3rd Practical work
EXPERIMENTAL DETERMINATION OF THE NUMERICAL
APERTURE OF AN OPTICAL FIBER
Purpose of the work: To acquire the skills of experimentally determining
the numerical apertures of optical fibers.
1. Theory
The numerical aperture, NA, is a measure of how much light can be
collected by an optical system, whether it is an optical fiber or a microscope
objective lens or a photographic lens. It is the product of the refractive index of the
incident medium and the sine of the maximum ray angle.
NA = ni sinmax.
In most cases, the light is incident from air and ni=1. In this case, the
numerical aperture of a step-index fiber is, from the equations above,
2
NA = ncore
- ncl2
When Δ«1, this equation can be approximated by
NA = (ncore + ncl )(ncore - ncl )= (2ncore )(ncore D)=ncore 2D .
The condition in which D «1 is referred to as the weakly-guiding
approximation. The NA of a fiber will be measured in Experiment 1.
In Fig. 1, two rays are shown. One, the axial ray, travels along the axis of the
fiber; the other, the marginal ray, travels along a path near the critical angle for the
core-cladding interface and is the highest-angle ray which will be propagated by the
fiber. At the point where the marginal ray hits the interface, the ray has traveled a
distance L2, while the axial ray has traveled a distance L1. From the geometry, it can
be seen that
sin= ncl/ncore = L1/L2.
arcsin ncl/ncore=arcsin L1/L2
Figure 1: The geometry for derivation of the differential delay of a step-index
fiber.
2. The task
Complete the task based on the given option numbers.
№
ncore
ncl
1
1,53
1,48
2
1,5
1,4
3
1,51
1,45
4
1,52
1,41
5
1,54
1,47
6
1,53
1,45
7
1,5
1,45
8
1,6
1,4
9
1,48
1,4
10
1,52
1,42
NA
