Refractive index design and validation for evanescent field power maximization in optical fibre sensors

The viability and operation of evanescent field-based optical fibre sensors is largely determined by the fraction of the total supported modal field power in the evanescent field. As this fraction is highly dependent on the refractive index profile of the fibre, one design strategy for fibre sensors is to maximize this field power fraction over the class of all refractive index profiles. This paper documents this design strategy for circular geometry optical fibres, where the goal is to maximize the evanescent field power fraction for a particular mode via the selection of an optimal refractive index profile. The axially symmetric profiles obtained approximate “holey” annular structures, the performance of which can be validated using existing waveguide analysis techniques.     

Non-linear propagation of laser beam and focusing due to self-action in optical fiber: Non-paraxial approach

A somewhat more general analysis for solving spatial propagation characteristics of intense Gaussian beam is presented and applied to the laser beam propagation in step-index profile as well as parabolic profile dielectric fibers with Kerr non-linearity. Considering self-action due to saturating and non-saturating non-linearity in the refractive index, a general theory has been developed without any kind of power series expansion for the dielectric constant as is usually done in other theories that make use of paraxial approximation. Result of the steady state self-focusing analysis indicates that the Kerr non-linearity acts as a perturbation on the radial inhomogeneity due to fiber geometry. Analysis indicates that the paraxial rays and peripheral rays focus at different points, indicating aberration effect. Calculated critical power matches with the experimentally reported result.     

有限元法求解任意折射率分布光纤模场分布

 应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

On the vertical structure of the sound field in a canonical waveguide at long ranges

The geometrical-acoustics approach is used to calculate the vertical structure of the sound field in an oceanic waveguide. The profile of the sound speed is specified to be canonical and range-independent along a 1000-km propagation path. A monochromatic sound source lies on the waveguide axis. It is shown that, at long distances from the source, the sound field formed by the water-path rays is mainly concentrated in the caustics, the number of which is determined by the number of the overlapping ray cycles at a given distance. A method for estimating the amplitude of the sound field produced by individual rays is proposed. The amplitudes obtained are used to calculate the total sound field along the vertical. A possible cause of the chaotic distribution of ray coordinates is considered. This cause may consist in the arbitrary choice of the number of rays and their departure angles without taking into account the discrete character of one of the variables. This mechanism of ray chaos formation furnishes an explanation for the fact that the chaos obtained in calculations is mainly associated with the flat rays.     

Mode analysis of realistic optical waveguide structures and microstructured holey fibers by modal field evolution

In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties.     

Mode excitation in circularly symmetric graded-index optical fibers by focused gaussian beams

Field distributions and propagation constants of modes in weakly guiding circularly symmetric optical waveguides having arbitrary radial refractive index distribution are determinable from a variational analysis, which uses the solution of the scalar wave equation for the infinitely extended parabolic refractive index profile as a reference (Laguerre-Gaussian functions). The power coupling coefficients of the power, which is transferred from a focused Gaussian beam to an LP_vp-mode, depend on frequency and on four normalized launching parameters. Once the field-describing matrix equation has been solved numerically, closed-form expressions are obtained. The condition for optimal matching of the fundamental mode is given, and it is found that the maximum power excitation coefficient may be close to 100% even for substantially disturbed profiles.     

Mode excitation in circularly symmetric graded-index optical fibers by focused gaussian beams

Field distributions and propagation constants of modes in weakly guiding circularly symmetric optical waveguides having arbitrary radial refractive index distribution are determinable from a variational analysis, which uses the solution of the scalar wave equation for the infinitely extended parabolic refractive index profile as a reference (Laguerre-Gaussian functions). The power coupling coefficients of the power, which is transferred from a focused Gaussian beam to an LP_vp-mode, depend on frequency and on four normalized launching parameters. Once the field-describing matrix equation has been solved numerically, closed-form expressions are obtained. The condition for optimal matching of the fundamental mode is given, and it is found that the maximum power excitation coefficient may be close to 100% even for substantially disturbed profiles.     

Ti：LiNbO3光波导导模的场分布

给出了Ti扩散LiNbO_3条波导任意阶导模场分布的试探解.通过变分法分析,不但可以合理地确定其中的待定参数,而且也得到了相应导模传播常数的近似值.与扩展的有效折射率方法比较:这种解不但在函数形式上简单,待定常数确定方便,而且具有精度高的优点.还可以得到等效一维波导折射率分布的解析表达式.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Focusing diffused waveguides

Focusing optical fibre and thin film guide can be made to have nearly the same group velocity for every mode if the optimum distribution of refractive index or thickness of the film is realized. A focusing optical fibre is manufactured from a multilayer glass rod by solid state diffusion. A thin film waveguide is prepared from nitrocellulose by controlling the airflow distribution. Undulation of light propagating in the film is observed, and it is confirmed that the focusing property is determined by the distribution of the film thickness. The field distributions of the TE modes have been analysed for an optical waveguide fabricated by solid state diffusion. Glass waveguide has been manufactured with the appropriate concentration of lead ions to give the maximum propagation constant. A low loss waveguide is fabricated by the diffusion of lead or thallium ion into glass followed by selective etching.     

(Al)GaAs/AlGaAs周期光波导中的等幅基模

本文应用周期介质光波导的模场分布函数和特征方程分析了(Al)GaAs/AlGaAs周期光波导中结构参量及介质折射率对模场分布形状的影响,研究了波导中形成等幅基模的条件,讨论了相应参量的优化选择。     

Mode field distribution of an integrated-optical waveguide generated by UV-laser radiation at the surface of a planar polymer chip

An integrated-optical strip-waveguide is directly written into the surface of a planar polymer substrate by an excimer laser beam. The mode field distribution, the surface refractive index and the refractive index depth profile of the waveguide have been examined. The intensity distribution of the mode field strongly depends on the refractive index depth profile, on the light coupling conditions and on the waveguide fabrication process parameters.     

Efficient coupling of a laser to a waveguide using a taper designed by conformal mapping

Maximising the optical power collected in a waveguide from the diffracting field of a semiconductor laser is desirable in optical fibre communication systems. However, the spot size and phase front curvature of the laser field usually makes a poor overlap with the mode of the receiving waveguide. Various proposals have been made to improve this coupling. This paper presents the design of a tapered waveguide section, having the correct geometry and refractive index profile, to efficiently capture and transform the rapidly diffracting light from a semiconductor laser to a planar wavefront in a straight waveguide. Experimentally, such an approach requires the refining of available techniques (UV exposure, ion implantation or diffusion) to obtain the required grading of the refractive index profile within the tapered input section of the receiving waveguide.     

Noise field anisotropy of surface sources in a coastal region with arbitrary bottom relief and sound velocity profile

The noise field anisotropy of surface sources in a coastal region with an arbitrary three-dimensional bottom relief and an arbitrary sound velocity profile is investigated. The results of computations performed by a computer code in two stages are presented. The first stage consists in the computation of horizontal rays, i.e., the projections of the real rays multiply reflected from the bottom and sea surface onto the horizontal plane. The second stage summarizes the contributions of the noise sources lying within the surface elements that are cut out on the sea surface by a narrow ray tube launched from the point of observation in a given direction. The computations show that, in the coastal region, the noise field is essentially anisotropic, and this anisotropy occurs not only in the vertical plane, which is characteristic of the deep ocean, but in the horizontal plane as well.     

Beam propagation in elliptical fibres

We apply an operator method, based on the scalar wave equation, to study the propagation of a Gaussian light beam in an optical fibre with an arbitrary, elliptically symmetric refractive-index profile. We discover that ray optical results, while not capable of predicting the rapid distortion of an optical beam in a non-ideal refractive-index profile, successfully simulate the general form of the optical power distributions, even in non-ideal profiles. We find that the propagation patterns for elliptical fibres with and without a strongly scattering central index dip show several unexpected similarities.     

聚焦法测量塑料光纤折射率分布的可行性研究

结合理论分析和实验验证,探讨了聚焦法测量塑料光纤纤芯的折射率分布的可行性。结果表明,对GI-POF而言,聚焦法是一种简单可行的技术.但是对SI-POF,由于入射光线在光纤边界处发生交叉,聚焦法不能精确测量其折射率分布.     

Probability distributions for the stress tensor in conformal field theories

The vacuum state—or any other state of finite energy—is not an eigenstate of any smeared (averaged) local quantum field. The outcomes (spectral values) of repeated measurements of that averaged local quantum field are therefore distributed according to a non-trivial probability distribution. In this paper, we study probability distributions for the smeared stress tensor in two-dimensional conformal quantum field theory. We first provide a new general method for this task based on the famous conformal welding problem in complex analysis. Secondly, we extend the known moment generating function method of Fewster, Ford and Roman. Our analysis provides new explicit probability distributions for the smeared stress tensor in the vacuum for various infinite classes of smearing functions. All of these turn out to be given in the end by a shifted Gamma distribution, pointing, perhaps, at a distinguished role of this distribution in the problem at hand.

     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

Investigation of the near field distribution in circular nanostructures using Stokes polarization states

In this paper, the near field distribution patterns formed from nanostripe corral and half spiral are investigated. Various near field distribution patterns are generated owning to the interference of propagating surface plasmon waves that emerged from the nanoslits or nanostripe. The half spiral nanoslits are illuminated with Stokes polarizations. Each polarization state shows a different field pattern at different locations on the surface of metal film. This is due to the excitation of surface plasmon waves at different parts of the nanostructures when illuminated with different types of polarization states. The same Stokes polarization states are also illuminated on a nanostripe corral structure. In this case, dipolar field distributions are observed when illuminated with different linear polarization states, while optical vortices are observed for circular polarization. It is believed that these interesting field patterns due to different arrangements of nanostructures could be used for near field imaging and polarization sensing.