Step-index Single-mode Fiber Research Articles

Single-Mode Fiber Design for Minimum Dispersion

The value of the radius of the core of a single-mode step-index optical fiber for minimum dispersion is calculated with the normalized frequency in the range 1.0/spl les/ V/spl les/2.5, using the approximation for the eigenvalue U proposed by Miyagi and Nishida [1]. This calculation is made by solving the total dispersion equation for the core radius when the wavelength assigned is assumed to be that necessary for minimum total dispersion. The computational procedure presented is simple enough to be accomplished on a programmable calculator or microcomputer. This work makes possible the characterization, with reasonable precision, of tbe ideal fiber that should be used with the available optical source.

Microbending loss in optical waveguides

The problem of coupling from a bound mode to the radiation field in an open waveguide subject to slow variations of its axis is considered. The derivation does not depend on statistical averaging over an ensemble of waveguides, as do earlier treatments of the same problem. Nevertheless, it is shown that an average loss can be defined, the average being taken over the length of the waveguide. For this reason, the results are applicable to the realistic experimental situation, when experiments are performed on single waveguides. As an example, we calculate the microbending loss of a single-mode step-index optical fibre as a function of wavelength and compare with some recent experimental measurements of the same quantity. Good agreement is shown when the Fourier transform of the curvature autocorrelation function is assumed to have an inverse power dependence on the Fourier frequency, but the agreement is less convincing for some other possible choices of autocorrelation function.

Transversely Anisotropic Optical Fibers: Variational Analysis of a Nonstandard Eigenproblem

The variational principle for nonstandard eigenvalue problems, recently reported by one of the authors, is applied for the study of guided-wave propagation in an anisotropic dielectric waveguide. A stationary functional is derived for the general dielectric waveguide with transverse anisotropy. The functional is tested for the well-known case of an isotropic step-index single-mode fiber. It is seen that for simple trial functions with only two parameters, a good accuracy is obtained. For two types of transversely anisotropic step-index fibers, relations between the propagation factor, anisotropy parameter, dielectric parameter, and frequency are calculated. The functional does not assume weak guidance condition nor perturbational anisotropy and, hence, is also applicable for other dielectic waveguides. In this application, only a modest computer or a programmable calculator is needed. Moreover, the spurious modes causing confusion in the finite-element method of calculation do not appear with the present method.

Coherence of a Laser Beam Passing through an Optical Fibre

The coherence of a laser beam passing through multimode fibres shows considerable variation. Experiments have been carried out in order to investigate this variation. The visibility of interference fringes is taken to be a measure of coherence. A He-Ne laser (632·8 nm wavelength) was used, with a multimode step-index fibre, a multimode graded fibre (Selfoc fibre) and a single-mode step-index fibre. The azimuthal angle of polarization and the degree of polarization of a beam passing through a single mode fibre show little variation compared to a multimode fibre. The visibility of interference fringes produced by two beams passing through either one or two single-mode fibres have an extremely small variation compared to the multimode fibre. The variation of the coherence of a beam passing through a multimode fibre is due to the superposition of different modes produced by the beams being transmitted. The value of visibility obtained by inserting a polarizer to get equal azimuthal angles of polarization is o...

Prediction of Laser Wavelength for Minimum Total Dispersion in Single-Mode Step-Index Fibers

Pulse dispersion in single-mode optical fibers with step-index profiles has been analyzed in the past using asymptotic methods. One of these methods is based on the approximate characteristic equation for the dominant mode of propagation in these structures, obtained using the "weakly guided" condition. Other methods use approximations for certain parameters of this equation. Utilizing numerical methods of differentiation and interpolation, we have developed a method for the analysis of pulse dispersion in these fibers that is based on solutions of the exact characteristic equation. Exact formulas for the parameters necessary for this study have been established and developed to the point where the steps that would follow, involving extensive analytical effort, are replaced by computational procedures. We make comparisons between our method and those that, although based on asymptotic expressions, present the best theoretical characteristics. The differences found are discussed. This method permits greater precision in prediction of the ideal laser wavelength for use with a given single-mode optical fiber.

Structural optimization for two-mode fiber: Theory and experiment

Structural design of two-mode optical fiber is investigated. It is clarified theoretically that the operating V -value V 0 with zero group delay time difference \Delta\tau between the LP 01 and LP 11 modes is extended to the quasi-two-mode region above the cutoff V -value of the next higher order LP 21 mode. The optimum operating V -value V_{0m} is numerically determined to be 6.45 with the optimum index profile parameter \alpha_{opt} = 2.24 for \Delta = 0.3 percent. It is also shown theoretically that an index depression at the core center increases \Delta\tau due to the V -value deviation from V 0 , and that V 0 becomes smaller than that with no central index depression for the same α. A low-loss two-mode test fiber designed for operating in the 1.3 μm wavelength region is prepared: the core diameter is 21μm with \alpha = 2.65 and \Delta = 0.31 percent, and the test fiber has a precisely controlled graded-index profile with a small central index depression. Experimental results show that the two-mode propagation is maintained in the quasi-two-mode spectral region. Furthermore, small \Delta\tau characteristics against V -value deviation \DeltaV from V 0 are verified experimentally. It is also shown that the two-mode test fiber has about two times larger tolerance for the misalignment at a splice than a step-index single-mode fiber.

Birefringence and polarization characteristics of single-mode optical fibers under elastic deformations

Birefringence and polarization dispersion caused by: 1) elliptical core, 2) twist, 3) pure bending, 4) transverse pressure, and 5) axial tension are studied by treating these deformations as perturbations to step-index single-mode fiber with a round core. These effects ate formulated in terms of fiber structure and perturbation parameters and are compared comprehensively. Birefringence depends strongly on factors 1)-4), while polarization dispersion depends on factors 1), 3), and 4). Polarization performance of twisted elliptical core fibers was also studied. Twist in an elliptical core fiber gives rise to a polarization whose major axis points in an intrinsic direction with an azimuthal angle \phi_{t}z , where φ t is the torsion per unit length and z is the fiber length.

Consistent refractive index profile measurements of a step-index monomode optical fiber attained by several techniques

The methods implemented in our laboratory-far field, near field, refracted near field, and interfetometry-allow one to characterize very accurately the parameters of a step-index single-mode fiber by comparing the results. The step-index profile is obtained with a silica core and a borosilicate cladding by the MCVD process. Experimental results from the above techniques show a good match, confirming the validity of the usual assumptions founding the theories employed. Among the techniques used, the refracted near field seems better to check any type of index profile, a delicate task to perform with other methods.

Sinusoidal Microbending Loss of Orthogonal Polarized Modes in a Single-mode Step-index Fibre

Sinusoidal microbending losses of the HE11 orthogonal polarized modes in a single-mode step-index fibre are studied and compared. The loss of the mode with polarization in a plane perpendicular to the plane of microbending is found to be higher than the loss of the orthogonal polarized mode with polarization in a plane parallel to the plane of microbending. The microbending loss difference of these two orthogonal polarized modes is more significant around the perpendicular directions with respect to the fibre axis than that in nearly parallel directions corresponding to different length periods of sinusoidal microbending.

Characterization of single-mode optical fiber filters

The fabrication of narrowband highly reflecting filters in single-mode step-index fibers was reported recently by Hill et al. [Appl. Phys. Lett. 32, 647 (1978)]. The underlying effect on which these filters are based is a photoinduced refractive-index change in the GeO(2) used as a core dopant in SiO(2) fibers. A study is reported aimed at the characterization of such optical fiber filters. A theoretical model is developed, and relevant fiber parameters are determined through intercomparison with experiment. In this way, both the magnitude of the photoinduced index change and its dependence on the writing power coupled into the fiber are determined.

Minimum dispersion in a single-mode step-index optical fiber

The cancellation between material and waveguide dispersions for weakly guiding single-mode step-index fibers has been analyzed to predict the optimum wavelength lambda(0) for zero first-order dispersion and the residual second-order dispersion T. Greater accuracy in our numerical calculation of waveguide dispersion results in significant change in lambda(0) and T compared to the previous work by another investigator. The dependence of lambda(0) and T on the normalized frequency and relative index difference has also been improved and extended numerically. Physical origin of this dependence is discussed; it is considered to be due to different optical power distributions between core and width of the source.

Practical microbending loss formula for single-mode optical fibers

Microbending loss in a step-index single-mode fiber is formulated in an expression which provides an explicit dependence on wavelength λ and relative index difference Δ. For the permissible mean bending radius <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R\dagger</tex> corresponding to a given loss, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta^{3/2}R\dagger/\lambda</tex> is the function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> of only a normalized frequency υ. This property resembles that for the uniform-bending loss. However, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> in the microbending loss depends less critically on υ than in the uniform-bending loss.

Minimum dispersion at 1.55 μm for single-mode step-index fibres

The single-mode step-index fibre parameters, relative index difference and core diameter, have been predicted to achieve first-order cancellation between material and waveguide dispersions at 1.55 μm. Our prediction by accurate solution of the characteristic equation results in fibre parameters different from those obtained by other investigators. The origin of this difference is examined.

Design Considerations of Broadband Dual-Mode Optical Fibers

We propose and present design data for a new type of graded index fiber which has a profile and radius such that only two mode groups (LP/sub 01/ and LP/sub 11/) propagate and both propagate with virtually identical group velocities. This dual-mode fiber has a core diameter approximately twice that of a conventional step index single-mode fiber. For example, a core diameter of 16.3 mu m is attainable with relative index difference Delta=0.3 percent at 1.25-mu m wavelength. Fabrication tolerances securing a group delay difference below 100 ps/km are given by a power-law profile parameter alpha=4.85/spl plusmn/0.25 and a normalized frequency upsilon=4.45/spl plusmn/0.11. The allowable upsilon-value deviation range to keep the group delay difference within 100 ps/km is about five times as large as that of a step-index fiber, in which group delays of two mode groups are matched. Comparison with a multimode graded-index fiber, with respect to group delay characteristics and bending loss of the dual-mode fiber, are also discussed.

Sinusoidal microbending loss of HE 11 -mode in step-index fibres

Sinusoidal microbending losses of the HE11-mode in step-index fibres are compared by using a perturbation solution of electromagnetic wave scattering theory. The HE11-mode in a multi-mode step-index fibre is found to suffer much higher bending loss than that in a single-mode step-index fibre, except that in nearly perpendicular directions and in the perpendicular direction with respect to the fibre axis the HE11-mode in the single-mode step-index fibre shows some higher bending loss than that in the multimode step-index fibre.

Radiation losses of parabolic-index slabs and fibers with bent axes

Using first-order perturbation theory, radiation losses of the lowest-order mode caused by deformations of the axes of slab waveguides and fibers with parabolic-index distributions were computed. It was found that sinusoidal bends, with a period that produces a very nearly forward directed radiation lobe, cause far more loss than bends with a shorter period that give rise to radiation escaping at larger angles relative to the axes of the waveguides. Parabolic-index fibers and slabs are far more tolerant of periodic sinusoidal axis distortions than step-index fibers and slabs, provided that the period of the distortion causes the beam to escape from the waveguide at relatively large angles (typically more than 10 degrees ). The result of this study suggests that single-mode fibers with parabolic-index profiles may have somewhat lower microbending losses than single-mode step-index fibers.

Asymptotic expression for the far field distribution of step-index single-mode fibers

Asymptotic expression for the far field distribution of step-index single-mode fibers