Biophotonics_Concepts_to_Applications

V

2 pa

k

n 1

ffiffiffiffiffiffi

2 D

p

¼

2 p 25 lm 1 : 480

0 : 860 lm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2  0 : 010

p

¼ 38 : 2

Using Eq. (3.5), the total number of modes at 860 nm is

M¼

V^2

2

¼ 729

(b) Similarly, V = 25.1 and M = 315 at 1310 nm.

(c) Finally, V = 21.2 and M = 224 at 1550 nm.

As is shown in Fig.3.4, thefield of a guided mode extends partly into the cladding.
This means that a fraction of the power in any given mode willflow in the cladding. As
the V number approaches the cutoff condition for any particular mode, more of the
power of that mode is in the cladding. At the cutoff point, all the optical power of the
mode resides in the cladding. Far from cutoff—that is, for large values of V—the
fraction of the average optical power propagating in the cladding can be estimated by

Pclad

P



4

3

ffiffiffiffiffi

M

p ð 3 : 6 Þ

where P is the sum of the optical powers in the core and in the cladding.

Example 3.6Consider a multimode step-index opticalfiber that has a core

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

the percentage of optical power that propagates in the cladding at 840 nm.

Solution: From Eq. (3.4) at an operating wavelength of 840 nm the value of

Vis

V

2 pa

k

n 1

ffiffiffiffiffiffi

2 D

p

¼

2 p 25 lm 1 : 480

0 : 840 lm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2  0 : 010

p

¼ 39

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

M¼

V^2

2

¼ 760

From Eq. (3.6) it follows that

Pclad

P



4

3

ffiffiffiffiffi

M

p ¼ 0 : 05

62 3 Optical Fibers for Biophotonics Applications