4.3 Principles of Laser Diodes
185
Fig. 4.22 Typical spectrum
from a Fabry-Perot
GaAlAs/GaAs laser diode
Possible
lasing
modes
Arbitrary wavelength
Peak
wavelength
Gaussian
output
profile
Δλ =
λ
2
2nL
=
c
2Ln
(4.45)
This can be related to the wavelength spacing through the relationship
= yielding
=
λ
2
2Ln
(4.46)
Thus, given Eqs. (4.41) and (4.46), the output spectrum of a multimode laser
follows the typical gain-versus-frequency plot given in Fig. 4.22, where the exact
number of modes, their heights, and their spacing depend on the laser construction.
Example 4.13 A GaAs laser operating at 850 nm has a 500-μm length and a refractive index n = 3.7. (a) What are the frequency spacing and the wavelength spacing?
(b) If, at the half-power point, λ − λ 0 = 2 nm, what is the spectral width σ of the
gain?
Solution (a) From Eq. (4.45) the frequency spacing is
=
3 × 10
8 m/s
2
500 × 10 −6 m
(3.7)
= 81 GHz
From Eq. (4.46) the wavelength spacing is
=
850 × 10
−9 m
2
2
500 × 10 −6 m
(3.7)
= 0.195 nm
(b) Using Eq. (4.41) with g(λ) = 0.5 g(0) and then solving for σ with λ − λ 0 =
= 0.195 nm yields