Showing papers in "Flow Turbulence and Combustion in 1984"

Polarization-Maintaining Fibers

Abstract: The parameters that determine the polarization-maintaining ability and the polarization-dispersion of a birefringent fiber are discussed in a tutorial fashion. Based on promising theoretical and experimental results, I conclude that fibers with adequate polarization-maintaining properties for sophisticated heterodyne and homodyne applications are physically realizable. It is also concluded that polarization-dispersion in nominally circular single-mode fibers is not likely to be a limitation for next-generation systems.

TE modes of a layered nonlinear optical waveguide

Abstract: The general theory is given of the propagation of electromagnetic TE modes in a layered structure consisting of a homogeneous dielectric layer between two homogeneous optically nonlinear semi-infinite dielectrics. Allowance is made for the nonlinear coefficients of the nonlinear media to be different and a detailed analysis is given, together with the appropriate formulae for the power flow down the guide, as a function of guide wave number, and layer thickness. Detailed consideration is given to the existence conditions for surface waves.

Elastostatics as a limit of elastodynamics – a matrix formulation

Abstract: A T matrix formulation of the three-dimensional elastostatic single inhomogeneity problem is presented. It is shown how it can be obtained as a zero frequency limit of the T matrix formulation of a corresponding time-harmonic scattering problem. Numerical results for some rotationally symmetric cavities are given.

Wave propagation in fluid lines

Abstract: The wave propagation in a fluid line consisting of a circular tube, initially stressed, viscoelastic, orthotropic, surrounded by external materials, containing a compressible linear elastic fluid is considered under isentropic conditions. The dispersion equation is derived and a number of simplifications are discussed. The impedances of the line and the transfer matrix are given.

Approximate dispersion equations for thin walled liquid-filled tubes

Abstract: The dispersion equation for an initially stressed thin walled viscoelastic tube filled with a linear elastic fluid is derived The validity is discussed of the long wavelength approximation, of an inviscid liquid in a viscoelastic tube, while a new approximate dispersion equation is derived, that can be applied in the higher frequency range

Leaky-wave modes and their role in the numerical evaluation of the field excited by a line source in a non-symmetric, inhomogeneously layered, slab waveguide

Abstract: In scattering problems in open-waveguide configuations source-type representations for the fieldcomponents in the cross sections of the waveguides are needed. The relevant representations can be found using a special approach with respect to time and with respect to the longitudinal coordinate. In the spectral representation we consider those spectral constituents that can be excited by a source of finite extent. Such an approach naturally leads to the concept of modes and it also gives a better understanding of the role of leaky-wave modes, the latter being part of the radiation field. In piecewise homogeneously layered (multi-step-index) waveguides, the spectrum can be constructed from analytical representations of the field, whereas in the more general, inhomogeneously layered (graded-index) waveguides the field representations as well as the spectrum has to be found numerically. In this context, we have investigated numerically the canonical problem of the line-source excitation of planar, open-waveguide configurations. In the subsequent computations, the spatial Fourier contour is deformed into a path of steepest descent that passes through a saddle point of the argument of the propagation factor of the field in the complex Fourier-transform variable plane. The latter path is situated on various sheets of a multi-sheeted Riemann-surface. The contribution from all poles (surface-wave as well as leaky-wave poles) that are circumvented in this process have to be determined. These are the surface-wave poles that are located on the physically acceptable Riemann sheet and two types of leaky-wave poles (air leaky-wave poles and substrate leaky-wave poles) that are located on other Riemann sheets. The properties of the field distributions of the corresponding surface-wave and leaky-wave modes, and Itlhere possible their interrelationship, are discussed for various syammetric and non-symmetric planarwaveguide configurations.

Transverse radiation pressure and torque exerted by a plane electromagnetic wave on a rotating circular cylinder of isotropic material

Abstract: Relativistically correct expressions are derived for the time-averaged total force and torque acting on a rotating conducting circular cylinder, immersed in an incident plane electromagnetic wave. With the help of Maxwell's stress tensor analytical expressions can be obtained for the time-averaged force and torque.

Natural convection heat transfer from square cylinders

Abstract: Experiments were carried out to measure the average natural convection heat transfer from the outside surface of isothermal square cylinders of different lengths and side-lengths at different angles of inclination in both the laminar and the turbulent regions. The heat transfer was found to depend on the side-length and the inclination. Due to the presence of edge-effects the heat transfer coefficient always exceeded that of the vertical plate and that of “the equivalent circular cylinder” in the same condition. General equations representing the experimental results are suggested.

Mode conversion analysis in a single-mode planar taper optical waveguide

Abstract: We have investigated mode conversion in a taper waveguide used in a planar multi-branch waveguide optical power divider designed for fundamental mode operation and fabricated by Ti-diffusion into a z-cut LiNbO3 substrate. With an appropriate aspect ratio and index distribution in the taper, mode conversion loss into a higher-order mode can be maintained under 5%.

Thermal oscillations of a particle-fluid mixture with horizontal temperature gradient

Abstract: The problem of thermal convection instability of a horizontal fluid layer with suspended particles has been studied for low-Prandtl number in the presence of vertical and horizontal temperature gradients. It has been found that the critical Rayleigh number (for both free and rigid conducting boundaries) increases due to the presence of particles. We also find the oscillatory modes for a vanishingly small Prandtl number. The critical Rayleigh number is inversely proportional to the wavelength. Due to the effect of suspended particles the frequency increases while the wavelength decreases. We have to find out the approximate stability characteristics.

Waves with random coupling and random propagation constants

Abstract: We study the mathematical treatment of transmission statistics of coupled wave devices with random imperfections. Such devices include multi-mode waveguides or optical fibers, directional couplers at waveguide or optical frequencies, dominant-wave transmission lines (with the reflected wave the spurious mode), lumped filters composed of circuit or of waveguide elements, multi-layer optical coatings to achieve high or low reflectivity. If the random parameters have very rapid spatial variations, we assume they have white spectra. Exact results for transmission statistics are obtained in such cases. These exact results can be extended to random parameters with almost-white spectra, and narrow-band spectra that are far from white. These calculations are carried out in a simple way by using Kronecker matrix products.

Flow through a helically coiled annulus

Abstract: In this paper the flow is studied of an incompressible viscous fluid through a helically coiled annulus, the torsion of its centre line taken into account. It has been shown that the torsion affects the secondary flow and contributes to the azimuthal component of velocity around the centre line. The symmetry of the secondary flow streamlines in the absence of torsion, is destroyed in its presence. Some stream lines penetrate from the upper half to the lower half, and if λ is further increased, a complete circulation around the centre line is obtained at low values of λ for all Reynolds numbers for which the analysis of this paper is valid, λ being the ratio of the torsion of the centre line to its curvature.

Throughput and Coupling in Optical Fibers

Abstract: We show how to apply the concept of optical throughput, product of area times solid angle to emitters and fibers, in order to simplify calculations of coupling efficiency. We show that throughput conservation yields readily the maximum theoretical coupling efficiency, independently of intervening optics.

Nonlinear wave propagation in optical fibres

Abstract: A generalised mathematical theory leading to the evolution equation of nonlinear pulses propagating in an optical fibre waveguide is presented. The magnitudes of the optical self-steepening and third-order dispersion coefficients are calculated and their relative importance is assessed. The possibility of self-steepening is carefully examined and represented on a pulse-displacement-distance parameter diagram. It is concluded, for specimen single mode fibre data, that, even for a 1% deviation from zero group dispersion, the shock term interacts with the group dispersion to produce a pulse distortion in the form of a velocity change limited by the group dispersion rather than selfsteepening. Also, for such a fibre, self-steepening is so small that vast runs down the fibre are required for it to be seen. Any observation of self-steepening in fibres will require much closer tuning to zero group dispersion and will need the suppression of the third-order term.

New physical effects on periodically grooved optical planar waveguides

Abstract: Open dielectric waveguides are of prime importance in the field of integrated optics. Almost all of the published literature concerned with guiding, radiating or scattering effects on open dielectric structures involves a surface wave striking a structural discontinuity at normal incidence. Under those conditions, the TE and TM modes remain independent of each other. When the surface waves are incident at an arbitrary angle, however, the TE and TM modes couple to each other at the geometrical discontinuity, giving rise to a rich variety of interesting and sometimes unexpected new physical effects. We have previously examined such TE-TM mode coupling, and the interesting new physical effects that result from it, in the context of uniform open waveguiding structures. We found that on most dielectric strip waveguides leaky modes can occur instead of the previously expected purely-bound modes, and that resonance effects appear in the leakage process. Furthermore, these leaky modes constitute a new class of leaky modes, since the leaking energy possesses a polarization opposite to tl~at present in the main body of waveguide, in contrast to customary leaky modes. Here we are concerned with periodically-grooved open dielectric waveguides, involving a wide planar dielectric layer. We find that guidance in a direction oblique to the grooves produces four stop bands instead of the usual two in the Bragg reflection region; also produced are interesting anisotropy phenomena such as beam steering and focusing, radiation at peculiar skew angles, and surprisingly large cross-polarization effects. The physical effects are relevant to integrated optics components such as multiplexers, filters and mode deflectors. The guidance of optical surface waves propagating in a direction normal to the grooves on a periodically:corrugated planar dielectric waveguide is well known, and various theoretical treatments are available. Such structures have been used in grating couplers and in distributed-feedback lasers, for example. The electromagnetic boundary-value problem for the case of normal incidence is scalar, however, where the TE and TM surface waves remain independent of each other. When the

Some thoughts on the education of optical waveguide engineers

Abstract: It is difficult to discuss education in optical waveguides in specific terms. Details of a course will depend on whether it is at undergraduate or postgraduate level, for technicians or as a form of re-education for practising engineers. The initial knowledge of the students is also of importance and this will depend on the country - the university systems in England and China, for example, will be rather different. In view of these difficulties you may ask, therefore, why I should say anything at all about the topic and the answer to this question is twofold. Firstly I have been asked to say something - but this is only a necessary, and not a sufficient, condition. Secondly, there are a number of fundamental principles which can be proposed for the education of all engineers and others who apply their knowledge for practical purposes. I propose to concentrate on these fundamentals, leaving the discussion of specific proposals to other speakers.

Curvature-induced oscillations of the loss of leaky modes in optical fibers: a ray analysis

Abstract: A new curvature loss formula for leaky modes is derived from a direct application of the volume current method. This formula is confirmed in the particular case of a leaky LP01 mode in a DIC fiber with a moderate curvature, by means of combination of the standard analytical perturbation analysis of DIC fibers with a ray analysis of the field in the outer cladding. Curvature induced oscillations of the leakage loss are predicted, due to an interference effect. The validity of the new loss formula for larger curvatures is discussed.

The classification of orthogonal electromagneto-fluid-dynamic flows

Abstract: A theoretical analysis based on the equations of electromagneto-fluid-dynamics is undertaken in order to completely classify the flow geometries admitted by these equations. The steady two-dimensional flow of a viscous incompressible fluid of finite electrical conductivity and non-zero electric charge density is considered. The flow equations are formulated in terms of the streamfunction and magnetic flux function as independent variables. The exact analytical solution of the resulting equations is obtained when the magnetic field and the velocity field are everywhere orthogonal to each other. It is shown that the only possible flow is a uniform parallel flow.

Noise analysis of refractive index profile measurements of an optical fibre and preform by deflection function techniques

Abstract: It is shown that many of the existing index profiling methods for optical fibre and preform are related to one another through the deflection function from which the index profile is reconstructed. These methods are classified into direct deflection function measurement, integral (or phase) measurement, and differential (or intensity) measurement. The deflection function from the integral method is obtained by measuring the phase distribution of the exit rays followed by numerical differentiation. Thus the reconstructed index profile has Gaussian noise. The deflection function from the differential method is obtained by measuring the light intensity distribution followed by a numerical integration. This process enhances low frequency noise but suppresses high frequency noise. The noise from direct method behaves in the similar manner as in the differential method except that it is less pronounced. Studies of the choice of methods for profiling of preform, multimode fibre and single mode fibre are also given.

Beam propagation in the paraxial approximation

Abstract: We present a new method for studying the propagation of beams in the paraxial approximation.

Radial jet in rotating outer flow

Abstract: The rotating radial jet formed by fluid introduced radially outwards into a rotating environment is studied by the momentum integral method and by perturbation for weak swirl, assuming incompressible laminar flow. For non-swirling outer fluid, the results slightly extend previously published results. For swirling outer fluid, the jet is characterized by a finite radial penetration distance. Its development over that distance is divided into three regions: an initial adjustment, a central pseudo-similarity region, and a final decay.

Dispersion of tubular modes

Abstract: I show that a theoretical expression for the dispersion (d2β/dω2) of tubular modes in dispersive multimode square-law fibers coincides with the wave-optics result.

Phase-locked InGaAsP laser array with diffraction coupling

Abstract: A phase-locked array of InGaAsP lasers has been fabricated for the first time. The array utilized diffraction coupling between 10 adjacent lasers to achieve phase locking. Threshold current as low as 200 mA is obtained for arrays with 250 μm cavity length. Smooth single-lobe far field patterns with beam divergence as narrow as 3° have been achieved.