17.2-7 Gain Profile. Consider a 1550-nm InGaAsP amplifier (n = 3.5) of the confi

Question

17.2-7 Gain Profile. Consider a 1550-nm InGaAsP amplifier (n = 3.5) of the configuration shown in Fig. 17.2-6, with identical antireflection coatings on its input and output facets. Calculate the maximum reflectivity of each of the facets that can be tolerated if it is desired to maintain the variations in the gain profile arising from the frequency dependence of the Fabry—Perot transmittance to less than 10% [see (7.1-32)].

Output photons rl Figure 17.2-6 Geometry of a simple semi conductor optical amplifier. Charge carriers travel perpendicularly to the p-n junction, whereas photons travel in the plane of the junction. Area A Input photons The injected-carrier concentration is therefore directly proportional to the injected current density so that the results shown in Figs. 172-3 and 172-4 with n as a parameter may just as well have J as a parameter. In particular, it follows from (17.2- 7) and (17.2-8) that within the linear approximation implicit in (17.2-7), the peak gain coefficient is linearly related to the injected current density J, i.e., It t212 (7.1-31) This expression is similar to (2.5-16) for the intensity of an infinite number of waves with equal phase differences, and with amplitudes that decrease at a geometric rate, as described in Sec2.5B. Assuming that arg(nr2} = 0, this expression can be written in the form (7.1-32) 1+(23/T sin where tit22 (1 ITl2 (12) (7.1-33) max = (1-1T1 r2D2 T1T2 and 1 IriT2 (7.1-34) Finesse

Explanation / Answer

Gain:

gain is a measure of the ability of a two port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port to the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units ("dB gain"). A gain greater than one (zero dB), that is amplification, is the defining property of an active component or circuit, while a passive circuit will have a gain of less than one.

Gain:

Light of frequency v can interact with the carriers of a semiconductor material of bandgap energy E, via band-to-band transitions, provided that v > E,/h. The incident photons may be absorbed resulting in the generation of electron-hole pairs, or they may produce additional photons through stimulated electron-hole recombination radiation . When emission is more likely than absorption, net optical gain ensues and the material can serve as a coherent optical amplifier. Expressions for the rate of photon absorption TV,, and the rate of stimulated emission TJV) were provided in . These quantities depend on the photon-flux spectral density 4,, the quantum-mechanical strength of the transition for the particular material under consideration (which is implicit in the value of the electron-hole radiative recombination lifetime T,.), the optical joint density of states e(v), and the occupancy probabilities for emission and absorption, f,(v) and f,(~). The optical joint density of states e(v) is determined by the E-k relations for electrons and holes and by the conservation of energy and momentum. With the help of the parabolic approximation for the E-k relations near the conduction- and valence-band edges, that the energies of the electron and hole that interact with a photon of energy hv are E, = E, + ?(hv - Eg), E, = E, - hv, C respectively, where m, and m, are their effective masses and l/m, = l/m, + l/m,.

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