Fiber-Optic Sensors - Applied Optics Fundamentals and Device Applications - page 179

Δγ is the linewidth of spontaneous emission in s −1
D is the thickness of emitting layer in cm
Q.E. is the quantum efficiency
α is the absorption coefficient
L is the length of active laser structure in cm
R is the reflectivity of Fabry-Perot surface

Note that for a homostructure laser the threshold current increases rapidly
with temperature [23].
In the steady state, when the laser is excited with a current and the laser is
at or above threshold, the energy of emission will be distributed in various
longitudinal modes. The laser may then be excited or modulated by an addi-
tional current. The application of the current pulse will cause a redistribu-
tion of power in the various longitudinal modes. If there are N longitudinal
modes, the amplitudes are defined by [24]:

2 2

[ − ( λ − λ ) / 2 σ ]

e

1 2

(4.7)

∑

n

2 2

[ − ( λ − λ ) / 2 σ ]

e

1 2

i = 1

where
λ c is the center wavelength
λ i is the wavelength of the i th mode
σ is the half width of the spectrum

Even though the energy may be redistributed, the total optical power is con-
stant and may be expressed as follows:

N

∑

a = 1 (4.8)

1

i = 1

Depending on the structure of the laser, the redistribution can occur in
0.5-5 ns [25]. Since semiconductor lasers have a very short photon lifetime,
modulation at high frequency can be achieved. At the peak amplitude of the
combined steady state plus the modulating current, the various longitudinal
modes will correspond to the continuous wave spectrum for the combined
current, assuming that the laser can respond to the modulating disturbance
and that the peak combined current does not exceed device limitations.
During switch on of the laser, the ratio of power in the i ith mode to that in
the j th longitudinal mode can be expressed (for pulsed or step excitation,
neglecting spontaneous emission) as follows [26]:

S t
S t

( )
( )

S t
S t

( =

=

0
0

)

i t

= e G G ( − ) (4.9)

i j t

( )

j j