Biophotonics_Concepts_to_Applications

mode having a different V limit). The wavelength at which no higher-order modes
exist in thefiber is called thecutoff wavelengthλc. Only the fundamental LP 01 mode
exists in single-modefibers.

Example 3.3A step-indexfiber has a normalized frequency V = 26.6 at a

1300-nm wavelength. If the core radius is 25μm, what is the numerical

aperture?

Solution: From Eq. (3.4) the numerical aperture is

NA¼V

k

2 pa

¼ 26 : 6

1 : 30 lm

2 p 25 lm

¼ 0 : 220

The V number also designates the number of modes M in a step-index MMF
when V is large. An estimate of the total number of modes supported in a MMF is

M¼

1

2

2 pa

k

 2

n^21 n^22



¼

V^2

2

ð 3 : 5 Þ

Example 3.4Consider a step-index MMF with a 62.5-μm core diameter and

a core-cladding index differenceΔof 1.5 %. If the core refractive index is

1.480, estimate the V number of thefiber and the total number of modes

supported in thefiber at a wavelength of 850 nm.

Solution: From Eq. (3.4) the V number is

V

2 pa

k

n 1

ffiffiffiffiffiffi

2 D

p

¼

2 p 31 : 25 lm 1 : 480

0 : 850 lm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2  0 : 015

p

¼ 59 : 2

Using Eq. (3.5), the total number of modes is

M¼

V^2

2

¼ 1752

Example 3.5Consider a multimode step-index opticalfiber that has a core

radius of 25μm, a core index of 1.48, and an index differenceΔ= 0.01. How

many modes does thefiber sustain at the wavelengths 860, 1310, and

1550 nm?

Solution:

(a) First, from Eq. (3.4), at an operating wavelength of 860 nm the value of

Vis

3.1 Light Guiding Principles in Conventional Optical Fibers 61