REFERENCES 127
photon lifetime. What is the threshold value of the electron population? Assume
that the gain varies asG=GN(N−N 0 )withGN= 6 × 103 s−^1 andN 0 = 1 × 108.
3.10Determine the threshold current for the semiconductor laser of Problem 3.9 by
taking 2 ns as the carrier lifetime. How much power is emitted from one facet
when the laser is operated twice above threshold?
3.11Consider the laser of Problem 3.9 operating twice above threshold. Calculate
the differential quantum efficiency and the external quantum efficiency for the
laser. What is the device (wall-plug) efficiency if the external voltage is 1.5 V?
Assume that the internal quantum efficiency is 90%.
3.12Calculate the frequency (in GHz units) and the damping time of the relaxation
oscillations for the laser of Problem 3.9 operating twice above threshold. Assume
thatGP=− 4 × 104 s−^1 , whereGPis the derivative ofGwith respect toP. Also
assume thatRsp= 2 /τp.
3.13Determine the 3-dB modulation bandwidth for the laser of Problem 3.11 biased
to operate twice above threshold. What is the corresponding 3-dB electrical
bandwidth?
3.14The threshold current of a semiconductor laser doubles when the operating tem-
perature is increased by 50◦C. What is the characteristic temperature of the laser?
3.15Derive an expression for the 3-dB modulation bandwidth by assuming that the
gainGin the rate equations varies withNandPas
G(N,P)=GN(N−N 0 )( 1 +P/Ps)−^1 /^2.
Show that the bandwidth saturates at high operating powers.
3.16Solve the rate equations (3.5.1) and (3.5.2) numerically by usingI(t)=Ib+
Imfp(t), wherefp(t)represents a rectangular pulse of 200-ps duration. Assume
thatIb/Ith= 0. 8 ,Im/Ith= 3 ,τp=3 ps,τc=2 ns, andRsp= 2 /τp. Use Eq.
(3.5.15) for the gainGwithGN= 104 s−^1 ,N 0 = 108 , andεNL= 10 −^7. Plot
the optical pulse shape and the frequency chirp. Why is the optical pulse much
shorter than the applied current pulse?
3.17Complete the derivation of Eq. (3.5.32) for the RIN. How does this expression
change if the gainGis assumed of the form of Problem 3.15?
3.18Calculate the autocorrelationCpp(τ)by using Eqs. (3.5.31) and (3.5.32). Use it
to derive an expression for the SNR of the laser output.
References
[1] Z. Alferov,IEEE J. Sel. Topics Quantum Electron. 6 , 832 (2000).
[2] G. P. Agrawal and N. K. Dutta,Semiconductor Lasers, 2nd ed., Van Nostrand Reinhold,
New York, 1993.
[3] A. R. Adams and Y. Suematsu,Handbook of Semiconductor Lasers and Photonic Inte-
grated Circuits, Chapman and Hall, New York, 1994.
[4] N. W. Carlson,Monolithic Diode Laser Arrays, Springer, New York, 1994.
