## Evolution of modes in a metal-coated nano-fiber |

Optics Express, Vol. 19, Issue 25, pp. 25206-25221 (2011)

http://dx.doi.org/10.1364/OE.19.025206

Acrobat PDF (3100 KB)

### Abstract

We report on the evolution of modes in cylindrical metal/dielectric systems. The transition between surface plasmon polaritons and localized modes is documented in terms of the real and imaginary parts of the effective refractive index as a function of geometric and optical parameters. We show the evolution process of SPP and localized modes. New phenomena of coupling between SPP and core-like modes, and of mode gap and super-long surface plasmon polaritons are found and discussed. We conclude that both superluminal light and slow light can be solutions of metallically coated dielectric fibers.

© 2011 OSA

## 1. Introduction

1. Y. Peng, X. Wang, and K. Kempa, “TEM-like optical mode of a coaxial nanowaveguide,” Opt. Express **16**(3), 1758–1763 (2008). [CrossRef] [PubMed]

5. U. Langbein, U. Trutschel, A. Unger, and M. Duguay, “Rigorous mode solver for multilayer cylindrical waveguide structures using constraints optimization,” Opt. Quantum Electron. **41**(4), 223–233 (2009). [CrossRef]

6. Y. Saito and P. Verma, “Imaging and spectroscopy through plasmonic nano-probe,” Eur. Phys. J. Appl. Phys. **46**(2), 20101 (2009). [CrossRef]

7. F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett. **8**(8), 2321–2327 (2008). [CrossRef] [PubMed]

9. F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. **5**(1), 67–72 (2010). [CrossRef] [PubMed]

10. A. Shinya, S. Mitsugi, E. Kuramochi, and M. Notomi, “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide,” Opt. Express **13**(11), 4202–4209 (2005). [CrossRef] [PubMed]

13. G. Ouyang, Y. Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express **10**(17), 899–908 (2002). [PubMed]

14. T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. Features of surface plasmon polaritons,” Phys. Rev. B **64**(4), 045117**(**2001). [CrossRef]

15. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B **62**(23), 15299–15302 (2000). [CrossRef]

16. L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **50**(5), 4094–4106 (1994). [CrossRef] [PubMed]

*mode-gap*(interspace cut-off) is observed. In these regions the existence of any kind of mode is forbidden. The model we consider is an ideal infinitely long dielectric/metal/dielectric submicron-fiber. Both the metallic and the dielectric parts are treated with a dispersion approach. In particular, in section 2, we will introduce the numerical method utilized for the present analysis. In section 3 we will discuss the dependence of the eigenmodes on the wavelength, radius, metal thickness, and background refractive index. Furthermore, we will discuss the coupling mechanisms between SPP- and core-like modes. In section 4, we will analyze the existence of virtually loss-free eigenmodes, named super-long SPP (SLSPP). In section 5, we shall report on the group velocity of the modes, and we will show the conditions for sub-luminal and super-luminal light speed. Finally, in section 6, we will give our conclusions.

## 2. Localized modes in submicron-fibers: numerical method

### 2.1 Determination of fiber modes

^{th}layer corresponds to the background media. In this model, any layer may show absorption, such as metal or some active media. Cylindrical coordinates are chosen in order to study the structure.

*z*of the electric- and magnetic- fields,

*e*and

_{z}*h*. They are expressed in Eq. (1) by means of the separation of variables method. In particular, the radial (ρ), azimuthal (φ) and axial (z) contribute are shown:

_{z}*ω*is the angular frequency,

*k*

_{0}is the wave number in vacuum and

*μ*

_{0}is the permeability in free space. Furthermore,

*j*denotes the

*j*

^{th}concentric layer and

*m*is an integer which represents the order in the azimuthal coordinate (associated to the angle

*φ*). Generally, the solutions include the guided (localized) modes and radiation modes.

*l*is for extinguishing every solution. It depends on azimuthal order

*m*. However, in this paper, we are focusing on the localized individual eigenmodes. For simplified expression, we ignore

*l*in following discussion. The contribute

*z*direction with an effective refractive index given by

*n*Its value is complex if any of the layers possess absorptive characteristics. It is important to notice that

_{m,z}.*n*is layer independent, namely it does not depend on the parameter

_{m,z}*j*. The relation relating the transversal and axial (z-axis) effective index is shown in Eq. (3), where

*ε*

^{(}

^{j}^{)}and

*μ*

^{(}

^{j}^{)}are the relative permittivity and permeability of the

*j*layer, respectively . Because

^{th}*n*is a complex quantity, this relation implies

_{m,z}*n*to be complex, too:

_{m,t}*m*-order Bessel functions

*H*(specifically Hankel functions, superscript (1) and (2) denote first and second kind of Hankel function.), as in Eq. (2).

_{m}**A**and

**B**are coefficients of the form

**A**= (

*a*,

_{1}*a*)

_{2}*,*

^{T}**B**= (

*b*,

_{1}*b*)

_{2}*, respectively. From the components along*

^{T}*z*of the electric and magnetic field, we can calculate their radial and azimuthal components. The procedure is shown in Eqs. (4) and (5) [17]:

**M**is a 4 by 4 matrix with 4 matrix components

**M**

_{α,β}.

**M**

_{α,β}is a 2 by 2 matrix. α and β denote 1 or 2.

*j*and

*j*+ 1 are variable parameters in matrix

**M**denote

*j*

^{th}and (

*j*+ 1)

^{th}layers. Sub-elements matrix

**M**

_{α,β}can be described as where

*q*and

*p*replace

*j*(or

*j*+ 1) as first and second variable parameters in matrix

**M.**. The

*p*-layer and

**I**is 2 by 2 unit matrix.

*j*

^{th}and (

*j*+ 1)

^{th}layer. By applying this approach to all the layers, we can obtain the total transition matrix as in Eq. (8):

*n*. Finally, we can determine the spatial distributions of the electromagnetic field.

_{m,z}*n*in a two dimensional complex plane, then solve Eq. (11), and find

_{m,z}*n*to minimize the left side of Eq. (11) close to zero. Reduce search area around this value, and repeat searching until it meets the accuracy requirement.

_{m,z}*m*= 1 for example, and ignore the m in following discussion, unless otherwise specified.

### 2.2 Materials modeling

_{2}, silver, and air is used to define a metallic fiber. We assume that both SiO

_{2}and Ag are dispersive media. We use the Sellmeier formulation to define the dielectric constant of SiO

_{2}[18

18. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. **55**(10), 1205–1209 (1965). [CrossRef]

## 3. Modes evolution

*m*= 1, since it represents the symmetry of single mode fibers.

### 3.1 Wavelength dependence

*n*associated to different modes are shown in Figs. 3A , 3B and 3C. In all cases the real part decreases by increasing the wavelength. The refractive index of core SiO

_{z}_{2}is drawn in Fig. 3A (dashed line). The colors denote different modes, each associated to a different radial number. The order mode increases scrolling the figures from right to left. For the type-A structure, when the wavelength is shorter than 0.693μm, the real part of

*n*associated to the fundamental mode (blue line) is bigger than the refractive index of silica. The mode is then an internal surface plasmon mode. The maximum light field is located at the interface between metal and SiO

_{z}_{2}. On the other hand, the minimum in intensity is at the center of the dielectric core. z direction Poynting vector is chosen for showing intensity distributions. Poynting vector is defined as

**S**= 0.5Re(

**E**×

**H***). This is clearly shown in Fig. 4(a) where λ = 0.5 μm has been chosen. A phenomenological explanation rises from considering that the effective refractive index of the fundamental mode is higher than SiO

_{2}. The field is then pushed out from the dielectric core towards its own edges, resulting in an internal-like SPP mode. Figure 3A also shows no intersections among the modes in the graph associated to the real part of the refractive index, intersections otherwise present in the imaginary part index. With wavelength increasing, the inner SPP mode, two segments will extend to center. Finally, fundamental mode becomes a localized mode, with maximum intensity of the field at the center of the dielectric core. No SPP features are present any longer, as is shown in Fig. 4(b). Similarly, the higher order modes have an effective refractive index always below SiO

_{2}, which localizes them mainly in the core for any considered wavelength.

*n*) decreases, which is opposite to the behavior showed by the imaginary part of the refractive index of Silver bulk, as shown in Eq. (13). It implies that this kind of mode tends to propagate along the cylinder for longer distances by increasing the wavelength (the same happens for flat metal/dielectric interfaces). This is physically supported by the fact that the refractive index of the mode tends to the unity (the refractive index of the surrounding medium), as graphically shown in Fig. 4(c). This mode, being then SPP-like, travels mostly in the dielectric which dramatically reduces its absorption.

_{z}*cut*the dispersion relation of the type-A structure. The intersection points correspond to two-modes overlapping spots. In the wavelength region close to 1.917 μm, the external SPP mode (green line) crosses the fundamental internally localized mode (blue line). However, the two modes are not degenerative because of the strong difference in the imaginary parts of the refractive indexes. This determines almost no change in the behavior of the fundamental mode when compared to the type-A structure, namely the mode maintains a core localized distribution. On the other hand, if we look at the first excited mode (green line) around λ = 1.917 μm, the mode evolves quickly from an external SPP-like shape to internal-core like to retake, for λ bigger than 1.917 μm, the external SPP-like form. The different behavior between the fundamental (blue line) and first excited mode (green line) can be well explained looking at the imaginary part of the effective refractive index as in Fig. 3C. In fact, around the critical value of λ = 1.917 μm, the fundamental mode does not show almost any change while the first excited mode presents a strong Fano oscillation which is associated to an increase of loss. Physically this corresponds to the shift of the field distribution from the external dielectric region (air) to the internal one (SiO

_{2}), that is the mode is no longer a SPP-like but core-like. Finally we notice that by increasing the wavelengths the loss tends to increase for the core modes. On the other hand, both the internal (type-A) and external (type-B) SPP modes show a strong decrease of the loss by increasing the wavelength. This will play an important role when later on we will discuss the super-long range SPP.

*z*component for the third dispersion line (red line) of the type-C structure as in Fig. 3C. Clearly the mode starts with a core-like distribution, to evolve into an external SPP-like shape at around 640 nm, to retake a core-like form around 930 nm. This swinging between SPP and core modes is due to external SPP mode and core-like mode coupled together. Original crossing dispersion relation curve, crossing point be split as two. Media 1 display the modes evolution process from core-like shape to external SPP-like shape, and tune back core-like shape again, with increasing wavelength.

*n*= 0, whereas the latter show no similar cut-off. Indeed, as shown in Figs. 3A and 3C, when the real part of

_{z}*n*is close to 0, the dispersion curves suddenly tend to longer wavelengths and the associated modes show a core-like shape. When this happens, we observe a marked increase of the mode attenuation, associated to a sudden increase of the imaginary part of the refractive index.

_{z}### 3.2 Core radius dependence

_{c}, respectively. Once again, an external SPP curve

*cuts*the internal modes. External SPP can then be seen as bridges connecting two different internal modes. When R

_{c}reaches zero, which means to fall in the type-B structure, only one mode survives (green line) similarly to Fig. 3B. As general behavior, the loss decreases with increasing the radius of core. However, for SPP the loss is small even at small radius. Let us focus on the red line. Figures 6(c) and 6(d) show a gap-mode for R

_{c}just above 0.86 μm. In fact, for these values of the core radius, the imaginary part of

*n*is not defined. This phenomenon was recently reported for planar structures [19

_{z}19. R. Adato and J. Guo, “Characteristics of ultra-long range surface plasmon waves at optical frequencies,” Opt. Express **15**(8), 5008–5017 (2007). [CrossRef] [PubMed]

20. X. L. Zhang, J. F. Song, G. Q. Lo, and D. L. Kwong, “The observation of super-long range surface plasmon polaritons modes and its application as sensory devices,” Opt. Express **18**(21), 22462–22470 (2010). [CrossRef] [PubMed]

*n*tends to values very close to 0. This result, which physically means no-loss eigenmodes, might sounds quite interesting considering that we are dealing with absorptive materials such as metals. From a mathematical point view it corresponds to a real solution of a more general complex matrix. In section 4 we shall refer to these kinds of modes as super-long SPP.

_{z}### 3.3 Dependence on thickness of the metal cladding layer

*h*of the silver cladding layer reaches zero, the structure becomes a conventional dielectric nano-fiber. Here we introduce the propagation length

*L*

_{τ}= 1/2

*k*

_{0}Im(

*n*), as shown in Fig. 7(b) . It represents the distance covered by the light before decaying to 1/

_{z}*e*(~4.34 dB) of its initial value.

_{2}. This implies that the mode is formed by a combination of intra- and extra-SPP contributes. In particular, these terms will exist mainly close to the metal interfaces due to the high effective refractive index induced optical filed fast decay from interface, in both side of core- and cladding- layers. By increasing the thickness h, we observe a reduction of the mode index, which reaches the constant value of 1 (the refractive index of the background) at around 10 nm. Of the two initial internal and external contributes to the field, only the external SPP is left, as shown in Figs. 8(a) and (b) . Media 3 displays the modes evolution process.

*h*= 3.5 nm and

*h*= 19.1 nm, when the SiO

_{2}core is equal to 0.30 μm. The effective index is from 1.0236 (

*h*= 0 nm) to the background index (

*h*= 3.5 nm; see the inset in Fig. 7(a)). Figures 8(c) and 8(d) show the field profile at the edges of the gap-mode. For

*h*= 2 nm, the mode is a combination of external SPP and core contributes. For

*h*= 30 nm, the SPP part disappears and the mode covers the core area, which is consistent with the reduction of the effective refractive index

*n*.

_{z}*h*= 50 nm at which point it starts decreasing, whereas the blue line shows three steps: a U-like shape as in Fig. 7(c) for the first few nanometers, then a fast decrease and finally a constant value is reached. The most important information raising from

*L*

_{τ}are its high values at the edges of the gap. This, once again, seems to lead to the possibility of having modes which can virtually travel indefinitely in space.

_{2}core is changed to

*R*= 0.5 μm, the situation is described by Fig. 9 . In this case no gap-mode is found. SPP and core-like modes are shown in green and blue, respectively. The SPP mode tends to Re(

_{c}*n*) = 1, namely the field is found on the background material. This is demonstrated in Fig. 10(a) . The real part of

_{z}*n*for the core-like mode is higher than the SPP mode, which is the opposite of the situation described in Fig. 7. This general behavior is well consistent with Fig. 6(a). From Figs. 7(b) and 9(b) we can see that the external SPP show lower transmission loss in submicron structures than the core-like modes.

_{z}### 3.4 Dependence on the background index

*R*= 0.30 and 0.50 μm. Furthermore, we have chosen the wavelength λ = 1.55 μm and the metal ring thickness

_{c}*h*= 50 nm. In Fig. 11 the radius

*R*= 0.30 μm is considered. We see that both Re(

_{c}*n*) and Im(

_{z}*n*) for external SPP (green line) increase with the refractive index of the background (

_{z}*n*). This phenomenon can be explained by considering the model of a simple planar surface plasmonic mode. In fact, for planar metal/dielectric SPP, the propagation index is described in Eq. (14). For the specific case of silver at wavelength λ = 1.55 μm, Eq. (14) is reduced to the expression described in Eq. (15). The real part of

_{b}*n*approaches a linear function of

_{z}*n*, whereas the imaginary part of

_{b}*n*shows a cubic dependence on

_{z}*n*:

_{b}*n*) for the core-like mode (blue line) shows very little dependence of the background refractive index. It looks like the metal layer is shielding the core from external effects. However the Im(

_{z}*n*) shows a slight decrease by increasing

_{z}*n*.

_{b}*R*= 0.50 μm instead of 0.30 μm. We can observe that for low

_{c}*n*the modes in the two figures have opposite behavior. In Fig. 11 no intersections are found between the external SPP mode (green line) and the core-like mode (blue line). Furthermore, Re(

_{b}*n*) of the SPP mode is always higher than that of the core-like mode. In Fig. 12 the situation is quite different. In fact, for low

_{z}*n*, we can observe an higher value of Re(

_{b}*n*) for the core-like mode with a close-to-crossing point at

_{z}*n*~1.2. At this value of the refractive index the two modes exchange their own nature. The core-like one takes a SPP form and the SPP mode turns in core-like mode. The meaning associated to the lines is then opposite on the right and left side of the crossing point

_{b}*n*~1.2. Hence, the blue line is core-like mode on the left side and SPP on the right side (similarly the green line). What happens at the crossing point is a conversion of the two modes. This is possible because at such a value of

_{b}*n*the two modes show the same value both for Re(

_{b}*n*) and Im(

_{z}*n*). This phenomenon was already observed in Figs. 3 and 6. This shows that

_{z}*n*has a similar effect as λ,

_{b}*h*or

*R*: in fact, by changing either these parameters we can have a SPP-to-core mode conversion.

_{c}## 4. Super-long SPP modes and gap-mode region

*n*was very close to zero, such as edge of gap-mode in Figs. 6(d) and 7(b). This means a very long propagation length, namely a loss-free fiber. To explain the origin of this gap we have to recall section 2.1, where we mentioned that in the background (last layer

_{m,z}*N*) the quantity Im(

*n*)→0, then Im(

_{m,z}*n*) = 0 is un-physical, but at least it can be approached. And it may offer a method for achieve lower loss SPP waveguide. From Fig. 6(d) and Fig. 7(b) we see that the gap regions are dependent on both the radius of core and the thickness of the silver cladding layer. Figure 13(a) summarizes this relation, and Fig. 13(b) shows

_{m,z}*n*(m = 1) versus thickness of the silver ring

_{m,z}*h*(similarly to Fig. 7). The wavelength is taken equal to 1.55 μm.

*m*= 1, the latter to

*m*= −1 (as clearly seen by comparing Figs. 14(b) and 15(b)). In both graphs (a) and (b) correspond to the blue circle of Fig. 13 (similarly, (c) and (d) correspond to the red circle). The silver thickness is fixed at

*h*= 0.30 μm. Even though no SPP modes are observed in Fig. 13, which induces the definition of core-like modes for the Fig. 13, we can see from Figs. 14 and 15 that some of the modes tend to extend far away from the core (see Fig. 14(b) or Fig. 15(b)). This behavior could result useful when light wave transmission is an issue, keeping however in mind that a very strong and sensitive dependence on

*h*and

*R*is inherent to these modes.

_{c}## 5. Subluminal and superluminal light speed

*group*refractive index by considering the dispersion of phase refractive index:Where

*n*is phase refractive index and equal to Re(

_{p}*n*). mode has different group velocity, thus it will induce the mode dispersion. Three kinds of dispersion relations in Fig. 3C are discussed. In Fig. 16 the graphs (a), (b) and (c) correspond to the blue, green and red line in Fig. 3C, respectively. In Fig. 16(a) the maximum value for the group index

_{z}*n*is close to 18 namely subluminal light speed. This value is found at λ~2.6 μm, which is associated to the flattening of the effective refractive index in the region Re(

_{g}*n*) close to 0. Moving up in wavelength we observe a decrease of

_{z}*n*to values below 1, and the opposite situation to the previous case occur, that is superluminal light speed. At λ~1.93 μm we observe a Fano-like shape, as shown in the inset of Fig. 16(a). This describes the external-SPP mode coupling with internal core-like mode.

_{g}*n*is found at the transition point between core-like and SPP mode. Consistently with Fig. 16(a), in the crossing point of SPP and core-like mode, the

_{g}*n*shows a ripple.

_{g}*n*can achieve as big as 20. At the coupling region, no strong Fano-like peaks are found, but instead by two of steps. They are at λ~0.65 μm and λ~0.93 μm.

_{g}## 6. Conclusion

*h*,

*R*or

_{c}*n*has been demonstrated. We displayed the modes evolutions. Furthermore, we have reported on the existence of modes gap. These gaps have shown strong dependence on some geometrical parameters such as

_{b}*R*and

_{c}*h*. Their edges are characterized by showing extremely low loss which, according to the mode kind (core-like or SPP) originates

*no-loss*or

*super-long*surface plasmon polaritons. Finally, by investigating the wavelength dependence of the group velocity, both superluminal and subluminal regions were identified.

## Acknowledgments

## References and links

1. | Y. Peng, X. Wang, and K. Kempa, “TEM-like optical mode of a coaxial nanowaveguide,” Opt. Express |

2. | J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. |

3. | A. S. Lapchuk, D. Shin, H. S. Jeong, C. S. Kyong, and D. I. Shin, “Mode propagation in optical nanowaveguides with dielectric cores and surrounding metal layers,” Appl. Opt. |

4. | U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B |

5. | U. Langbein, U. Trutschel, A. Unger, and M. Duguay, “Rigorous mode solver for multilayer cylindrical waveguide structures using constraints optimization,” Opt. Quantum Electron. |

6. | Y. Saito and P. Verma, “Imaging and spectroscopy through plasmonic nano-probe,” Eur. Phys. J. Appl. Phys. |

7. | F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett. |

8. | A. K. Sharma and B. D. Gupta, “Comparison of performance parameters of conventional and nano-plasmonic fiber optic sensors,” Plasmonics |

9. | F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. |

10. | A. Shinya, S. Mitsugi, E. Kuramochi, and M. Notomi, “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide,” Opt. Express |

11. | H. Zhao, R. P. Zaccaria, P. Verma, J. F. Song, and H. B. Sun, “Validity of the V parameter for photonic quasi-crystal fibers,” Opt. Lett. |

12. | P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. |

13. | G. Ouyang, Y. Xu, and A. Yariv, “Theoretical study on dispersion compensation in air-core Bragg fibers,” Opt. Express |

14. | T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. Features of surface plasmon polaritons,” Phys. Rev. B |

15. | I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B |

16. | L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

17. | J. A. Buck, |

18. | I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. |

19. | R. Adato and J. Guo, “Characteristics of ultra-long range surface plasmon waves at optical frequencies,” Opt. Express |

20. | X. L. Zhang, J. F. Song, G. Q. Lo, and D. L. Kwong, “The observation of super-long range surface plasmon polaritons modes and its application as sensory devices,” Opt. Express |

**OCIS Codes**

(060.2400) Fiber optics and optical communications : Fiber properties

(130.2790) Integrated optics : Guided waves

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 18, 2011

Revised Manuscript: October 22, 2011

Manuscript Accepted: October 25, 2011

Published: November 23, 2011

**Citation**

Junfeng Song, Remo Proietti Zaccaria, Guancai Dong, Enzo Di Fabrizio, M. B. Yu, and G. Q. Lo, "Evolution of modes in a metal-coated nano-fiber," Opt. Express **19**, 25206-25221 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25206

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### References

- Y. Peng, X. Wang, and K. Kempa, “TEM-like optical mode of a coaxial nanowaveguide,” Opt. Express16(3), 1758–1763 (2008). [CrossRef] [PubMed]
- J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett.22(7), 475–477 (1997). [CrossRef] [PubMed]
- A. S. Lapchuk, D. Shin, H. S. Jeong, C. S. Kyong, and D. I. Shin, “Mode propagation in optical nanowaveguides with dielectric cores and surrounding metal layers,” Appl. Opt.44(35), 7522–7531 (2005). [CrossRef] [PubMed]
- U. Schröter and A. Dereux, “Surface plasmon polaritons on metal cylinders with dielectric core,” Phys. Rev. B64(12), 125420 (2001). [CrossRef]
- U. Langbein, U. Trutschel, A. Unger, and M. Duguay, “Rigorous mode solver for multilayer cylindrical waveguide structures using constraints optimization,” Opt. Quantum Electron.41(4), 223–233 (2009). [CrossRef]
- Y. Saito and P. Verma, “Imaging and spectroscopy through plasmonic nano-probe,” Eur. Phys. J. Appl. Phys.46(2), 20101 (2009). [CrossRef]
- F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008). [CrossRef] [PubMed]
- A. K. Sharma and B. D. Gupta, “Comparison of performance parameters of conventional and nano-plasmonic fiber optic sensors,” Plasmonics2(2), 51–54 (2007). [CrossRef]
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