Abstract

We analyze the modal attenuation properties of silica hollow-core fibers with a gold-wire based indefinite metamaterial cladding at 10.6 µm. We find that by varying the metamaterial feature sizes and core diameter, the loss discrimination can be tailored such that either the HE11, TE01 or TM01 mode has the lowest loss, which is particularly difficult to achieve for the radially polarized mode in commonly used hollow-core fibers. Furthermore, it is possible to tailor the HE11 and TM01 modes in the metamaterial-clad waveguide so that they possess attenuations lower than in hollow tubes composed of the individual constituent materials. We show that S-parameter retrieval techniques in combination with an anisotropic dispersion equation can be used to predict the loss discrimination properties of such fibers. These results pave the way for the design of metamaterial hollow-core fibers with novel guidance properties, in particular for applications demanding cylindrically polarized modes.

© 2016 Optical Society of America

1. Introduction

Hybrid optical fibers, sometimes called multi-material fibers, incorporate novel materials such as semiconductors and metals and enable the integration of sophisticated photonic and electrical functionality directly into the optical fibers [1, 2], thus enhancing the performance of fibers beyond light guidance. If the included structures have (at least in one dimension) feature sizes much smaller than the operating wavelength, an effective medium, or metamaterial (MM) is formed, which can possess vastly different optical properties to that of the individual constituent materials [3]. In the case of dense arrays of subwavelength-size metallic wires [4], fiber-based MMs can form indefinite metamaterials (iMMs) [5], i.e., effective anisotropic materials in which the tangential and longitudinal components of their permittivity tensor do not possess the same signs. Currently, metal nano- and micro-wires are routinely integrated into optical fibers (e.g., gold or gold-based alloys in silica [6,7], or indium in polymer [8]) either by direct-drawing [9,10] or post-processing [11,12]. By tuning the sizes of these subwavelength features, it is possible to reach optical properties beyond that of conventional step index fibers. In recent years, a number of groups have investigated fiber-based MMs [8,10,13–16], which can exhibit either negative electric permittivity with sub-wavelength metallic wires [8,10] or negative magnetic permeability via slotted-cylinder metallic resonators [17–19] with practical applications ranging from sub-wavelength terahertz imaging [20] to low-loss waveguiding in the infrared [14].

The dispersion equations and guidance conditions of hollow (air) core fibers with iMM cladding have recently been derived [21,22], showing that sub-wavelength guidance within the THz and GHz domain is possible [23]. The analysis considered core sizes comparable to (and smaller than) the operation wavelength neglecting material losses, which, however, strongly influence the modal attenuation and discrimination [24]. No explicit comparison to realistic structures containing discrete sub-wavelength units (or âǍIJmeta-atomsâǍİ), such as wires and split resonators, was presented.

In this contribution, we investigate the guidance of light inside of hollow-core iMM cladding fibers with large air cores (several hundred micrometers âǍŞ similarly to commercially available hollow-core bandgap fibers [25]) for low-loss guidance in the far-infrared (λ = 10.6µm, where metals have substantially lower losses than in the visible) due to the important applications in material processing and medicine [25–27]. Starting from the formalism presented in [21], and following a straightforward Scattering-parameter (or S-Parameter) retrieval procedure [28], we show that such fibers possess loss discrimination properties not found in hollow core waveguides with conventional isotropic claddings [e.g., glass-tube (i.e., capillary) or metal-tube waveguides]. Specifically, we find that the geometry can be tailored such that the linearly polarized HE11 mode possesses the lowest loss, in contrast to hollow metal or dielectric tubes, where the TE01 mode dominates (see for example [29] and references therein). Results obtained by solving the anisotropic Eigenvalue equation with retrieved parameters are in agreement with finite element simulations considering the full structure. Additionally, we show that it is possible to design an iMM cladding fiber where the radially polarized mode possesses the lowest loss, a situation which is not commonly found in other types of fiber structures. These results thus pave the way for the design of metamaterial hollow-core fibers with novel guidance properties, particularly at mid-IR wavelengths.

2. Device operation

The device under consideration is defined by an air-core fiber of diameter D = 2R (R: radius) with a iMM cladding formed by an array of sub-wavelength gold wires (d: wire diameter, a: centre-to-centre distance between two wires) in a silica background [Fig. 1(a)]. In all calculations, we take the separation between the centre of the wire and the inner edge of the silica wall to be a/2, which is always much smaller than the wavelength considered here (a < λ/5,λ = 10.6µm). Unless otherwise stated, we consider three layers of radially aligned wires, where a is the azimuthal separation between wires in the first layer, and also the center-to-center separation in the radial direction. The cladding is thus a concentrically arranged iMM which can be well-approximated as possessing an anisotropic diagonal permittivity and permeability tensors ε¯¯=ε0{εr,εϕ,εz} and μ¯¯=μ0{μr,μϕ,μz}, respectively [Fig. 1(b)], with the the radial and azimuthal tensor components being identical (εr = εϕ = εt and µr = µϕ = µt).

 figure: Fig. 1

Fig. 1 (a) Concept of the proposed iMM hollow-core fiber. Left: air-core fiber with diameter D = 2R with densely packed sub-wavelength gold wires embedded in silica defining the iMM cladding. Inset: square unit cell (diameter d, pitch a) used for the parameter retrieval. Right: equivalent metamaterial hollow-core fiber with permittivity tensors as defined in the text. (b) Sketch of the parameter retrieval procedure and the corresponding unit cell. Permittivity and permeability tensors are retrieved from the transmitted and reflected fields at the input/output ports boundaries using FE simulations. The unit cell is located in air and surrounded by periodic boundary conditions.

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2.1. Modal equations

A detailed derivation of the modal dispersion equations and guidance conditions of iMM cladding hollow-core fibers is found in [21], here we present the most important results relevant for this contribution. The Eigenvalue equation to be solved is given by

[μ0κJm(κR)Jm(κR)μ0μtκHκt2Km(κHR)Km(κHR)][ε0κJm(κR)Jm(κR)ε0εtκEκt2Km(κER)Km(κER)]=(mβRω)2(1κt21κ2)2,
where β = k0neff is the propagation constant (k0: free space wavenumber), angular frequency ω, effective index neff, κ2=k02β2, κt2=k02εtμtβ2, κE2=εzεtβ2k02μtεz, κH2=μzμtβ2k02μzεt. Jm is the Bessel function of the first kind and Km is the modified Bessel function of the second kind, where m is the order of the Bessel functions of the z-components of the fields. For m = 0, the RHS of Eq.(1) vanishes and the TE- and TM dispersion relations are as follows:
[μ0κJ0(κR)J0(κR)μ0μtκHκt2K0(κHR)K0(κHR)]=0
[ε0κJ0(κR)J0(κR)ε0εtκEκt2K0(κER)K0(κER)]=0
Numerically solving Eqs. (1)(3) for β then yields the dispersion of a desired mode, i.e., the complex effective index neff.

2.2. Metamaterial cladding parameter retrieval

The dielectric properties of the iMM cladding are investigated using a parameter retrieval procedure described in [28] [Fig. 1(b)]. Using the constituent material properties at λ = 10.6µm (gold: εgold = −3866.3 + 1711.9i [30], silica: εsilica = 4.6861 + 0.23483i [31]) we retrieve the complex permittivity and permeability tensors of the cladding from the S-parameters [28] as a function of wire diameter d and inter-wire spacing a, using a 2D finite element (FE) solver (COMSOL). Figure 2 shows the real and imaginary parts of εz and εt, obtained by considering the electric field polarized parallel (εz) and perpendicular (εt) to the gold wires, respectively. The permittivity tensor is highly anisotropic [4], in particular ℜe(εz) varies over two orders of magnitude. Furthermore, εz and εt suggest a predominantly metallic- (ℜe(εz) < 0) and dielectric- (ℜe(εt) > 0) character respectively, with exceptions at low- and high- filling fractions, where εz and εt reveal a mixed dielectric and metallic character, respectively. Compared to ε¯¯, the relative magnetic permeability tensor μ¯¯ only varies comparatively weakly in this parameter range (|ℜe(µt)| = 1.24 − 2.23, |ℜe(µz)| = 0.1 − 1.0, whereas |ℜe(εt)| = 0.01 170, |ℜe(εz)| = 0.003 − 1576) and thus is not shown. To exemplify the various guidance properties, we choose three combinations of a and d [marked by the colored points in Fig. 2 (MM1, MM2 and MM3)] leading to the permittivity and permeability values summarized in Tab. 1.

 figure: Fig. 2

Fig. 2 Pitch/diameter dependence of the different components of the retrieved permittivity tensors (gold wires, silica background, λ = 10.6µm) (a) ℜe(εz), (b) ℜe(εt), (c) ℑm(εz), (d) ℑm(εt). Coloured points in (a)–(b) number the example iMM cladding parameters discussed in the text and shown in Tab. 1.

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Tables Icon

Table 1. Summary of metamaterial parameters.

2.3. Modal discrimination

We now investigate the properties of the three lowest order modes of the hollow-core MM-clad fibers for various geometric parameters. We consider fibers with large core diameters (D > 100µm, corresponding to several tens of wavelengths), which are inherently multi-mode and have modal losses in the range of dB/m, which is sufficient for many practical applications. We consider only the most important fundamental- and higher-order modes, namely the HE11, TM01 and TE01 modes, which are typically relevant in real-world applications, and analyze how their attenuation varies for fibers possessing different iMM claddings. It should be noted that the modes in such large core diameter hollow-core fibers have comparable ℜe(neff), slightly smaller than unity. Consequently, we will present only the corresponding ℑm(neff), which determines modal attenuation and thus relative mode discrimination.

We first present the modal attenuation of (isotropic) hollow tubes of the individual constituent materials, as a function of D. In the case of a hollow gold tube [Fig. 3(a)], the lowest-loss mode is the TE01 mode, with the other two modes having ℑm(neff) orders of magnitude larger, as a result of the small field penetration of the TE01 mode into the metal [24, 32]. Even in the case of a silica tube [Fig. 3(b)], the TE01 is the lowest-loss mode, but its loss is comparable to that of the HE11 mode, in contrast to the metal tube situation. In both cases, the TM01 is the mode with the highest loss. If we then consider a iMM cladding with large metal filling fraction, (MM1, ℜe(εz) < 0 and ℜe(εt) < 0, see Fig. 2), we find similar properties. In this case, both axial and transverse permittivity have metallic-like behaviour, and the relative modal discrimination behaviour is comparable to that of a metal tube, whereby the TE01 has the lowest loss. However, comparing Figs. 3(a), 3(b) and 3(c), we see that in the latter case the HE11 and TM01 modes have lower loss, and the attenuation properties of the TE01 MM1 mode lies somewhere between its purely isotropic counterparts. Note that the numerical solutions of Eqs. (1)(3) using the retrieved parameters of Tab. 1 [Figs. 2(c) and 2(d), solid lines] are in good agreement with the FE simulations using the discrete wire structure [Figs. 2(c) and 2(d), circles], confirming the viability of using retrieved metamaterial parameters for iMM cladding hollow core fiber designs.

 figure: Fig. 3

Fig. 3 Modal attenation [ℑm(neff) and loss] vs. air core diameter for the three lowest-order modes in hollow-core fibers possessing claddings formed by (a) gold, (b) silica, (c) MM1 and (d) MM2 as defined in Tab. 1. Solid lines: numerical solutions of Eqs. (1)(3). Circles: results obtain by FE modeling. Solid lines in (c), (d) use the permittivity tensors shown in Tab. 1. Also shown are the normalized axial Poynting vectors for the three modes with claddings formed by (e) MM2, D = 600µm and (f) MM3, D = 20µm (numbers below the repective row indicate the scale bar). Note that in (f) the TM01 mode has the lowest loss. Arrows indicate the direction and magnitude of the electric field at a fixed point of time.

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In the case of an iMM cladding, (MM2, ℜe(εz) < 0 and ℜe(εr) > 0, see Fig. 2), the situation is radically different [Fig. 3(d)]. Most remarkably, the HE11 mode now possesses the lowest loss [red points and curve in Fig. 3(d)], whereas the TE01 mode reveals the largest loss. This can be qualitatively understood from the larger propagation constant of the HE11 mode compared to all other modes, leading to a more grazing incidence (i.e., smaller incidence angle) onto the iMM cladding assuming a ray-type picture. One particularly unusual aspect is that in the case of the iMM hollow-core fiber [MM2, Fig. 3(b)] the HE11 and TM01 modes both possess ℑm(neff) values which are lower than in hollow tubes composed of the individual constituent materials [Figs. 3(a) and 3(b)]. Also at this point FE calculations (circles) are in agreement with calculations using Eqs. (1)(3) (solid lines), confirming the feasibility of using retrieved parameters as a design pathway for hollow core iMM fibers. For completeness, Fig. 3(e) shows the axial Poynting vector profiles of the modes under consideration for a MM2 clad fiber, D = 600µm. Note that for D = 600µm at least 99.999% of the power is within the air core for all modes considered, making this hollow-core fiber geometry well-suited for high-power applications.

To fully illustrate the discrimination flexibility of iMM-HCFs, we investigate whether a material and geometry combination exists that enables the radially polarized (TM01) mode to possess the lowest loss of all modes. A preliminary parameter search shows that this occurs for a fiber with D = 20µm and a MM3 cladding (d = 0.1µm, a = 0.2µm, see Fig. 2). In this configuration [Fig. 3(f), one-wire iMM layer], the TM01 mode has significantly lower loss than the other supported modes, which confirms that our structure uniquely allows to adjust the modal discrimination.

2.4. Geometry dependence

As a further analysis, we now consider how changes in wire diameters affect the modal attenuation properties of the fibers presented thus far. For this purpose, we consider the largest wire separation examined (a = 2µm), and vary the wire diameter d, for a fixed core diameter D [Fig. 4(a)]. The modal behaviour transitions from a low-loss dielectric-type HE11 towards a low-loss TE01 mode [light green and blue regions in Fig. 4(a)], both for FE calculations with discrete wires [circles in Fig. 4(a)] and retrieved parameter model [solid lines in Fig. 4(a)]. Notice in particular the signs of the retrieved axial- and transverse-permitivitties change, as indicated by the different colored regimes in Fig. 4(a). It is important to note that within the iMM domain, the TE01 mode has the highest loss, which indicates that the iMM cladding allows to adjust the modal loss by balancing between the penetration of the electromagnetic field of the different modes with the imaginary parts of the iMM tensor components. Interestingly, the HE11 is the lowest loss mode even when all elements of the permittivity tensor are positive, which is contrast to what was observed for the case of a simple silica capillary presented earlier [see Fig. 3(b)]. To understand this further, we consider an entirely hypothetical case, yielding a qualitative explanation of the observed behavior. Assuming no magnetic reponse µ¯¯µ0I¯¯, we consider the case where εt = εsilica and investigate the modal loss variation when changing ℜe(εz), keeping a constant ℑm(εz) = 1i. We observe that while the HE11 mode possesses the lowest loss for ℜe(εz) ≪ 0, a transition occurs in the vicinity of ℜe(εz) ~ ℜe(εsilica), causing its loss to increase above that of the TE01 mode – notice that the TE01 modal properties are not dependent on εz, resulting from the vanishing longitudinal electric field component of TE-modes in general [Eq.(2)]. Considering εz = εsilica and varying ℜe(εr) for a constant ℑm(εr) = 1i, we see that the HE11 and TM01 modes only slightly depend on ℜe(εr), and that the TE01 mode has the lowest loss across most of the parameter space, except for a region close to ℜe(εr) ~ ℜe(εsilica).

 figure: Fig. 4

Fig. 4 (a) Modal attenuation [ℑm(neff) and loss] vs. wire diameter d for a constant air-core diameter (D = 600µm) and pitch (a = 2µm, solid lines: FE simulations, dashed line anisotropic dispersion model). (b) Hypothetical calculations to investigate the modal transition behavior (D = 600µm, μ¯¯~0I¯¯) Top: ℑm(neff) vs. ℜe(εz) [ℑm(εz) = 1i], εr = εsilica. Bottom: ℑm(neff) vs. ℜe(εr) [ℑm(εr) = 1i], εz = εsilica.

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3. Conclusion

In conclusion, we have shown that the loss properties of indefinite metamaterial-cladding hollow-core fibers can differ significantly from those composed of conventional claddings and that the highly anisotropic cladding allows to tune modal discrimination such that either the HE11, TE01 or TM01 mode has the lowest loss of all modes. By incorporating material attenuation into the anisotropic modal equations via complex optical parameters obtained from simple S-parameter retrieval, we reproduced the loss properties of such fibers as predicted by full finite element simulations, also elucidating the role of anisotropy. The unusual properties of the metamaterial cladding hollow core fibers emerge as a result of the fine balance between the field penetrations into the metal, and intrinsic material loss. These additional degrees of engineering freedom allows to uncover new loss regimes, for example regimes in which the TM01 mode is the lowest loss mode. These results pave the way for the design of novel hollow-core fibers with guidance and tuning properties which are especially important for applications demanding cylindrical polarization states, for example laser cutting and materials processing [33,34], sharp focusing [35], particle trapping [36], particle acceleration [37], or alternatively enabling in-fiber guidance of the fundamental linearly polarized beam. Fabrication of iMM-HCFs with feature sizes and material combinations discussed here is feasible on the basis of either direct drawing a single preform or using pressure-assisted melt filling [6,9,10,12,20].

Acknowledgments

A.T. acknowledges financial support from the Alexander Von Humboldt Foundation.

References and links

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2. A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007). [CrossRef]   [PubMed]  

3. W. Cai and V. M. Shalaev, Optical Metamaterials (Springer, 2006).

4. C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012). [CrossRef]  

5. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003). [CrossRef]   [PubMed]  

6. H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010). [CrossRef]   [PubMed]  

7. C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mater. Express 6(6), 1790–1799 (2016). [CrossRef]  

8. A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010). [CrossRef]  

9. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef]   [PubMed]  

10. O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013). [CrossRef]  

11. H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011). [CrossRef]   [PubMed]  

12. P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express 20(27), 28409–28417 (2012). [CrossRef]   [PubMed]  

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References

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  1. M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers â Ӑ Ş an innovative platform for in-fiber photonic devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
    [Crossref]
  2. A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
    [Crossref] [PubMed]
  3. W. Cai and V. M. Shalaev, Optical Metamaterials (Springer, 2006).
  4. C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
    [Crossref]
  5. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
    [Crossref] [PubMed]
  6. H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010).
    [Crossref] [PubMed]
  7. C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mater. Express 6(6), 1790–1799 (2016).
    [Crossref]
  8. A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
    [Crossref]
  9. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
    [Crossref] [PubMed]
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2016 (3)

2015 (2)

2013 (3)

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30(4) 851–867 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

2012 (5)

2011 (3)

2010 (4)

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. S. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010).
[Crossref] [PubMed]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Y. I. Salamin, “Low-diffraction direct particle acceleration by a radially polarized laser beam,” Phys. Lett. A 374(48), 4950–4953 (2010).
[Crossref]

2009 (3)

2008 (1)

2007 (1)

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

2005 (2)

D. Torres and et al., “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310–321 (2005).
[Crossref]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

2002 (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (2)

V.G. Niziev and A.V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D. Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

A.V. Nesterov, V.G. Nizlev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D. Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

1998 (1)

1960 (1)

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Abouraddy, A. F.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

AlâARJanabi, A. H.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

Aleksandrova, A.

Anthony, J.

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Argyros, A.

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers â Ӑ Ş an innovative platform for in-fiber photonic devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
[Crossref]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30(4) 851–867 (2013).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial metamaterial cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29(9) 2462–2477 (2012).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

Atakaramians, S.

Atrashchenko, A. V.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
[Crossref]

Bartal, G.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

Bayindir, M.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Belov, P. A.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
[Crossref]

Bendavid, A.

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

Benoit, G.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

Bird, D.

Cai, W.

W. Cai and V. M. Shalaev, Optical Metamaterials (Springer, 2006).

Castelli, A.

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Chashnikova, M.

Constable, E.

Djurišic, A.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Elazar, J.

Engeness, T. D.

Fedosenko, O.

Fink, Y.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Fischer, B. M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

Fleming, S. C.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30(4) 851–867 (2013).
[Crossref]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial metamaterial cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29(9) 2462–2477 (2012).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Flores, Y.

Fredericks, W.

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Genov, D. A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

George, A.

Gruska, B.

Halik, M.

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Hart, S. D.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

Hou, J.

Hunt, P. G.

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

Ibanescu, M.

Ishikawa, A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

Iyer, A. K.

Jacobs, S. A.

Jain, C.

Joannopoulos, J. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Johnson, S. G.

Joly, N.

Joly, N. Y.

Kaltenecker, K. J.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

Karatchevtseva, I.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

Kischkat, J.

Kivshar, Y. S.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
[Crossref]

Klinkmüller, M.

Knight, J. C.

Koschny, Th.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

Kuhlmey, B. T.

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30(4) 851–867 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial metamaterial cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29(9) 2462–2477 (2012).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
[Crossref] [PubMed]

Kuriki, K.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Large, M. C. J.

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

Lee, H. W.

Lei, M.

Leonhardt, R.

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Lewis, R. A.

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

Li, Q.

Liu, Z.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

Lwin, R.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Machulik, S.

Maier, S.

Majewski, M.

Masselink, W. T.

Mei, Y.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

Monastyrskyi, G.

Mortensen, N. A.

Naman, O. T.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

Nesterov, A.V.

A.V. Nesterov, V.G. Nizlev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D. Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

V.G. Niziev and A.V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D. Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

New-Tolley, M. R.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

Niziev, V.G.

V.G. Niziev and A.V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D. Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Nizlev, V.G.

A.V. Nesterov, V.G. Nizlev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D. Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Orf, N.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Peng, F.

Peters, S.

Pogson, E. M.

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

Pollock, J. G.

Pratap, D.

Pristera, F.

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Rakic, A.

Ramakrishna, S. A.

Rettenmayr, M.

Reuther, K.

Russell, P. S. J.

Russell, R. F.

Salamin, Y. I.

Y. I. Salamin, “Low-diffraction direct particle acceleration by a radially polarized laser beam,” Phys. Lett. A 374(48), 4950–4953 (2010).
[Crossref]

Scharrer, M.

Schmidt, M. A.

Schmidt, O. G.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Semtsiv, M.

Shalaev, V. M.

W. Cai and V. M. Shalaev, Optical Metamaterials (Springer, 2006).

Shapira, O.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Simovski, C. R.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
[Crossref]

Singh, N.

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

Skorobogatiy, M.

Smith, D. R.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Smith, E. J.

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

Soljacic, M.

Sorin, F.

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers â Ӑ Ş an innovative platform for in-fiber photonic devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
[Crossref]

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Soukoulis, C. M.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

Temelkuran, B.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

Torres, D.

D. Torres and et al., “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310–321 (2005).
[Crossref]

Townsend, S.

Tuniz, A.

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mater. Express 6(6), 1790–1799 (2016).
[Crossref]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Tyagi, H. K.

Uebel, P.

Vier, D. C.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

Walther, M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

Wang, A.

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

Weidlich, S.

Weisberg, O.

Wieduwilt, T.

Yakunin, V. P.

A.V. Nesterov, V.G. Nizlev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D. Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

Yan, M.

Yan, S.

Yao, B.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Zhang, S.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

Zhang, X.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

Zhao, W.

Zhou, S.

Adv. Mat. (1)

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24(31), 4229–4248 (2012).
[Crossref]

Adv. Opt. Mat. (2)

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers â Ӑ Ş an innovative platform for in-fiber photonic devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
[Crossref]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. AlâǍŘJanabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for the THz and mid-IR,” Adv. Opt. Mat. 1(12), 971–977 (2013).
[Crossref]

Anal. Chem. (1)

F. Pristera, M. Halik, A. Castelli, and W. Fredericks, “Analysis of explosives using infrared spectroscopy,” Anal. Chem. 32(4), 495–508 (1960).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. D. Appl. Phys. (2)

A.V. Nesterov, V.G. Nizlev, and V. P. Yakunin, “Generation of high-power radially polarized beam,” J. Phys. D. Appl. Phys. 32(22), 2871–2875 (1999).
[Crossref]

V.G. Niziev and A.V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D. Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Nano Lett. (1)

E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010).
[Crossref]

Nat. Commun. (1)

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 42706 (2013).
[Crossref] [PubMed]

Nat. Mater. (1)

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mater. 6(5), 336–347 (2007).
[Crossref] [PubMed]

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916) 650–653 (2002).
[Crossref] [PubMed]

Opt. Express (8)

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
[Crossref] [PubMed]

M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17(17), 14851–14864 (2009).
[Crossref] [PubMed]

S. Townsend, S. Zhou, and Q. Li, “Design of fiber metamaterials with negative refractive index in the infrared,” Opt. Express 23(14), 18236–18242 (2015).
[Crossref] [PubMed]

D. Pratap, S. A. Ramakrishna, J. G. Pollock, and A. K. Iyer, “Anisotropic metamaterial optical fibers,” Opt. Express 23(7), 9074–9085 (2015).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express 20(27), 28409–28417 (2012).
[Crossref] [PubMed]

A. Tuniz, R. Lwin, A. Argyros, S. C. Fleming, E. M. Pogson, E. Constable, R. A. Lewis, and B. T. Kuhlmey, “Stacked-and-drawn metamaterials with magnetic resonances in the terahertz range,” Opt. Express 19(17), 16480–16490 (2011).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Mat. Express (2)

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2(9), 1254–1259 (2012).
[Crossref]

A. Wang, A. Tuniz, P. G. Hunt, E. M. Pogson, R. A. Lewis, A. Bendavid, S. C. Fleming, B. T. Kuhlmey, and M. C. J. Large, “Fiber metamaterials with negative magnetic permeability in the terahertz,” Opt. Mat. Express 1(1), 115–120 (2011).
[Crossref]

Opt. Mater. Express (1)

Phys. Lett. A (1)

Y. I. Salamin, “Low-diffraction direct particle acceleration by a radially polarized laser beam,” Phys. Lett. A 374(48), 4950–4953 (2010).
[Crossref]

Phys. Rev. B (1)

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. B 71(3), 036617 (2005).
[Crossref]

Phys. Rev. Lett. (3)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength THz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009)
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Proc. SPIE (1)

D. Torres and et al., “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310–321 (2005).
[Crossref]

Other (2)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

W. Cai and V. M. Shalaev, Optical Metamaterials (Springer, 2006).

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Figures (4)

Fig. 1
Fig. 1 (a) Concept of the proposed iMM hollow-core fiber. Left: air-core fiber with diameter D = 2R with densely packed sub-wavelength gold wires embedded in silica defining the iMM cladding. Inset: square unit cell (diameter d, pitch a) used for the parameter retrieval. Right: equivalent metamaterial hollow-core fiber with permittivity tensors as defined in the text. (b) Sketch of the parameter retrieval procedure and the corresponding unit cell. Permittivity and permeability tensors are retrieved from the transmitted and reflected fields at the input/output ports boundaries using FE simulations. The unit cell is located in air and surrounded by periodic boundary conditions.
Fig. 2
Fig. 2 Pitch/diameter dependence of the different components of the retrieved permittivity tensors (gold wires, silica background, λ = 10.6µm) (a) ℜe(εz), (b) ℜe(εt), (c) ℑm(εz), (d) ℑm(εt). Coloured points in (a)–(b) number the example iMM cladding parameters discussed in the text and shown in Tab. 1.
Fig. 3
Fig. 3 Modal attenation [ℑm(neff) and loss] vs. air core diameter for the three lowest-order modes in hollow-core fibers possessing claddings formed by (a) gold, (b) silica, (c) MM1 and (d) MM2 as defined in Tab. 1. Solid lines: numerical solutions of Eqs. (1)(3). Circles: results obtain by FE modeling. Solid lines in (c), (d) use the permittivity tensors shown in Tab. 1. Also shown are the normalized axial Poynting vectors for the three modes with claddings formed by (e) MM2, D = 600µm and (f) MM3, D = 20µm (numbers below the repective row indicate the scale bar). Note that in (f) the TM01 mode has the lowest loss. Arrows indicate the direction and magnitude of the electric field at a fixed point of time.
Fig. 4
Fig. 4 (a) Modal attenuation [ℑm(neff) and loss] vs. wire diameter d for a constant air-core diameter (D = 600µm) and pitch (a = 2µm, solid lines: FE simulations, dashed line anisotropic dispersion model). (b) Hypothetical calculations to investigate the modal transition behavior (D = 600µm, μ ¯ ¯ ~ 0 I ¯ ¯) Top: ℑm(neff) vs. ℜe(εz) [ℑm(εz) = 1i], εr = εsilica. Bottom: ℑm(neff) vs. ℜe(εr) [ℑm(εr) = 1i], εz = εsilica.

Tables (1)

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Table 1 Summary of metamaterial parameters.

Equations (3)

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[ μ 0 κ J m ( κ R ) J m ( κ R ) μ 0 μ t κ H κ t 2 K m ( κ H R ) K m ( κ H R ) ] [ ε 0 κ J m ( κ R ) J m ( κ R ) ε 0 ε t κ E κ t 2 K m ( κ E R ) K m ( κ E R ) ] = ( m β R ω ) 2 ( 1 κ t 2 1 κ 2 ) 2 ,
[ μ 0 κ J 0 ( κ R ) J 0 ( κ R ) μ 0 μ t κ H κ t 2 K 0 ( κ H R ) K 0 ( κ H R ) ] = 0
[ ε 0 κ J 0 ( κ R ) J 0 ( κ R ) ε 0 ε t κ E κ t 2 K 0 ( κ E R ) K 0 ( κ E R ) ] = 0

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