About Fiber

I need to go over some basic knowledge on fibers.

1. V number.
The number of modes in a step index circular waveguide is determined by the V number.

V =

2πaNA λ0

(1)

For single-mode fiber, V < 2.405. For multi-mode fiber the number of modes allowed in the fiber is approximately V²/2.

2. Numerical aperture.
The sine of the half acceptance angle is NA.
NA = (n_core² - n_clad²)^1/2.
For reference,
f# = 1/(2 NA).
Note that it is not necessarily true that a fiber's output beam's divergence angle will equal to its acceptance angle. Instead, the fiber tends to preserve the angle of incidence during propagation of the light, causing it to exit the fiber at the same angle it entered.

References:
1. http://www.fiberoptix.com/technical/numerical-aperature.html
2. Wilson and Hawkes, Optoelectronics, 3rd ed., Prentice Hall Europe 1998.