3.5. LASER CHARACTERISTICS 115
Figure 3.23: RIN spectra at several power levels for a typical 1.55-μm semiconductor laser.wherei,j=P,N,orφ, angle brackets denote the ensemble average, andDijis called
thediffusion coefficient. The dominant contribution to laser noise comes from only
two diffusion coefficientsDPP=RspPandDφφ=Rsp/ 4 P; others can be assumed to be
nearly zero [82].
The intensity-autocorrelation function is defined as
Cpp(τ)=〈δP(t)δP(t+τ)〉/P ̄^2 , (3.5.30)whereP ̄≡〈P〉is the average value andδP=P−P ̄represents a small fluctuation. The
Fourier transform ofCpp(τ)is known as therelative-intensity-noise(RIN) spectrum
and is given by
RIN(ω)=∫∞−∞Cpp(τ)exp(−iωt)dt. (3.5.31)The RIN can be calculated by linearizing Eqs. (3.5.26) and (3.5.27) inδPandδN,
solving the linearized equations in the frequency domain, and performing the average
with the help of Eq. (3.5.29). It is given approximately by [2]
RIN(ω)=2 Rsp{(Γ^2 N+ω^2 )+GNP ̄[GNP ̄( 1 +N/τcRspP ̄)− 2 ΓN]}
P ̄[(ΩR−ω)^2 +Γ^2 R][(ΩR+ω)^2 +Γ^2 R] , (3.5.32)whereΩRandΓRare the frequency and the damping rate of relaxation oscillations.
They are given by Eq. (3.5.21), withPbreplaced byP ̄.
Figure 3.23 shows the calculated RIN spectra at several power levels for a typi-
cal 1.55-μm InGaAsP laser. The RIN is considerably enhanced near the relaxation-
oscillation frequencyΩRbut decreases rapidly forωΩR, since the laser is not able
to respond to fluctuations at such high frequencies. In essence, the semiconductor laser