Relative Index Difference Research Articles

Single‐mode optical fibers with zero total dispersion at wavelength 1.3 and 1.55 μm. fiber with α‐power index core and triple clad

AbstractSingle‐mode optical fibers with an α‐power index core (α = 1, 2, 6, ∞) and a triple clad have been designed under the following two conditions: (I) the total dispersion at wavelengths of 1.3 and 1.55 μm is zero; and (II) the cut‐off wavelength λc for the second mode is less than 1.15 μm. In this paper, the sensitivity of the total dispersion, the equivalent bending radius (the radius at which the bending loss is 0.01 dB/km), and the splice loss of those fibers are discussed. The clad has an ideal triple layer structure (the relative index difference between the first and outer cladding is Δ2 and that between the second and outer cladding is Δ3). For a given value of α which determines the core refractive index profile, Δ1. (the relative index difference between the core and outer cladding), and a (core radius) can be chosen freely. In this paper, for a given α the fiber, satisfying conditions (I) and (II), was designed under the conditions that (1) Δ1 = const, and (2) \documentclass{article}\pagestyle{empty}\begin{document}$ A\mathop \Delta \limits_ = \int\limits_0^{a/w} {n(r/w,\;\lambda)dr\; = - const(w\mathop \Delta \limits_ = a + t_1 + t_2, t_m;} $\end{document} m‐th cladding layer width, m = 1, 2). Comparing the fiber with a core of α = 1, 2 and 6 (t2/t1 = 1.0, Δ2 < 0, Δ3 < 0), the step index core fiber (α = ∞). has the following characteristics whether the fiber is designed under condition (1) or (2): 1) a lower sensitivity for the core radius and wavelength; 2) a smaller equivalent bending radius; 3) a smaller splice loss in the case where d/a = const (d: axial displacement). For the case where α = ∞, the structure with Δ2 > 0 and Δ3 < 0 was investigated and compared with the structure with Δ2 < 0 and Δ3 > 0.

Wholly synthesised fluorine-doped silica optical fibres by sol-gel method

Low-loss, single-mode optical fibres have been successfully fabricated by the sol-gel method, using fluorine-doped silica glasses in association with the outdiffusion method. Triangular-index-profile, single-mode optical fibres with a relative index difference of 0·30% have been obtained with an optical loss of 0·43dB/km at 1·30μm wavelength

Design method for triple–clad silica core optical fibers with zero total dispersion at wavelengths of 1.3 and 1.55 μm

AbstractThis paper describes the design method for triple‐clad silica core optical fibers with zero total dispersion at wavelengths of 1.3 and 1.55 μm; (ac, Sc) is the point where the total dispersion (= S) at wavelengths of 1.3 μm becomes equal to that at 1.55 μm when the core radius (= a) is varied. We denote the relative index difference between the core and the mth clad at 1.55 μm by Δm+1 (> 0, m × 1, 2, 3), the thickness of the mth clad by tm (m × 1, 2, 3), the cut‐off wave length for the second mode by λc and the equivalent bending radius (= radius where the bending loss is 0.01 dB/km as R. The following conclusions have been obtained: (1) even if the conditions for the zero dispersion are satisfied in an ideal triple clad (TC type), the zero dispersion condition cannot be satisfied when fluctuations and round shoulders happen to exist in the clad layers (nonideal TC type); (2) to fabricate fibers of TC type and nonideal TC type with |Sc| < 0.1 ps/km/nm, λc ≤ 1.15 μm and R < 5 cm. The following conditions should be satisfied: Δ2 = 2Δ4, Δ3 ≤ Δ4, Δ4 ≥ 0.7% and t1/ac ≤ 1.04 for t2/t1 × 0.5; (3) if the item (2) is satisfied, the sensitivities of Sc to ac, Δ2, and Δ3 for wavelength of 1.3 μm are constant when t1/ac ≤ 2.0. However, at wavelength of 1.55 μm, they decrease as t1/ac decreases; and (4) R for wavelength of 1.55 μm is about 10 times larger than R for wavelength of 1.3 μm.In this paper, the total dispersion is computed by the differentiation formula for determinant. Therefore the significant digits of the total dispersion in our results are more than four.

Parameter optimization in graded-index dispersion-shifted single-mode fibers

The characteristics of graded-index single-mode nonsegmented-core fibers with a single cladding region, in which the wavelength of zero dispersion is shifted to 1.55 μm, are studied analytically. It is found that for a given relative index difference above a certain value, there are two core sizes at which this zero dispersion shifting is realized. The larger core has certain advantages and has been invariably used in practice. For fibers in which the core is Ge-doped and the index of refraction has a triangular or a parabolic profile, we calculate the rate of change of dispersion with wavelength, the sensitivity of the zero dispersion wavelength to small changes in the core radius and in the refractive index difference, and the outer radius of the cladding needed to limit microbending losses in the cabled fiber. There is a doping level at which the wavelength of zero dispersion is not sensitive to the exact level of doping. The factors involved in choosing a doping level are expounded.

Performance of optical cable composed of dispersion-shifted single-mode fibers

A low-loss dispersion-shifted single-mode fiber cable has been fabricated. The index-profile of the fiber is nearly parabolic and the relative index difference is 0.8 percent. An average cable loss is 0.229 dB/km at 1.55 μm, and excellent loss stability has been achieved in the cabling process and in the temperature and mechanical test.

Theoretical limit of repeater spacing in an optical transmission line utilizing Raman amplification

The limit of repeater spacing is investigated theoretically for optical transmission lines utilizing stimulated Raman scattering to amplify the signal light. Achievable repeater spacing is numerically estimated on the basis of coupled power equations and measured fiber characteristics for various signal wavelengths and relative index differences. Three types of transmission line configurations are considered, i.e., utilization of forward only, backward only, and bidirectional amplification. In the third case, a transmission distance of more than 400 km is predicted for an input signal light power of 100 μW, a signal wavelength of 1.57 μm, and a pump power of 0.5 W using a fiber with a relative index difference of 1 percent for signal light amplification.

Configuration of the optical transmission line using stimulated Raman scattering for signal light amplification

Expansion of a repeater spacing of optical transmission line is investigated using forward stimulated Raman scattering generated by a 1.34-μm Nd:YAG laser to amplify the signal light. Achievable repeater spacing at the 1.42-μm wavelength transmission is numerically estimated on the basis of coupled power equations and experimentally obtained Raman gain for various core-cladding index difference. A transmission distance of more than 200 km is predicted for an input signal light power of 100 μw and a pump power of 200 mW using a fiber with a relative index difference of 1 percent.

Dependence of Raman gain on relative index difference for GeO_2-doped single-mode fibers

Raman gain has been measured for five single-mode fibers with different relative index differences up to 1.0%. Using an experimental equation relating the mode-field radius to the relative index difference, a simple and practical relation between the Raman gain and the relative index difference has been established. The Raman-gain constant for pure SiO(2) has been evaluated to be 7.4 x 10(-14) m/W.

Numerical analysis of polarization‐maintaining optical fibers with circular pits in a circular core

This paper proposes new optical fibers with angularly nonuniform index distributions featured by one circular pit in the core, two circular pits in the core, and noncoaxial W‐type distribution. The field problems are analyzed by the improved point‐matching method. Waveguide parameters of single circular‐pit fibers, double circular‐pit fibers, and noncoaxial W‐type fibers that provide the largest modal birefringence are investigated. It is found that (1) the maximum modal birefringence Bmax for single circular‐pit fibers and noncoaxial W‐type fibers is much larger than those for double circular pit fibers, (2) noncoaxial W‐type fibers exhibit larger modal birefringence than single circular‐pit fibers in the range Δn < 1.8% (Δn is relative index difference), and (3) the value Bmax of 1.7 × 10−4 has been attained for Δn = 0.42%. These results are quite reliable because (1) the relative error of the modal birefringence computed by our method is less than 10−4, and (2) this new method never produces ghost solutions.

Design of multimode graded-index fiber parameters in the long-wavelength region

Structural design of multimode graded-index fibers in the long-wavelength region around 1.3 μm is described. Suitable fiber parameters for operating with a laser source for determined: outer diamter 125 μm, core diameter 50 μm, and refractive-index difference 0.015 (relative-index difference ~1%), for transmission systems around 100 Mb/sec. These values agree with the optimum values for short-wavelength transmission systems.

Transmission characteristics of a single-mode fiber in the 1.3-µm wavelength region

Transmission characteristics of 1.3-μm-band single-mode optical fibers were studied experimentally and theoretically. OH-ion content dependence of optical loss in the 1.3-μm region was investigated on single-mode fibers fabricated by the VAD method. The optical loss was evaluated for OH-ion content by calculating correlation factors between the optical loss and 1.39-μm OH-peak absorption loss. It was clarified that the optical loss calculated by correlation factors agreed approximately with the loss given by Lorentzian absorption in case of 0.0253-μm absorption half width, Next, the relationship between chromatic dispersion and fiber parameters was studied for step-index single-mode fibers. It was found that the zero-dispersion wavelength and the incline at the wavelength was expressed as simple functions of effective cutoff wavelength and relative index difference. Experimentally obtained zero-dispersion wavelengths on single-mode fibers fabricated by the VAD method were found to be in excellent agreement with the calculated values.

Accuracy of scalar approximation for single-mode fibers

Total dispersion in single-mode fibers has been computed from the exact numerical solution of scalar and vector wave equations and the accuracy of the scalar approximation has been discussed. It has been shown that for larger values of relative index difference between core and cladding, although the values of total dispersion obtained by the two approaches differ appreciably in the vicinity of zero dispersion, the optimum core radii and the zero dispersion wavelengths obtained by the two methods differ negligibly for all practical purposes.

Prediction of the ultimate performance of side-tunnel single-polarisation fibre

As the result of recent progress in polarisation-maintaining optical waveguiding schemes, a basic question now arises: which of stress-induced type or geometrical type approach will finally offer better characteristics? The letter discusses the ultimate performance of a side-tunnel fibre which offers the strongest polarisation-maintaining capability among various geometrical-type ones. The result indicates that, if the structure is optimised, a relative bandwidth of truly single-polarisation characteristics of 0.21 and a normalised birefringence of 0.0045 can be achieved for a relative core-cladding index difference of 0.01. These values are comparable to or higher than the best data reported so far with stress-type ones.

Birefringence caused by thermal stress in elliptically deformed core optical fibers

Birefringence and polarization dispersion introduced by thermal stress in single-mode fibers with elliptical core are formulated here in terms of fiber structure parameters, thermal expansion coefficients, and thermoelastic constants. Thermal stress distribution and birefringence characteristics are estimated within first-order perturbation with respect to fiber core ellipticity. Normalized frequency dependence of birefringence and polarization dispersion is also derived in this paper. Birefringence and polarization dispersion in elliptical core fiber are seen to depend on thermal stress rather than geometrical anisotropy for relatively small relative index differences. Numerical examples are presented for germanosilicate, borosilicate, and phosphosilicate glass fibers.

Fabrication of high N.A. graded‐index optical fibers by mcvd method

AbstractCracks in the host material have posed a problem in the fabrication of high‐M.A. silica fibers. This paper examines a high‐NA fiber with a graded refractive index profile to prevent these cracks. A high‐N.A. (= 0.39) graded fiber was fabricated by the MCVD method, in which the accumulation temperature is varied in accordance with the difference in composition of the core glass film. A method was developed for generating a host material with high‐N.A. and low losses. We realized a loss of 2.49 dB/km (at the measured wavelength of 1.67 μm) and a relative index of refraction difference Δ = 3.3%. For the core materials GeO2 ‐ P2O5 ‐ SiO2 and P2O5 ‐ SiO2 we experimentally found a relation between the relative index difference Δ and the loss. Rayleigh scattering, structural imperfection scattering and OH absorption were examined for the propagation loss characteristics. At longer wavelengths, the Rayleigh scattering and the OH absorption can be reduced and the high N.A. fiber is more practical. When Δ is larger than 3%, the structural imperfection loss increases rapidly and it is necessary to improve the processing. For the bending loss the number of windings, the bending radius and the Δ dependence are derived. For a bend diameter R, the bending loss was found to be (1/R)1.31 exp (−k Δ).

Dispersionless Single-Mode Lightguides With α Index Profiles

By means of a numerical solution to Maxwell's equations, we calculate those parameters necessary to design and fabricate single-mode lightguides. These include optimum core radius and profile parameter α. In the design the dispersion is minimized by varying the core radius while the relative index difference Δ, the wavelength λ and profile parameter are held fixed. A comparison of calculated dispersion with experimental data shows excellent agreement

Transmission Characteristic Measurement of Two-Mode Optical Fiber with a Nearly Optimum Index-Profile

Two-mode optical fibers are studied experimentally and theoretically. A fiber with a nearly optimum index profile, designed for the material dispersion-free spectral region of 1.3 mu m has been fabricated. The fiber core diameter is 20 mu m with a 0.26 percent of relative-index difference between the core and cladding. Group delay time differences Delta tau between LP/sub 01/ and LP/sub 11/ modes are measured in the spectral region 1.06-1.44 mu m by using a fiber Raman laser. As a result, the zero-modal dispersion characteristic is confirmed to occur near 1.4 mu m. It is shown that a gently sloping Delta tau characteristic against V-value is obtained when the central index dip in core index profile is eliminated. In the present test fiber, Delta tau = 230 ps/km, caused by a V-value deviation of 5 percent from the optimum V/sub 0/ at which Delta tau = 0. The theory predicts 200 ps/km with an optimum index profile.

Microbending loss evaluation in arbitrary-index single-mode optical fibers. Part I: Formulation and general properties

Microbending loss formula is derived for arbitrary-index profile optical fibers by using analytical curved fiber fields to the first-order perturbation theory. Relation between loss and fiber curvature power spectral statistics is studied in detail. Normalized frequency giving the minimum microbending loss value scarcely depends on the power spectrum. The larger the propagation constant difference between the guided and quasi-guided modes, the smaller the microbending loss is in regard to wavelength, relative index difference, and normalized frequency dependence. The obtained formulas for single-mode fiber show the same dependence as the graded-index multimode fiber, with respect to fiber structure and curvature statistical parameters.

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.