Page 197 - Introduction to Information Optics

182 3. Communication with Optics

maximum bit rate is B & I/T = 20 Mbps. This is not that high; thus, multimode
fiber is not suitable for high-speed long-haul communication.
Fortunately, when the normalized frequency is V < 2.4, we can have single
mode fiber operation. In this case, there is only one mode; there will not be
intermodal dispersion. Thus, the expected dispersion will be significantly
smaller. However, the dispersion is still not zero. In this case, we have
intramodal dispersion due to material dispersion and waveguide dispersion,

3.2.3,4.1, Material Dispersion for Single Mode Tiber
Since refractive index is a function of wavelength (i.e., n = «[/.]), different
wavelength light will propagate at different speeds (i.e., v(A) — t-/n[/t]). Since
any real light source always has a finite size spectral bandwidth A/I, we will
have dispersion. This type of dispersion is called material dispersion.
For long-haul fiber-optic communication, the single longitudinal mode
diode laser is used as the light source, which has a very narrow spectral line
width (A/ ^ 0.1 nm). Thus, a very low material dispersion can be achieved.
The mathematical description of material dispersion is

(3.38,

Example 3.8. A pure silica fiber has a length L = 1 km. Use Eq. (3.38) to
calculate the pulse broadening, AT, due to the material dispersion and maxi-
mum bit rate of a laser light source that has spectral line width Ax, = 2 nm,
operating wavelength A. — 1.55 /mi, and

2
= -0.00416491 Cum' ).

Solve:

2
. L d n(A)
AT- — /
L\i A ,
c a A"
3
2
A;. = - —5J!L^ x 1.55 nm x (-0.00416491 jum~ ) x 2 x 10 um
8
3xl0 m/s
^s 40 ps.
The corresponding maximum bit rate is B = I/At % 25 Gbps.