question archive The laser package laser welding is used to hold various parts of the assembly becomes a part of the transmitter package, which includes a associated with the driving circuit
The laser package laser welding is used to hold various parts of the assembly becomes a part of the transmitter package, which includes a associated with the driving circuit
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The laser package laser welding is used to hold various parts of the assembly becomes a part of the transmitter package, which includes a associated with the driving circuit. The choice of transmitter package depends on this 122 udes other electrical components type of application: a dual-in-line package or a butterfly housing with multiple pins typically used. Testing and packaging of optical transmitters are two important parts of the many facturing process [135]. and both of them add considerably to the cost of a transmitted" The development of low-cost packaged transmitters is necessary, especially for locer area and local-loop applications. Problems 3.1 Find the composition of the quaternary alloy InGaAs for making semiconduct. lasers operating at 1.3- and 1.55-um wavelengths. 3.2 The active region of a 1.3-um InGaAsP laser is 250 um long. Find the active region gain required for the laser to reach threshold. Assume that the internal loss is 30 cm-1, the mode index de index is 3.3, and the confinement factor is 0.4. 3.3 Derive the eigenvalue equation for the transverse-electric (TE) modes of a pla nar waveguide of thickness d and refractive index ni sandwiched between two cladding layers of refractive index n2. (Hint: Follow the method of Section 2.2.2 using Cartesian coordinates.) 3.4 Use the result of Problem 3.3 to find the single-mode condition. Use this condi- tion to find the maximum allowed thickness of the active layer for a 1.3-um semi- conductor laser. How does this value change if the laser operates at 1.55 um? Assume n1 = 3.5 and n2 = 3.2. 3.5 Solve the rate equations in the steady state and obtain the analytic expressions for P and N as a function of the injection current I. Neglect spontaneous emission for simplicity. 3.6 A semiconductor laser is operating continuously at a certain current. Its output power changes slightly because of a transient current fluctuation. Show that the laser power will attain its original value through an oscillatory approach. Obtain the frequency and the damping time of such relaxation oscillations. 3.7 A 250-um-long InGaAsP laser has an internal loss of 40 cm . It operates at 1.55 um in a single mode, with the modal index 3.3 and the group index 3.4. Calculate the photon lifetime. What is the threshold value of the electron popu lation? Assume that the gain varies as G = GN(N - No) with GN = 6 x 103 s- 1 and No = 1 x 108 3.8 Determine the threshold current for the semiconductor laser of Problem 3.7 by taking 2 ns as the carrier lifetime. How much power is emitted from one facet when the laser is operated twice above threshold? 3.9 Consider the laser of Problem 3.7 operating twice above threshold. Calculate the differential quantum efficiency and the external quantum efficiency for the
122 Chapter 3. Optical Transmitters laser. What is the device (wall-plug) efficiency if the external voltage is 1.5 V? Assume that the internal quantum efficiency is 90%. 3.10 Calculate the frequency (in GHz units) and the damping time of the relaxation oscillations for the laser of Problem 3.7 operating twice above threshold. Assume that Gp = -4 x 10's"', where Gp is the derivative of G with respect to P. Also assume that Rsp = 2/tp. 3.11 Determine the 3-dB modulation bandwidth for the laser of Problem 3.7 biased bandwidth? to operate twice above threshold. What is the corresponding 3-dB electrical 3.12 The threshold current of a semiconductor laser doubles when the operating tem- perature is increased by 50C. What is the characteristic temperature of the laser? 3.13 Derive an expression for the 3-dB modulation bandwidth by assuming that the gain G in the rate equations varies with N and P as G(N, P) = GN(N - No) (1 + P/PS)-1/2. Show that the bandwidth saturates at high operating powers. 3.14 Solve the rate equations (3.3.1) and (3.3.2) numerically by using I(t) = 16 + Imfp(t), where fp(t) represents a rectangular pulse of 200-ps duration. Assume that Ib/ Ith = 0.8, Im/ Ith = 3, To = 3 ps, To = 2 ns, and Rsp = 2/ Up. Use Eq. (3.3.15) for the gain G with GN = 10* s , No = 108, and ENL = 10-7. Plot the optical pulse shape and the frequency chirp. Why is the optical pulse much shorter than the applied current pulse? 3.15 Complete the derivation of Eq. (3.3.31) for the RIN. How does this expression change if the gain G is assumed of the form of Problem 3.15? 3.16 Calculate the autocorrelation Cop(7) by using Eqs. (3.3.30) and (3.3.31). Use it to derive an expression for the SNR of the laser output. 3.17 Show that the external quantum efficiency of a planar LED is given approx- imately by next = n"(n + 1)-2, where n is the refractive index of the semi- conductor-air interface. Consider Fresnel reflection and total internal reflection at the output facet. Assume that the internal radiation is uniform in all directions. 3.18 Prove that the 3-dB optical bandwidth of a LED is related to the 3-dB electrical bandwidth by the relation f3dB (optical) = V3f3dB(electrical). 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, 1993 Wiley, Hoboken, NJ, 2008.
