Core-cladding Interface Research Articles

Empirical Evaluation of Profile Variations in an MCVD Optical Waveguide Fiber Using Modal Structure Analysis

This paper presents a computer modeling evaluation of the effect on mode propagation of typical perturbations in the refractive index profile produced as a result of the MCVD process. Certain profile variations were eliminated, singly and/or collectively, and the resultant changes in modal structure analyzed. The most important factor in the deterioration of the bandwidth is the presence of a refractive index dip at the core center. Small shifts in the level of dopant were seen to broaden pulse shapes and thus reduce bandwidth. Much less effect on bandwidth is associated with the ripples in the profile, as is also true for dips in refractive index below the index of the cladding near the core-cladding interface. A perpendicular rise, or step, in index of refraction at the core-cladding interface reduces the number of altered modes near the cladding.

A fluoride glass optical fiber operating in the mid-infrared wavelength range

An optical fiber operating in the mid-infrared wavelength range is fabricated using ZrF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> -based fluoride glass. Material purification, the fiber fabrication process, and transmission properties are presented. The starting materials, ZrF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> , BaF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , GdF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> , AlF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> , and SbF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> are carefully purified by sublimation techniques. The "built-in" casting technique, specially developed for fluoride glass fiber, is used for preparing cladded type fiber with a smooth core-cladding interface. Spectral loss is measured in the 0.7- to 5.5-μm wavelength region, and a minimum loss of 12 dB/km is attained at 2.55 μm. Based on the refractive-index spectrum measured in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.4-5-\mu</tex> m range, material dispersion characteristics are also investigated. It is indicated that material dispersion falls to zero at 1.52 μm and exhibits a gentle wavelength dependence in the present glass system.

Sensitivity analysis of the Sagnac-effect optical-fiber ring interferometer

The sensitivity of a recently reported optical-fiber ring interferometer as a gyroscope has been analyzed. Photomixing SNRs were derived for the detection schemes. Noise sources due to the Rayleigh, Brillouin, Mie, and core-cladding interface light scattering processes are assessed quantitatively. Optimum gyroscope sensitivities are discussed via numerical examples for optical wavelengths lambda = 0.633 microm and lambda = 1.1 micro and both spontaneous and stimulated noises. Results show that (a) to reduce trapped scattered light by a factor of 100, mode stripping is essential, (b) lambda = 1.1 microm is a more promising wavelength to use, and (c) high optical power operation, where the only noise is due to stimulated Brillouin scattering, gives better sensitivity than the low-power case. Examples show that at lambda = 0.633 microm, the achievable sensitivities are 0.0078 deg/h at 2 mW and 0.0009 deg/h at 81 mW; and at lambda = 1.1 microm, they are 0.0025 deg/h at 2 mW and 0.0007 deg/h at 14.4 mW. These calculated sensitivities are better than those of current laser ring gyroscopes.

Optical fiber preform diagnostics

A sensitive, nondestructive, and noncontacting method is described for obtaining structural information on the preforms from which optical fibers are produced. The technique allows the determination of the core size and the core eccentricity from direct observation of light traversing the preform normal to its axis. Also observable are the core-cladding interface structure, individual deposition layer structure and variations, imperfections within the core and the cladding, and the presence of an axial refractive-index depression. Results and implications from a variety of multimode and single-mode preforms are presented along with a theoretical analysis of the observations.

The step index limit of power law refractive index profiles for optical waveguides

We demonstrate the breakdown of the usual WKB expressions for tunneling ray power transmission coefficients on multimode optical wavequides with power law refractive index dependence, when the profile approaches the step index limit. A qualitative analysis provides a solution valid in this transition region, which also quantifies the domain of applicability of the WKB analysis. The latter is much more restricted than the usual condition on the slope of the profile predicts, and is due to the abrupt change in slope at the core-cladding interface.

Coupling of Torsional Modes in a Clad-Rod Having a Sinuosidally Perturbed Core-Cladding Interface

A multiple scales perturbation technique is presented for the propagation of torsional acoustic modes in a clad-rod ultrasonic delay line in which the radius of the core varies sinusoidally in the axial direction. The cladding is assumed to have a finite thickness in the analysis. It is shown that two forward guid+ modes are strongly coupled by the undulations if the difference between their wavenum- bers is n+ly equal to the wavenumber of the wall kW Also, if kW is nearly equal to the difference of the wavenumbers of a forward mode and a backward mode, then they are strongly coupled; in this case, the true modes of the perturbed system may be cut off depending on the detuning. These findings can be utilized in the design of single-mode waveguides and mode couplers. Examples are given for a clad rod at a frequency of 10'MHz. N THIS paper we consider mode coupling in a clad-rod ultrasonic delay line whose corecladdhg interface is sinu- soidally perturbed in the direction of propagation. This prob- lem is encountered in delay line work as'a result of the com- mercid extrusion process of wires'( 11 . his effect is undesirable in practice because the energy of the incident mode is shared by other modes, leading to time delay distor- tion of a signal. However, as shok in this paper, mode coupling cari be a desirable feature, if the periodic nonuni- formity is built into the waveguide in an orderly manner and for a specified length so as to produce energy transfer from one propagating mode into another. Armenlkas (2) and Thurston (3) investigated the propaga- tion of torsional waves in a clad rod with finite cladding thick- ness. Waldron (4) treated the problem of wave propagation in a uniform homogeneous rod surrounded by an infinitely thick cladding, while Lai, Dowell, and Tauchert (S) treated the problem of wave propagation in a uniform homogeneous rod surrounded by a finitely thick cladding. Boyd, Coldren, and Thurston (6) proposed the use of clad rods as ultrasonic de- lay lines because the cladding minimizes the effects of the supports. Thurston (3) considered the case of a uniform homogeneous rod immersed iri a viscous fluid and showed that modes higher than the firit are sharply attenuated. This pro- cess yields a single-mode waveguide operating with the lowest mode.

Scattering and Absorption Losses of Multimode Optical Fibers and Fiber Lasers

We present an approximate theory of loss coefficients for modes of step-index fibers with various types of distortions and for fibers with lossy claddings. The fiber irregularities are assumed to be sinusoidal and random variations of the core-cladding interface. Formulas for the loss coefficients are presented and plotted for different values of the compound mode number M. For fiber lasers, we plot the loss coefficients as functions of the mirror tilt angles. We consider as an example a Nd-YAG fiber laser with refractive index n 1 = 1.8 and a core radius of a = 40 µm operating at a wavelength of λ = 1.06 µm. For this example, we find that radiation losses are caused by Fourier components of fiber irregularities in the spatial wavelength range between 0.4 and 1.3 µm. Intrinsic losses may be as low as 2α = 10−3 cm−1. It is thus desirable to limit scattering losses to values below 10−3 cm−1. This requirement imposes tolerance restrictions of 0.01 µm on the permissible core radius fluctuations. For core radius fluctuations of this order of magnitude, mirror tilts should not exceed approximately 5 degrees. Cladding losses are not critical, but their influence on laser losses depends on the refractive index ratio of the core and cladding materials. Tolerable cladding losses may range from 10 to 300 cm−1.

Design consideration for digital systems using multimode fibre with lossy cladding

Digital systems using multimode fibres with a step-index profile, a lossy cladding and a low-loss core are treated in the letter. The influence of fibre numerical aperture (n.a.) on repeater spacing is examined when the total core-cladding interface loss results from Fresnel reflection. It is shown, by way of example, that in this case there is no advantage in using low n.a. values, even at moderate modulation rates, owing to a diminishing receiver incident optical power with decreasing n.a.

Optical fiber modes using stimulated four photon mixing

Stimulated four photon mixing has been used to excite separately all the modes of a ten-mode optical fiber. Photographs were taken and the mode intensities scanned with a moving pinhole. Measured intensities were found to agree well with the intensities calculated for an ideal guide with an abrupt core-cladding interface. In addition a locking effect was observed in which two separate Stokes:anti-Stokes pairs, which normally occur at slightly different frequency shifts from the pump, locked together at the same frequency.

Modal dispersion in multimode graded-index fibers

A complete analysis of the propagation characteristics of a ray through an axially symmetric graded-index medium is carried out in the geometrical optics approximation. First, two constants of the motion are shown to exist for a ray propagating in an infinite medium. Secondly, these constants of the motion are shown to be invariant when reflection occurs on the core-cladding interface of cladded graded index fibers. This conservation law allows the study of the propagation characteristics of a ray through a fiber even though its trajectory may be discontinuous because of reflection at the core-cladding interface. The temporal behavior of various cladded parabolic-index fibers is given by their impulse responses when excited uniformly by parallel beams under different input angles. Rays are shown to propagate in two different ways: a reflected type of propagation takes place through reflections on the core-cladding interface, and a selfocusing type of propagation where rays go through the fiber core without touching the cladding.

Calculation of the matching of an injection laser to a dielectric waveguide

Calculations are reported of the parameters of a rectangular-core fiber waveguide needed to achieve an efficient matching to an injection laser which is in direct optical contact with the waveguide. Simple expressions are obtained for the relationships between the permittivity discontinuity at the core-cladding interface and the optimal thickness of the core on the one hand, and the laser parameters on the other. The requirements which the passband of the waveguide must satisfy impose restrictions on the laser-waveguide coupling coefficient. If the permissible distortion of a laser pulse is 30 nsec/km, about 65% of the injection laser radiation can be coupled into the waveguide.

Tunnelling leaky modes on optical waveguides

The lossless dielectric waveguide of circular cross section with an index of refraction greater than its surround supports trapped modes in addition to two subclasses of leaky modes: refracting and tunnelling modes. Refracting modes leak because their fields are formed by waves that undergo refraction at the core-cladding interface. Tunnelling modes leak because their fields are formed by waves that undergo a form of electromagnetic tunnelling at the core-cladding interface due to the curvature of its cross section. Tunnelling modes have a very slow leakage compared to refracting modes and are therefore important for the understanding of propagation in multimode, optical waveguides of circular cross section.

Evaluation of Fiber Optical Waveguides Using Brillouin Spectroscopy

Optical scattering loss in fiber optical waveguides is the sum of the bulk material scattering and excess scattering loss due to imperfections in the waveguide structure. The recently developed Brillouin spectroscopic technique for evaluating bulk scattering has been extended to fiber waveguides, and a detailed investigation has been performed on a borosilicate clad-pure fused silica core waveguide. The technique has been found to be useful in evaluating scattering due to waveguide imperfections that have been determined to occur at the core-cladding interface. In addition to providing a measure of the waveguide scattering loss, the Brillouin technique has also been found to be useful in determining the molar composition of the borosilicate cladding glass and the partition of guided optical power between the core and cladding regions. The unusual capabilities of this technique should make it generally useful for characterizing integrated optical structures.

Theory of scattering from the core of a multimode fibre waveguide

A theory suitable for the interpretation of measurements of light scattering from cladded multimode optical fibres is presented. The model used is based on geometrical optics and enables the effects of depolarization, the angular distribution of the propagating beam, as well as refraction and reflection at the core-cladding interface to be taken into account. Good agreement is obtained between the theory and experiment.

A New Optical Fiber

Currently there is strong interest in optical fibers for use as a transmission medium, analogous to the use of coaxial or wire pairs in the low-frequency region. Most work is devoted to a fiber structure consisting of a central glass core surrounded by a cylindrical glass cladding having a slightly lower index of refraction. This in turn requires that the chemical composition of the core glass differs from that of the cladding glass, leading to undesired effects at the core-cladding interface and perhaps limiting the minimum fiber losses achievable.

Higher-Order Scattering Losses in Dielectric Waveguides

This paper discusses the scattering losses of dielectric slab waveguides that are caused by higher-order grating lobes of the sinusoidally distorted core-cladding interface. The results of this paper are used in a companion paper to evaluate the radiation losses of multimode guides with intentional mode coupling. An exact system of equations is derived for the amplitudes of all grating orders. This system is used to derive first- and second-order approximations that hold for small amplitudes of the sinusoidal interface distortion. The theory is used to derive formulas for the average power loss coefficient for first- and second-order scattering processes.

Pulse Propagation in Multimode Dielectric Waveguides

Using coupled power equations to describe the average performance of a multimode waveguide with random coupling, it is shown that a Gaussian input pulse remains approximately Gaussian with a pulse width that increases proportionally to the square root of the length of the waveguide. The proportionality factor is determined for the model of a slab waveguide. Since coupling between guided modes of necessity causes coupling of some of the guided modes to radiation modes, radiation losses are un-avoidable. A desired improvement in pulse distortion that is accomplished by coupling the guided modes intentionally to each other must be paid for by a certain loss penalty. This loss penalty is also evaluated for the special case of the slab waveguide model. Pulse dispersion improvement can be achieved by providing intentional roughness of the core-cladding interface of the dielectric waveguide. The “power spectrum” of the core-cladding interface function must be designed very carefully in order to minimize the radiation loss penalty that accompanies any attempt to reduce pulse dispersion. The dependence of the loss penalty on the shape of the “power spectrum” of the core-cladding interface function is studied in this paper. Design criteria for the improvement of multimode pulse dispersion are given based on the slab waveguide model. The connection between the slab waveguide model and the round optical fiber is pointed out.

Propagation model for multimode optical-fibre waveguide

Pulse dispersions of 5 ps/m have been measured in cladded-glass and liquid-core multimode fibres. A theoretical model is proposed which gives excellent agreement with measured propagation delay and pulse dispersion. In the fibres used, there is little light scattering either in the core or at the core-cladding interface.

Power Distribution and Radiation Losses in Multimode Dielectric Slab Waveguides

Guided modes of multimode waveguides exchange power if the waveguide deviates in any way from its perfect geometry. The power exchange problem is studied for a multimode slab waveguide under the assumption that the power coupling is caused by irregularities of the core-cladding interfaces. The problem is treated by means of coupled power equations. The main result of this study is the realization that the power distribution versus mode number settles down to a steady state distribution if the waveguide is sufficiently long. The shape of the steady state distribution depends on the correlation length of the function describing the core-cladding interface irregularities. For very short correlation length only the lowest-order mode carries an appreciable amount of power while the power carried by all the other modes is orders of magnitude smaller. For very long correlation length, on the other hand, all guided modes carry equal amounts of power. The steady state distribution is achieved regardless of the way in which the power was distributed over all the modes at the beginning of the guide. However, the total power in the steady state mode distribution is dependent on the initial power distribution.

Influence of Temperature and Pressure on Dispersion Properties of Nonlinear Single Mode Optical Fibers

Near field distribution, propagation constant and dispersion characteristics of nonlinear single-mode optical fibers have been investigated. Shooting-method technique is used and implemented into a computer code for both profiles of step-index and graded-index fibers. An error function is defined to estimate the discrepancy between the expected electric-field radial derivative at the core-cladding interface and that obtained by numerically integrating the wave equation through the use of Runge-Kutta method. All of the above calculations done under the ocean depth in which the depth will affect the refractive index that have a direct effect on all the optical fiber parameters.KeyWords: Nonlinear refractive index, Normalized propagation constant, Mode delay factor, Material dispersion, Waveguide dispersion.