Fiber-Optic Sensors - Applied Optics Fundamentals and Device Applications - page 178

number of photons generated
number of electron hole pairs in

QE

int =

− jected

The quantum efficiency can also be described as the fraction of the excited
carriers that combine radiatively to the total recombination [21]:

R
R

T

R NR

QE = =

)

(4.5)

( T + T

NR R

where
T NR is the nonradiative lifetime
T R is the radiative lifetime
R R is the radiative recombination rate
R is the total recombination rate

It is important to note that the quantum efficiency decreases with increasing
temperature.
Lasing action occurs when a photon encounters a hole-electron pair at
the proper energy separation. When this happens the hole-electron pair
recombines and a photon is emitted. The photon emitted will have the same
energy, direction, phase, and polarization. The emission will be highly col-
limated and the spectral width will be in the 1-25 Å range.

4.17.2 Effect of Modulation and Modulation Depth on Mode Spectrum

To begin the discussion assume we have a laser structure that oscillates
predominately in a single longitudinal mode when biased at some minimal
threshold current level. The threshold current is defined as the minimum
current density to obtain the threshold condition. Threshold occurs when
the number of photons generated by the structure exactly equals the number
of photons lost. Loss mechanisms include scattering loss (loss due to imper-
fections, voids, or contamination within the lattice), absorption loss (loss
that occurs when a photon gives up its energy to an electron or hole in the
conduction band or valence band respectively), and emission from the laser.
For a simple p-n junction laser, the current density required to obtain
threshold is [22]:

2

8 π en ⎛

⎜

1 1 ⎞

⎟

J th = α + ln (4.6)

( QE ) λ

2

L R

0

where
J th is the threshold current density in Coulombs s −1 cm −2
N is the index of refraction