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.     

Trapezoidal index single-mode fibers for the 1.55 µm band

An analytical study is made of single-mode fibers with a trapezoidal index of refraction profile for low dispersion operation in the 1.55-μm band using Ge doped silica core and pure silica cladding. It is found that certain trapezoid proportions give a fiber with a combination of less Ge doping, larger core diameter, faster decay of the field in the radial direction within the cladding, and smaller rate of change of dispersion with wavelength than is simultaneously possible with either the step index or triangular profiles.     

A Generalized Analysis of Zero Cross over Timing Systems for Semiconductor Detectors

A generalized analysis of zero cross-over timing systems is developed and applied to the case of germanium planar detectors to determine operating parameters which give smallest timing dispersion under the constraints of available charge-sensitive preamplifier risetimes. Charts are given using normalized values to indicate these parameters. The conclusions are verified by experimental results published elsewhere.     

A numerical method for the analysis of single-mode low-dispersion graded-index fibers

A numerical integration method for the calculation of the time dispersion of optical-fiber modes is introduced and used to determine the parameters of single-mode graded-index silica-based fibers for the 1.55-μm band. The method gives an accuracy on the order of 0.001 ps/km/nm, and it was possible to quantify the error in assuming the overall time dispersion to be the sum of the material and waveguide dispersions. The analysis indicates that when large material dispersion is to be neutralized by waveguide dispersion, the outer diameter of the cladding must be increased to avoid higher microbending losses. When the difference between the refractive indices at the center of the core and in the cladding decreases, the ratio between the cladding and core diameters must be increased.     

Event Timing in High Purity Germanium Coaxial Detectors

The timing of gamma ray radiation in systems using high purity coaxial germanium detectors is analyzed and compared to that of systems using Ge(Li) detectors. The analysis takes into account the effect of the residual impurities on the electric field distribution, and hence on the rate of rise of the electrical pulses delivered to the timing module. Conditions under which the electric field distribution could lead to an improvement in timing performance, are identified. The results of the analysis confirm the experimental results published elsewhere and when compared with those for Ge(Li) detectors, which usually operate under conditions of charge carrier velocity saturation, confirm that high purity germanium detectors need not have inferior timing characteristics. A chart is given to provide a quantitative basis on which the trade-off between the radius of the detector and its time resolution may be made.     

Zero Cross-Over Timing with Coaxial Ge(Li) Detectors

The performance of zero cross-over timing systems of the constant fraction or amplitude rise time compensated type using coaxial Ge(Li) detectors is analyzed with special attention to conditions that compromise their energy-independence advantage. The outcome is verified against existing experimental results, and the parameters that lead to minimum dispersion, as well as the value of the dispersion to be expected, are given by a series of charts.