Mode classification and loss mechanism in air-core Bragg fibers

With an equivalent mode-solving model, the mode spectra in air-core Bragg fibers are systematically studied by using an improved full-vector finite-difference method. All supported modes are classified into four categories, namely, guided modes, cladding modes, leaky modes and PML modes, among which the leaky modes can be further subdivided into radiation-like and evanescence-like leaky modes. To ensure that the modes are solved accurately and efficiently with this model, the strategy for choosing model parameters is suggested. Benefiting from this convenient mode solver, the characteristics of cladding modes are observed in details, and potential applications are suggested. Moreover, the rapid loss of a hybrid mode at lower frequencies is explained by an evanescence-like leaky mode induced cutoff, which is different from that of TE₀₁ mode due to the failure of band gap confinement.     

全矢量有限元模型及其在光波导中的应用

为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.     

Phase matching in ?erenkov second-harmonic generation: a leaky-mode analysis

Use of leaky modes allows us to demonstrate very simply that ?erenkov second-harmonic generation is not free of phase matching. The ?erenkov phase-matching condition is derived for what is to our knowledge the first time. The way to overcome the difficulty linked with the divergence at infinity of the leaky modes is discussed.     

Phase-matched four-wave mixing of guided and leaky modes in an optical fiber

Dispersion analysis of guided and leaky modes in an optical fiber shows that these two classes of modes can be coupled to each other through phase-matched four-wave mixing. This process can contribute to the generation of broad and flat supercontinua in highly nonlinear fibers, opening, at the same time, an additional channel of loss through radiation energy transfer from guided to leaky modes.     

Modes of capillary photonic-crystal fibers with hollow core

A rigorous method of integral equations has been used to calculate the dispersion characteristics, fields, and radiation patterns of the leaky modes of photonic-crystal fibers with a shell in the form of a bounded 2D photonic crystal composed of parallel quartz capillaries contacting each other and a core in the form of a defect of a photonic crystal with one capillary removed. It is shown that, when thick-walled capillaries (with an air content in the shell of about 28%) are used, these fibers can be single mode and have an overlap integral of the fundamental-mode field with the dielectric medium that is smaller by a factor of more than two (in comparison with similar fibers formed by air channels of circular cross section). The significant dispersion of the group velocity of the fundamental modes of fibers near the edge of the photonic crystal band gap has been found.     

Explicit finite difference solution of the power flow equation in W-type optical fibers

Using the power flow equation, we have calculated spatial transients of power distribution and a steady-state distribution that are due to coupling of guided to leaky modes in W-type optical fibers (doubly clad fibers). A numerical solution has been obtained by the explicit finite difference method. Results show that power distribution in W-type optical fibers depends on both the intermediate layer width and the coupling strength. W-shaped index profile of optical fibers is effective in reducing modal dispersion and therefore in improving the fiber bandwidth. We have also shown that explicit finite difference method is effective and accurate for solving the power flow equation in W-type optical fibers.     

Resonant directional coupling of hollow Bragg fibers

Coupling between the lowest-loss TE01 modes of two touching hollow-core Bragg fibers is considered with a view to designing a directional coupler. We have found that for fibers with core radii larger than 10 microm one can identify broad frequency ranges in which intermodal coupling strength exceeds supermode radiation losses by an order of magnitude, thus opening the possibility of building a directional coupler. We attribute such unusually strong intermode coupling both to the resonant effects in the intermirror cavity and a proximity interaction between the leaky modes localized in the mirror.     

Hollow Bragg fiber bundles: when coupling helps and when it hurts

Coupling between leaky modes of collinear hollow-core Bragg fibers is considered. It is found that coupling is unusually strong because of resonant effects in the interfiber cavity when the fibers are touching each other and decreases dramatically with the first tens of nanometers of fiber separation. However, residual coupling with a strength proportional to the fiber radiation loss is long range, decreasing as an inverse square root of the interfiber separation and exhibiting periodic variation. The possibility of building a directional coupler from touching Bragg fibers is discussed in view of the findings.     

Mode attenuation in microstructured optical fibers with absorbing coating

The characteristics of leaky modes in microstructured fibers with finite-thickness absorbing coatings are studied theoretically and experimentally. It is shown that, if the thickness of the coating is constant, the fiber has a quasi-periodic transmission spectrum. The period and depth of modulation of the spectrum are determined by resonance coupling between the modes of the fiber and coating. Since the constants of mode propagation in the coating are very sensitive to environmental parameters, the discovered effect seems to be promising for sensor applications.     

Circular Fourier analysis of modes in optical waveguides under critical and supercritical conditions

An extension of the circular Fourier analysis of the mode field is presented that makes it possible to obtain a successively correctable solution to the scalar waveguide problem posed for 3D optical waveguides. The critical frequencies of rectangular and elliptic waveguides, as well as the characteristics of leaky modes in microstructural optical fibers formed by elliptical air channels, are studied.     

Leaky mode analysis of circular optical waveguides

A leaky mode is a bound mode below its cut-off frequency. It attenuates in the direction of propagation and approximates the portion of the radiation field within the optical waveguide that is significant far from the source. The characteristics, including attenuation coefficients, of leaky modes on the circular fibre are compared with those of the more familiar slab waveguide. Except for the HE_1m leaky modes, leaky modes attenuate much faster on the slab than on the circular fibre. The greater the /(azimuthal field variation) the smaller the attenuatioN. Thus, theI?1 leaky modes are important even at great distances from the source. An effective cut-off frequency is proposed. Above this frequency the mode is either weakly leaky or trapped. An expression for the number of weakly leaky and trapped modes is given. The power of leaky modes due to illuminating one end of the fibre is determined. The effect of material absorption is considered.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

The influence of the input beam width on the bandwidth of multimode step index fibers

A detailed theoretical investigation of the influence of the input on the bandwidth of multimode step index fibers is given. The calculations take into account mode coupling, absorption and leaky modes. For 100 m of a typical large numerical aperture fiber the bandwidth can vary with excitation from 1.8 GHz to 15 GHz. The numerical calculations agree with published experimental results.     

Optical fibre: Spatial transient and steady state

The concept of spatial transient is introduced to better appreciate the role of leaky modes on optical waveguides of circular cross section. Refracting leaky modes represent a relatively fast transient while tunnelling leaky modes represent a relatively slow transient. Bound modes provide the spatial steady-state solution. The greater the waveguide parameter V, the greater the duration of the transient. The relevance of leaky modes on fibres with loss and irregularities is discussed.     

Advanced boundary conditions for eigenmode expansion models

In order to realise the full potential of eigenmode expansion models, advanced boundary conditions are required that can absorb the radiation impinging on the walls of the discretisation volume. In this paper, we will discuss and compare a number of these boundary conditions, like perfectly matched layers (PMLs), open (leaky mode) boundary conditions and transparent boundary conditions (TBCs). We will also introduce the case of PMLs with infinite absorption and discuss its relation to leaky mode expansion, leading to a deeper insight into the physics of PML.     

Advanced boundary conditions for eigenmode expansion models

In order to realise the full potential of eigenmode expansion models, advanced boundary conditions are required that can absorb the radiation impinging on the walls of the discretisation volume. In this paper, we will discuss and compare a number of these boundary conditions, like perfectly matched layers (PMLs), open (leaky mode) boundary conditions and transparent boundary conditions (TBCs). We will also introduce the case of PMLs with infinite absorption and discuss its relation to leaky mode expansion, leading to a deeper insight into the physics of PML.     

Grating resonances in air-silica microstructured optical fibers

We report what is believed to be the first demonstration of optical fiber gratings written in photonic crystal fibers. The fiber consists of a germanium-doped photosensitive core surrounded by a hexagonal periodic air-hole lattice in a silica matrix. The spectra of these gratings allow for a detailed characterization of the fiber. In particular, the gratings facilitate coupling to higher-order leaky modes. We show that the spatial distribution and the effective index of these modes are determined largely by the design of the lattice and that the grating spectra are unaffected by the refractive index surrounding the fiber. We describe these measurements and corresponding simulations and discuss their implications for the understanding of such air-hole structures.     

Subsonic leaky Rayleigh waves at liquid-solid interfaces

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.