRef]

26.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991). [CrossRef]

27.

A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208–211 (1998). [CrossRef] [PubMed]

28.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, “Study on thermal oxidation of Si nanowires,” Phys. Stat. Sol. A 168, 441–446 (1998). [CrossRef]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.2400) Fiber optics and optical communications : Fiber properties
(260.2030) Physical optics : Dispersion
(310.6860) Thin films : Thin films, optical properties

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 7, 2006
Revised Manuscript: July 11, 2006
Manuscript Accepted: July 16, 2006
Published: August 7, 2006

Citation
Jingyi Lou, Limin Tong, and Zhizhen Ye, "Dispersion shifts in optical nanowires with thin dielectric coatings," Opt. Express 14, 6993-6998 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-16-6993


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References

  1. P. P. Bishnu, Fundamentals of Fibre Optics in Telecommunication and Sensor Systems (John Wiley & Sons, New York, 1993).
  2. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, "Integrated tunable fiber gratings for dispersion management in high-bit rate systems," J. Lightwave Technol. 18, 1418-1432 (2000). [CrossRef]
  3. G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 2001).
  4. M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12, 2880-2887 (2004). [CrossRef] [PubMed]
  5. J. N. Kutz, C. Lyngå, and B. J. Eggleton, "Enhanced Supercontinuum Generation through Dispersion-Management," Opt. Express 13, 3989-3998 (2005). [CrossRef] [PubMed]
  6. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003). [CrossRef] [PubMed]
  7. G. Brambilla, V. Finazzi, and D. J. Richardson, "Ultra-low-loss optical fiber nanotapers," Opt. Express 12, 2258-2263 (2004). [CrossRef] [PubMed]
  8. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, "Supercontinuum generation in submicron fibre waveguides," Opt. Express 12, 2864-2869 (2004). [CrossRef] [PubMed]
  9. Y. K. Lize, E. C. Magi, V. G. Ta'eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, "Microstructured optical fiber photonic wires with subwavelength core diameter," Opt. Express 12, 3209-3217 (2004). [CrossRef] [PubMed]
  10. M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. Yang, "Nanoribbon waveguides for subwavelength photonics integration," Science 305, 1269-1273 (2004). [CrossRef] [PubMed]
  11. J. Bures and R. Ghosh, "Power density of the evanescent field in the vicinity of a tapered fiber," J. Opt. Soc. Am. A 16, 1992-1996 (1999). [CrossRef]
  12. M. Sumetsky, Y. Dulashko, and A. Hale, "Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer," Opt. Express 12, 3521-3531 (2004). [CrossRef] [PubMed]
  13. V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004). [CrossRef]
  14. F. Le Kien, V. I. Balykin, and K. Hakuta, "Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber," Phys. Rev. A 70, 063403 (2004). [CrossRef]
  15. C. J. Barrelet, A. B. Greytak, and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004). [CrossRef]
  16. A. Zheltikov, "Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibers and photonic wires," J. Opt. Soc. Am. B 22, 1100-1104 (2005). [CrossRef]
  17. G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires," Electron. Lett. 41, 400-402 (2005). [CrossRef]
  18. L. M. Tong, J. Y. Lou, R. R. Gattass, S. L. He, X. W. Chen, L. Liu, and E. Mazur, "Assembly of silica nanowires on silica aerogels for microphotonic devices," Nano Lett. 5, 259-262 (2005). [CrossRef] [PubMed]
  19. M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, "Optical microfiber loop resonator," Appl. Phys. Lett. 86, 161108 (2005). [CrossRef]
  20. J. Y. Lou, L. M. Tong, Z. Z. Ye, "Modeling of silica nanowires for optical sensing," Opt. Express 13, 2135-2140 (2005). [CrossRef] [PubMed]
  21. P. Polynkin, A. Polynkin, N. Peyghambarian, and M. Mansuripur, "Evanescent field-based optical fiber sensing device for measuring the refractive index of liquids in microfluidic channels," Opt. Lett. 30, 1273-1275 (2005). [CrossRef] [PubMed]
  22. J. Villatoro, and D. Monzón-Hernández, "Fast detection of hydrogen with nano fiber tapers coated with ultra thin palladium layers," Opt. Express 13, 5087-5092 (2005). [CrossRef] [PubMed]
  23. L. M. Tong, J. Y. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004). [CrossRef] [PubMed]
  24. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  25. U. Schroter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001). [CrossRef]
  26. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991). [CrossRef]
  27. A. M. Morales and C. M. Lieber, "A laser ablation method for the synthesis of crystalline semiconductor nanowires," Science 279, 208-211 (1998). [CrossRef] [PubMed]
  28. J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998). [CrossRef]

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