Page 391 - Fiber Bragg Gratings

368 Chapter 8 Fiber Grating Lasers and Amplifiers

for modeling the laser: the reflectivities of the front and rear facets, the
reflectivity and length of the grating, and the phase offset between the laser
and the grating (passive fiber cavity), as well as the electrical contribution
due to leakage, parasitics in the packaging, bias, and modulation signals.
Premaratne et al. [33] have presented a comprehensive rate-equation
model for strong feedback taking account the many internal reflection of
the composite cavity, based on the work of Park et al. [34], as well as the
delayed fields from the reflections. Multiple reflections are accounted for
by assuming that the field components are stationary [35]. Their analysis
is therefore restricted to periodic and nonperiodic steady-state solutions.
Transient response of FGLs has been investigated by Berger [36], while
mode locking of the FGL to produce soliton like pulses has been modeled by
Morton^al. [37,38].
The rate equations used to model the FGL are of the form [39,40]

where G(AT) is the spatially averaged gain at the average carrier density,
N, resonant cavity, to is the operating angular frequency with external
feedback, a scatt is the scattering loss, a) r is the reference angular frequency
of the field envelope, E(t),

I(i) is the instantaneous intensity at time, t, and <p(t) the instantaneous
phase.
In Fig. 8.13 is shown the modeled steady-state L-I characteristics
of a typical FGL with strong feedback and relatively large front-facet
reflectivity of 0.04, and grating length of 8 mm. The choice of the initial
phase condition at the interface determines the occurrence of the mode
hop at around 30 mA, at either side of which the laser operates in a
single longitudinal mode. The instability in this region is a result of the
multimode nature of the long external cavity, predominantly due to the
residual front-facet reflection.
Mode hopping can be eliminated by careful choice of operating temper-
ature, as shown in Fig. 8.6, or by the reduction of the front-facet reflecti-
vity. Interference effects due to delayed fields of the external cavity have
been shown to be critical for predicting the stable performance of the FGL
[33]. This effect of resonance-peak spectral splitting (RPSS) is shown in
Fig. 8.14.