Numerical Aperature and the Mode Field Diameter

Numerical Aperature

The far-field region is the region far from the fiber-end face. The far-field power distribution describes the emitted power per unit area as a function of angle ÿ some distance away from the fiber-end face. The distance between the fiber-end face and detector in the far-field region is in the centimeters (cm) range for multimode fibers and millimeters (mm) range for single mode fibers.

EIA/TIA-455-47 describes various procedures, or methods, for measuring the numerical aperature or the far-field power distribution of optical waveguides. These procedures involve either an angular or spacial scan.

The picture below illustrates an angular and spacial scan for measuring the far-field power distribution.

Angular and spacial scan methods for measuring the far-field power distribution.

The picture shown above (method A) illustrates a far-field angular scan of the fiber-end face by a rotating detector. The fiber output radiation pattern is scanned by a rotating detector in the far-field. The detector rotates in a spherical manner. A record of the far-field power distribution is kept as a function of angle ÿ.

The picture above (method B) illustrates a far-field spacial scan of the fiber-end face by a movable (planar) detector. In a far-field spacial scan, lens L1 performs a Fourier transform of the fiber output near-field pattern. A second lens, L2, is positioned to magnify and relay the transformed image to the detector plane. The image is scanned in a plane by a movable detector. The scan position y in the Fourier transform planeis proportional to the far-field scan angle ÿ. A record of the far-field power distribution is kept as a function of the far-field scan angle.

The normalized far-field pattern is plotted as a function of the far-field scan angle ÿ. The next picture shown below shows the plot of the normalized far-field radiation pattern as a function of scan angle.

Normalized far-field radiation pattern.

Fiber NA is defined by the 5 percent intensity level, or the 0.05 intensity level, as indicated in in the picture. The 0.05 intensity level intersects the normalized curve at scan angles ÿA and ÿB. The fiber NA is defined as

where ÿ5 is the 5 percent intensity half angle. ÿ5 is determined from ÿA and ÿB as shown below:

Mode Field Diameter

The mode field diameter (MFD) of a single mode fiber is related to the spot size of the fundamental mode. This spot has a mode field radius w0. The mode field diameter is equal to 2w0. The size of the mode field diameter correlates to the performance of the single mode fiber. Single mode fibers with large mode field diameters are more sensitive to fiber bending. Single mode fibers with small mode field diameters show higher coupling losses at connections.

The mode field diameter of a single mode fiber can be measured using EIA/TIA-455-167. This method involves measuring the output far-field power distribution of the single mode fiber using a set of apertures of various sizes. This far-field power dis-tribution data is transformed into the near-field before using complex mathematical procedures.

The mode field diameter is calculated from the transformed near field data. The mathe-matics behind the transformation between the far-field and near-field is too complicated for discussion in this section. Refer to EIA/TIA-455-167 for information on this transformation pro-cedure.

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