(7-30)
A. Spot size of the fundamental mode
A single-mode fiber supports only one mode that propagates through the fiber. This mode is also referred to as the fundamental mode of the fiber. The transverse field distribution associated with the fundamental mode of a single-mode fiber is an extremely important quantity. It determines various important parameters like splice loss at joints, launching efficiencies, bending loss, etc. For most single-mode fibers, the fundamental mode-field distributions can be approximated by a Gaussian function, which may be written in the form
|
(7-30) |
where w is referred to as the spot size of the mode-field pattern. When r = w, the value of y is equal to 1/e of the value A at r = 0. For a step-index (single-mode) fiber, one has the following empirical expression for w [Marcuse]:
 |
(7-31) |
where a is the core radius and V is the V-number given by Equation 7-28. We may mention here that the light coming from a HeNe laser (or from a laser pointer) has a transverse intensity distribution very similar to that coming from a single-mode fiber except that the spot size for the HeNe laser is much larger. The quantity 2w is also referred to as the mode-field diameter (MFD) of the fiber and is a very important property of single-mode fibers. In fact, MFD is a more important property than core diameter in the case of single-mode fibers, since it determines the splice loss across a joint, bending loss, dispersion, etc. of single-mode fibers.
Example 7-14
Consider a step-index fiber (operating
at 1300 nm) with n2 = 1.447, D = 0.003, and
Example 7-15
For a step-index fiber (operating at 1550 nm) with n2 = 1.444, D = 0.0075, and a = 2.3 mm (see Example 7-13), V » 1.65, giving w » 3.6 mm. The same fiber will have a V-value of 1.97 at l0 = 1300 nm, giving a value of the spot size » 3.0 mm.
