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Abstract:We demonstrate a new class of hollow-core Bragg fibers that are composed of concentric cylindrical silica rings separated by nanoscale support bridges. We theoretically predict and experimentally observe hollow-core confinement over an octave frequency range. The bandwidth of bandgap guiding in this new class of Bragg fibers exceeds that of other hollow-core fibers reported in the literature. With only three rings of silica cladding layers, these Bragg fibers achieve propagation loss of the order of 1 dB/m. References and Links1. P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978). 2. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, "Photonic band gap guidance in optical fibers,"Science 282, 1476-1478 (1998). 3. R. F. Cregan et al., "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999). 4. J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003). 5. Y. Fink et al., "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 17, 2039-2041 (1999). IntroductionThe concept of hollow-core Bragg fibers, in which the fiber cladding is composed of cylindrical dielectric layers with alternating refractive indices ( Fig. 1(a) -4]. In both cases, light is confined to a central hollow-core due to Bragg reflection from the periodic cladding structure. With little overlap between the propagating modes and the cladding materials, hollow core fibers are ideal for applications involving high optical powers [5,6]. Other potential advantages include significantly reduced nonlinearity and lower propagation loss [7,8]. In addition, hollow core fibers also provide an attractive paradigm to study novel nonlinear optical phenomena in gas phase materials [9,10]. One major challenge in fabricating Bragg fibers involves the identification of dielectric materials with not only a large index contrast, but also compatible rheological and thermal properties. In this paper, we report a new class of Bragg fibers that are composed of cylindrical dielectric layers in air, separated by nanoscale support bridges. Consequently, such Bragg fibers can be constructed from a single dielectric material such as a glass or a polymer. Furthermore, they have the unique property of supporting bandgap guiding over an octave frequency range, which is much larger than what has been achieved by any other hollow-core fiber [6,7,[11][12][13][14][15]. Ideally, our theoretical calculations indicate that such hollow-core air-silica Bragg fibers can achieve confinement loss of the order of 0.1 dB/km with only four silica cladding rings. This paper is organized as follows. In section 2, we theoretically analyze the properties of hollow-core air-silica Bragg fibers and demonstrate some of the unique features of this new class of Bragg fibers. In section 3, we discuss the fabrication and the experimental characterization of the hollow-core air-silica Bragg fibers in some details. The paper is summarized in section 4.

The theory of Trukhan [Sov. Phys. Solid State (Engl. Trans/.), 1963, 4, 25601 for t h e calculation of the complex permittivity of a conducting dielectric film containing a binary 1 : 1 electrolyte is critically reviewed. It is shown that the final result of Trukhan is correct, in spite of some errors and odd procedures in the original derivation. The method of Trukhan is changed to a more concise procedure which is better suited to generalisations, and t h e theory is generalised to binary electrolytes of a n y charge type. The dimensionless excess impedance (over and above the Maxwell-Wagner-Sillars impedance) and t h e complex relative permittivity are functions of t h e type of electrolyte, the dimensionless frequency, t h e ratio of the ionic diffusion coefficients and t h e film thickness scaled by t h e Debye length. The complex relative permittivity has a Debye-like relaxation, but for very different values of t h e two diffusion coefficients and for films which are thin compared with the Debye length, one can clearly distinguish two dielectric relaxations, one for each ion. The peak in t h e dielectric loss corresponding to the ion of higher valency, is dominating in thin films. W h e n t h e film is thicker, (or when t h e electrolyte concentration is increased) t h e low-frequency peak diminishes relative to the high-frequency peak. The maximum in the loss tangent is positioned at higher frequencies t h a n the maximum in t h e dielectric loss. Therefore it is often an advantage to fit the loss tangents to actual measurements, since measurements at low frequencies are generally more difficult. Two applications of t h e theory are treated: the low-frequency dielectric relaxation of a dry copolymer of vinylidene cyanide and vinyl acetate with conducting ions (T. Furukawa, M. Date, K. Nakajima, T.

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