Fiber numerical aperture measurements
The numerical aperture is an important optical fiber parameter as it affects characteristics such as the light-gathering efficiency and the normalized frequency of the fiber (V). This in turn dictates the number of modes propagating within the fiber (also defining the singlemode region) which has consequent effects on both the fiber dispersion (i.e. intermodal) and, possibly, the fiber attenuation (i.e. differential attenuation of modes). The numerical aperture (NA) is defined for a step index fiber as:
where ϴa is the maximum acceptance angle, n1 is the core refractive index and n2 is the cladding refractive index.
It is assumed that the light is incident on the fiber end face from air with a refractive index (n0) of unity. Although Eq. (4.17) may be employed with graded index fibers, the numerical aperture thus defined represents only the local NA of the fiber on its core axis (the numerical aperture for light incident at the fiber core axis). The graded profile creates a multitude of local NAs as the refractive index changes radially from the core axis
For the general case of a graded index fiber these local numerical apertures NA(r) at different radial distances r from the core axis may be defined by:
Therefore, calculations of numerical aperture from refractive index data are likely to be less accurate for graded index fibers than for step index fibers unless the complete refractive index profile is considered. The numerical aperture may be determined by calculation.
` An example of an experimental arrangement with a rotating stage is shown in Figure 4.18. A 2 m length of the graded index fiber has its faces prepared in order to ensure square smooth terminations.
The fiber output end is then positioned on the rotating stage with its end face parallel to the plane of the photodetector input, and so that its output is perpendicular to the axis of rotation. Light at a wavelength of 0.85 μm is launched into the fiber at all possible angles (overfilling the fiber) using an optical system similar to that used in the spot attenuation measurements.
The photodetector, which may be either a small-area device or an apertured large-area device, is placed 10 to 20 cm from the fiber and positioned in order to obtain a maximum signal with no rotation (0°). Hence when the rotating stage is turned the limits of the far-field pattern may be recorded. The output power is monitored and plotted as a function of angle, the maximum acceptance angle being obtained when the power drops to 5% of the maximum intensity. Thus the numerical aperture of the fiber can be obtained from Eq. (4.17).
A less precise measurement of the numerical aperture can be obtained from the far-field pattern by trigonometric means. The experimental apparatus is shown in Figure 4.19.
where the end prepared fiber is located on an optical base plate or slab. Again light is launched into the fiber under test over the full range of its numerical aperture, and the farfield pattern from the fiber is displayed on a screen which is positioned a known distance D from the fiber output end face. The test fiber is then aligned so that the optical intensity on the screen is maximized. Finally, the pattern size on the screen A is measured using a calibrated vernier caliper. The numerical aperture can be obtained from simple trigonometrical relationships where:
It must be noted that the accuracy of this measurement technique is dependent upon the visual assessment of the far-field pattern from the fiber. The above measurement techniques are generally employed with multimode fibers only, as the far-field patterns from single-mode fibers are affected by diffraction phenomena
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