3.5. LASER CHARACTERISTICS 111
Figure 3.21: Measured (solid curves) and fitted (dashed curves) modulation response of a 1.55-
μm DFB laser as a function of modulation frequency at several bias levels. (After Ref. [70];
©c1997 IEEE; reprinted with permission.)
wherePbandNbare the steady-state values at the bias currentIb,|pm|and|nm|are small
changes occurring because of current modulation, andθmandψmgovern the phase lag
associated with the small-signal modulation. In particular,pm≡|pm|exp(iθm)is given
by [2]
pm(ωm)=PbGNIm/q
(ΩR+ωm−iΓR)(ΩR−ωm+iΓR), (3.5.19)
where
ΩR=[GGNPb−(ΓP−ΓN)^2 / 4 ]^1 /^2 , ΓR=(ΓP+ΓN)/ 2 , (3.5.20)
ΓP=Rsp/Pb+εNLGPb, ΓN=τc−^1 +GNPb. (3.5.21)ΩRandΓRare the frequency and the damping rate ofrelaxation oscillations. These two
parameters play an important role in governing the dynamic response of semiconductor
lasers. In particular, the efficiency is reduced when the modulation frequency exceeds
ΩRby a large amount.
Similar to the case of LEDs, one can introduce thetransfer functionas
H(ωm)=pm(ωm)
pm( 0 )=
Ω^2 R+Γ^2 R
(ΩR+ωm−iΓR)(ΩR−ωm+iΓR). (3.5.22)
The modulation response is flat [H(ωm)≈1] for frequencies such thatωmΩR, peaks
atωm=ΩR, and then drops sharply forωmΩR. These features are observed exper-
imentally for all semiconductor lasers [67]–[70]. Figure 3.21 shows the modulation