Biophotonics_Concepts_to_Applications

Example 3.1Consider a multimode step-index silicafiber that has a core

refractive index n 1 = 1.480 and a cladding index n 2 = 1.460. Find (a) the

critical angle, (b) the numerical aperture, and (c) the acceptance angle.

Solution:

(a) From Eq. (3.1), the critical angle is given by

uc¼sin^1

n 2

n 1

¼sin^1

1 : 460

1 : 480

¼ 80 : 5 

(b) From Eq. (3.3) the numerical aperture is

NA¼ n^21 n^22

 1 = 2

¼ 0 : 242

c) From Eq. (3.3) the acceptance angle in air (n = 1.00) is

hA¼sin^1 NA¼sin^10 : 242 ¼ 14 : 0 

Example 3.2Consider a multimode step-indexfiber that has a core refractive

index of 1.480 and a core-cladding index difference of 2.0 % (Δ= 0.020).

Find (a) the numerical aperture, (b) the acceptance angle, and (c) the critical

angle.

Solution: The cladding index is n 2 =n 1 (1−Δ) = 1.480(0.980) = 1.450.

(a) From Eq. (3.3) the numerical aperture is

NA¼n 1

ffiffiffiffiffiffi

2 D

p

¼ 1 : 480 ð 0 : 04 Þ^1 =^2 ¼ 0 : 296

(b) Using Eq. (3.3) the acceptance angle in air (n = 1.00) is

hA¼sin^1 NA¼sin^10 : 296 ¼ 17 : 2 

(c) From Eq. (3.1), the critical angle is given by

uc¼sin^1

n 2

n 1

¼sin^10 : 980 ¼ 78 : 5 

3.1 Light Guiding Principles in Conventional Optical Fibers 59