Page 691 - Introduction to Information Optics

12.2. Optical Network Elements 675
several wavelengths; the absorption bands at 980 and 1480 nm are the most
efficient. As Fig. 12.4 shows, erbium ions are pumped up to an upper energy
level by the absorption of pump light at 1480 nm or 980 nm. The transition to
the ground state emits a photon and may be either spontaneous (the natural
decay of the excited ion in the absence of any interactions) or stimulated (in
the presence of photons possessing the transition energy, stimulated emission
produces additional photons identical to the stimulating photons at a rate
proportional to their flux). Signal photons in the EDFA stimulate depopula-
tion of the excited state (the metastable level), which amplifies the signal. The
long lifetime of the excited state, approximately 10 milliseconds, assures that,
instead of emitting noise by spontaneous emission, most erbium ions will wait
to amplify signals by stimulated emission.
Theoretical models based on the three-level-lasing system of Fig. 12.4 are
quite successful in explaining the observed properties of EDFAs [10, 11]. The
three levels are ground level, metastable level, and pump level. The rate
equations describing the effects of the pump (P p), signal (P p\ and ASE (P /? )
power on the population densities are [11]

££I_£rp 4. p + + p + 4. p-\
r
r
, A \ x ^ a ^ ' a , A a ' * a I
hvA hv pA
_
^iLffP 4. P+ 4. P~ ) 4. A
I ] , A \ s ^ a " ' 21
, r +
e

By conservation, N 3 = N t — N l — N 2, where N 15 N 2, and N 3 are the popula-
tion densities of the ground level, metastable level, and pump level, respectively,
and N t is the total erbium ion density. The superscript + designates pump and
ASE copropagating with the signal, and — designates when they counter-
propagate to the signal. The absorption a and emission e cross sections of the
pump p and signal s are ff Stp. a<ete2- (For example, a pe2 represents the cross
section for pump emission from the metastable level.) With pumping into the
metastable level (A p ~ 1450-1500 nm), the amplifier behaves as a two-level
system and v pe2 = a pe. Pumping into other absorption bands (e.g., A p = 980
nm) have a p(, 2 = 0. Other parameters are the fiber core area A, the signal-to-