Biophotonics_Concepts_to_Applications

Solution: First, from Eq. (3.4)

V¼

2 pa

k

NA¼

2 p 25 lm

1 : 31 lm

 0 : 22 ¼ 26 : 4

Then from Eq. (3.14) the total number of modes forα=2is

Mg

a

aþ 2

V^2

2

¼

V^2

4

¼ 174

3.2.3 Cutoff Condition in Graded-Index Fibers.

Similar to step-indexfibers, graded-indexfibers can be designed as single-mode
fibers at a desired operational wavelength. An empirical expression (an expression
based on observation) of the V parameter at which the second lowest order mode is
cut off for graded-indexfibers has been shown to be [ 1 ]

Vcutoff¼ 2 : 405

ffiffiffiffiffiffiffiffiffiffiffiffi

1 þ

2

a

r

ð 3 : 15 Þ

Equation (3.15) shows that for a graded-indexfiber the value of Vcutoffdecreases
as the profile parameterαincreases [ 5 ]. This equation also shows that the critical
value of V for the cutoff condition in parabolic graded-indexfibers (α=2)isa
factor of√2 larger than for a similar-sized step-indexfiber. Furthermore, from the
definition of V given by Eq. (3.4), the numerical aperture of a graded-indexfiber is
larger than that of a step-indexfiber of comparable size.

3.3 Performance Characteristics of Generic Optical Fibers

When considering whatfiber to use in a particular biophotonics system application,
some performance characteristics that need to be taken into account are optical signal
attenuation as a function of wavelength, optical power-handling capability, the degree
of signal loss as thefiber is bent, and mechanical properties of the opticalfiber [ 5 – 11 ].

3.3.1 Attenuation Versus Wavelength

Attenuationof an optical signal is due to absorption, scattering, and radiative power
losses as light travels along afiber. For convenience of power-budget calculations,

66 3 Optical Fibers for Biophotonics Applications