Acoustic wave propagation in piezoelectric fibers of hexagonalcrystal symmetry

An exact analysis is presented for acoustic wave propagation in cladded acoustic fibers having a core and an infinite thick cladding both made of piezoelectric hexagonal crystal of 6 mm point group symmetry. The crystalline Z axes of both the core and cladding coincide with the fiber axis. A general dispersion equation is derived for all the acoustic modes propagating along the fiber axis. Two simpler and independent equations which represent the dispersion relations of torsional and radial-axial modes can be separated from the general dispersion equation. It has been found that the radial-axial and general flexural modes are piezoelectrically active while the torsional modes are not. Approximate dispersion relations for pure guided modes in weakly guiding weakly piezoelectric fibers which are much simpler than the exact ones are also given. Numerical results are only presented for pure guided modes. Exact and approximate dispersion curves of several lower order pure guided flexural, radial-axial and torsional modes in a weakly guiding ZnS fiber are compared and they are in good agreement     

Analysis of cladded acoustic fibers of hexagonal crystal symmetry

A cladded acoustic fiber consisting of a core and an infinite thick cladding both having a hexagonal crystal symmetry is analyzed. The crystalline Z axes of both core and cladding are parallel to the fiber axis. Dispersion equations and field distributions for all modes are derived, and previously reported results for the isotropic case are retrieved. Numerical results for a few lowest-order pure guided torsional, radial-axial and flexural modes are shown. Material considerations are discussed.     

Comparative study of dispersion characteristics of uniaxial crystalline optical fiber under the extreme cases of helix pitch angles

Some special cases of dispersion characteristics of a uniaxial crystalline optical fiber with a helical winding on the core-cladding boundary are investigated theoretically. In the present case, the optical fiber is doubly unconventional: (i) in the choice of uniaxial crystalline optical fiber and (ii) in the choice of sheath helix between the core and cladding. Field components, boundary conditions, and eigenvalue equations for HE and EH modes are obtained. We consider two special cases, i.e. ψ = 0° and ψ = 90° to obtain simpler eigenvalue equations which contain Bessel and modified Bessel functions and their derivatives. The nature of the dispersion curve remains unaffected with the anisotropy and only cutoff frequency is lowered for the positive uniaxial crystals. The helix pitch angle does not affect the modal cutoffs but it effectively controls the number of guided modes. This property has promising importance in long-distance communication where only a few modes are desired to be guided in order to minimize the inter-modal dispersion.     

Acoustic wave propagation along cladded fibers of trigonal crystalsymmetry

An approximate method is proposed to analyze the acoustic wave propagation characteristics in nonpiezoelectric cladded LiNbO₃ fibers of trigonal crystal symmetry. The fiber axis coincides with the crystalline Z axis and the cladding thickness is infinite. This method utilizes coupled mode equations and exact solutions for corresponding cladded fibers of hexagonal crystal symmetry are used as the approximation base. The analysis concentrates on the trigonal materials of 32, 3 m, and ¯3 m groups. Dispersion curves of flexural F₁₁, F₂₁ and F₁₂ modes in such a fiber are presented for the first time with a focus on the fundamental F₁₁ mode. Acoustic modal birefringence phenomenon (or polarization dispersion) has been observed, which means that the dispersion relation of a mode depends on the relative transverse polarizations of the corresponding coupled modes. It was also found that in trigonal cladded fibers there are generally no pure torsional and radial-axial modes, which agrees with results previously obtained for trigonal rods     

Acoustic modes in optical fiberlike waveguides

A perturbation analysis of guided and leaky modes in fiber acoustic waveguides with core and cladding parameters that are slightly different is presented. The perturbing parameter is the shear-velocity difference between the core and cladding material epsilon(s). Acoustic fields and eigenvalues are expanded in power series of epsilon (s)(1/2) for radial and flexural modes and in powers of epsilon(3) for torsional modes. Expansion of leaky longitudinal modes is also in terms of epsilon(s), but the nature of perturbation analysis for these modes is somewhat different from that of guided modes. Zero-order solutions for all types of modes are obtained, and some important higher-order effects are discussed. Common features of optical and acoustic modes in weakly guiding fibers are addressed. It is shown that with respect to zero-order solutions of guided modes, optical and acoustic fibers have identical propagation characteristics. Exact and zero-order propagation characteristics for several lower-order shear-type modes are calculated and compared.     

左手材料薄板波导中的传导模

推导了左手材料薄板波导中传导模的色散方程,分析了波导中存在传导模与波导材料和包敷材料参数取值范围之间的关系.数值算例证实了这些关系.     

Eigenvalue and field equations of three-layered uniaxial fibers and their applications to the characteristics of long-period fiber gratings with applied axial strain

By using the Debye potentials, the exact eigenvalue equations and the corresponding field distributions of the core and cladding modes for three-layered, radially stratified, and dielectric uniaxial optical fibers are derived completely; the modes include TE, TM, and hybrid HE/EH modes. The strain characteristics of long-period fiber gratings' (LPFGs') with applied axial strain are investigated theoretically by studying three-layered uniaxial optical fibers. When uniform axial strain is applied to fiber, the core, and inner and outer cladding become uniaxial crystal optically; that is, the optical axes are parallel to the fiber's axis. Analytic expressions of the strain sensitivities of LPFGs are derived. The analysis reveals that the strain sensitivities of LPFGs based on various cladding modes, including the shift value and direction of the resonance wavelength, differ greatly.     

Acoustic wave propagation along cladded fibers of cubic crystalsymmetry

An approximate method is proposed to analyze the acoustic wave propagation characteristics in nonpiezoelectric cladded fibers of cubic crystal symmetry. The fiber axis coincides with the crystalline Z axis. This approximate method utilizes coupled mode equations and the exact solutions for the corresponding cladded isotropic fiber are used as the approximation base. We concentrate our analysis on cubic fibers with weak anisotropy where the first order approximation obtained from the coupled mode equations can provide accurate results. Dispersion curves of a few lower order flexural, torsional and radial-axial modes in such a fiber with infinite cladding are presented for the first time. Higher order approximations are also discussed. We show the accuracy of the perturbation formula, reveal that the torsional and radial-axial modes are not pure in cubic fibers, and inspect the modal birefringence phenomenon     

Comparative study of mid-infrared fibers for modal filtering

We compare the filtering capabilities of two infrared fibers developed to achieve a high rejection ratio of the higher order modes in order to obtain compact modal filters devoted to stellar interferometry. Two types of double-clad fibers are studied: a fiber with a second thin absorbing cladding and a fiber with a second thick absorbing cladding closer to the fiber core; both are single mode around the CO(2) band (10.6 μm). We present the single-mode spectral domain and the nulling capabilities of both fibers for different fiber lengths, comparing simulations with experimental results. We show that the filtering capabilities are improved when the absorbing clad is closer to the fiber core, as the propagation distance needed to filter out these modes is shorter. Thus, to obtain high rejection ratios in compact devices, an absorbing cladding close to the core of the fiber is compulsory in order to suppress cladding modes that could eventually recouple into the waveguide. We present an empirical model that allows determining the minimum filter length, considering only one effective leaky mode with low attenuation, which considerably simplifies the theoretical studies.     

Fiber mode coupling in transmissive and reflective tilted fiber gratings

Whereas core-mode reflection and core-mode-to-radiation-mode coupling in tilted fiber Bragg gratings is well understood, as is coupling between a core mode and higher-order core and cladding modes in untilted gratings, here we analyze in detail the coupling among core modes and cladding modes in reflective and transmissive tilted fiber gratings. We show that strong coupling between an LP(01) core mode and the exact (1m) cladding modes occurs in a transmissive tilted grating for nearly any tilt angle except angles close to 90 degrees , whereas the LP(01)-to-(lm) cladding mode coupling (l not equal 1) is appreciable only for tilt angles just below 90 degrees (~88 degrees ). In a reflective grating, strong coupling between the LP(01) core mode and the exact (1m) cladding modes occurs only for angles less than ~5 degrees , whereas coupling to (1m) cladding modes for m > 1 occurs only for angles greater than ~5 degrees . Coupling among bound core modes exhibits a similar behavior, except that in general the coupling is stronger. Experimentally we show coupling to both higher-order bound core modes and cladding modes in a transmissive tilted grating at visible and near-infrared wavelengths.     

Bending loss of elliptical-hole core circular-hole holey fibers bent in arbitrary bending directions

A holey fiber having a core with an elliptical-hole lattice structure, which is referred to as an elliptical-hole core circular-hole holey fiber (EC-CHF), can be easily designed as a single-polarization fiber by using the fundamental space-filling modes of the core and cladding lattices. However, because the guided mode in an EC-CHF has a polarization that arises from the large geometric anisotropy of the core lattice, the influence of the bending direction on the bending loss is a crucial issue for the practical implementation of EC-CHFs. Here, the bending losses of an EC-CHF bent in arbitrary angular orientations with respect to the core cross section are calculated numerically using the equivalent anisotropic step-index circular fiber model for a real EC-CHF, and the influence of the bending direction of the fiber on the bending loss is discussed.     

Nonlinear Dispersion Coefficients of a Cylindrical Optical Waveguide

Abstract

The nonlinear carrier wave dispersion relation at weak nonlinearity is derived for the linearly polarized (LP) modes of a step-index optical fibre that has both a nonlinear core and a nonlinear cladding. The calculation begins with the exact equations for the nonlinear fibre and the nonlinear shift (coefficient), from its linear value, of the propagation wave-number is given in closed analytical form. The nonlinear coefficient is completely general and accounts both for the nonlinearity and the structure of the guided mode. Some numerical results for the LP₀₁ mode are presented which show that significant deviations occur from the conventionally accepted (averaged) nonlinear coefficient.     

Control of the characteristics of a long-period grating by cladding etching

We have analyzed the effects of the fiber cladding radius on the characteristics of long-period fiber gratings. By etching the cladding of a common single-mode fiber, we verified the characteristics experimentally. When by etching we reduce the cladding radius of a common single-mode fiber on which a long-period refractive-index modulation has been imposed, the coupling strength of the core and the cladding modes increases. In addition, the difference in the propagation constants (for a fixed wavelength) between the core mode and the cladding modes increases; hence the resonant transmission dip wavelengths shift to longer wavelengths. The proposed method can be useful in making and detuning long-period fiber grating filters.     

Modeling of the loss and mode coupling due to an irregular core-cladding interface in step-index plastic optical fibers

The core-cladding boundary in step-index plastic optical fibers is imperfect. Surface irregularities locked in during the manufacturing process couple the guided modes by reflecting them in directions that deviate unpredictably from the expected directions. This causes an additional loss as the multiple reflections from surface elements with directions randomized around the nominal for the cylinder transfer the power to the radiation modes that are carried away from the core into the cladding. We model such loss and mode coupling by ray tracing. The irregular core-cladding interface is represented by nominally cylindrical surface elements with orientations randomly perturbed around two geometric axes. The results show mode coupling and relative loss per unit fiber length caused by the core-cladding interface irregularities. The loss is high close to the input fiber end where mode coupling is intense. It drops farther along the fiber as mode coupling slows down and stabilizes where the equilibrium mode distribution is reached.     

Propagation and coupling of hybrid modes in twisted fibers

The first-order paraxial approximation is used to obtain the distributions of the electric and magnetic fields for the core and cladding hybrid fiber modes. The coupling coefficients of these modes are found for fibers subject to twist. The longitudinal electric field component determines the mode coupling in twisted fibers. It is shown that in the first-order paraxial approximation the cladding hybrid modes propagating in a twisted fiber rotate along the direction of the twist at the same rate as the core mode, independently of the azimuthal and radial mode numbers. Four hybrid modes constituting one linearly polarized mode have different longitudinal components, and the corresponding cladding-mode resonances of a long-period fiber grating undergo different shifts owing to different mode self-coupling coefficients. This results in the removal of mode degeneracy and splitting of resonances of long-period gratings in twisted fibers.     

Electronically reconfigurable superimposed waveguide long-period gratings

The perturbation to the refractive index induced by a periodic electric field from two systems of interdigitated electrodes with the electrode-finger period l is analyzed for a waveguide with an electro-optically (EO) active core-cladding. It is shown that the electric field induces two superimposed transmissive refractive-index gratings with different symmetries of their cross-section distributions. One of these gratings has a constant component of an EO-induced refractive index along with its variable component with periodicity l, whereas the second grating possesses only a variable component with periodicity 2l. With the proper waveguide design, the gratings provide interaction between a guided fundamental core mode and two guided cladding modes. Through the externally applied electric potential, these gratings can be independently switched ON and OFF, or they can be activated simultaneously with electronically controlled weighting factors. Coupling coefficients of both gratings are analyzed in terms of their dependence on the electrode duty ratio and dielectric permittivities of the core and cladding. The coupled-wave equations for the superimposed gratings are written and solved. The spectral characteristics are investigated by numerical simulation. It is found that the spectral characteristics are described by a dual-dip transmission spectrum with individual electronic control of the dip depths and positions. Within the concept, a new external potential application scheme is described in which the symmetry of the cross-sectional distribution of the refractive index provides coupling only between the core mode and the cladding modes, preventing interaction of the cladding modes with each another. This simple concept opens opportunities for developing a number of tunable devices for integrated optics by use of the proposed design as a building block.     

Evaluation of some GRIN fiber parameters and the associated fraction mode loss due to mechanically induced optical anisotropy

Some of the optical parameters of the bent multimode graded-index (GRIN) optical fiber in terms of indices of refraction, where the bending stresses broke the radial symmetry, are evaluated by use of multiple-beam Fizeau fringes. The variation of the index difference between the cladding index and core index in both the compression and tensile fiber regions is measured. The accuracy of measuring the index is +/- 1 x 10(-4). The spatial resolution of the method is 1.39 microm. Evaluation of the acceptance angle, the numerical aperture, and the V number profiles of the bent fiber from the interference pattern at both sides of the bent fiber are presented. The fraction of the mode number lost has been evaluated. The method was used to study the influence of compression on diminishing the index difference that leads to a dissipation of energy and a considerable mode loss. It is obvious from the experimental data that the change of the index difference due to bending strongly affects the fraction of propagating mode number, especially at the small radii of curvature. Ignoring the variation of the index difference we evaluating the number of propagated modes number leads to an insufficient determination of the mode loss. It subsequently leads to an incorrect determination of the mode dispersion and the interface loss in bent GRIN fibers. The study confirms that the deviation of the guide axis from straightness with the radius of curvature of less than 1 cm could lead to a significant fraction mode loss.     

Modal Characteristics of Five-Layered Slab Waveguides with Double-Clad Metamaterials

The guided modes are investigated in a five-layered slab waveguide with double claddings of metamaterials using a new graphical method. The dispersion equations in the symmetric and asymmetric five-layered slab waveguide are derived from the presented graphical method, and corresponding field distributions are plotted for the oscillating guided and surface guided modes. The energy flux distribution along the axis is plotted for the surface TE₁ mode.     

Coupling characteristics of cladding modes in tilted optical fiber bragg gratings

We have studied both theoretically and experimentally the effect of grating tilting on the coupling between the fundamental core mode and the cladding modes in an optical fiber Bragg grating. The coupling is shown to be very sensitive on the tilting angle. It is also shown that tilting angle has to be minimized in fibers with designs to suppress the coupling between the fundamental core mode and the cladding modes. We have also studied the single, strong loss peak accompanying the Bragg reflection peak in depressed-cladding fibers, thus showing a good agreement between behavior that is measured and that is predicted theoretically.     

光纤灰度分布的高斯函数拟合法测量光纤几何参数

光纤的几何参数影响着光纤的光学传输和机械性能等,是衡量光纤质量的重要指标。近场光分布法是国标GB 15972.20-2008中推荐的几何参数测量方法。该方法在对光纤纤芯的测量中需对光纤通光照明,以区分纤芯和包层的边界。通光的纤芯端面是一个边缘并不清晰的发光亮斑,因而无法准确判断纤芯与包层的真实边缘。本文分析了光纤内光传播模场的分布,理论上光纤模场电磁矢量的解满足贝塞尔函数,但在近似情况下也可以用高斯函数代表光纤模场分布。因此本文利用高斯函数拟合光纤纤芯端面灰度分布,进而由拟合后的高斯函数得到纤芯与包层的真实边缘。本方法是对国标GB15972.20-2008的测量方法的进一步完善。实验测量结果表明,当光纤的切割效果不佳或成像质量较差时,模场灰度分布的高斯函数拟合法仍能保证测量的重复精度和测量数据的稳定性。