Analytical solution of the rate equation in direct modulation of semiconductor laser
ABSTRACT We studied the rate equations of a semiconductor laser operating in a direct modulation mode for the purpose of obtaining the direct dependence of output photon density on modulating current. We show that the system of differential equations may be reduced to a special case when the spontaneous carrier decay rate is equal to the photon decay rate. The unique solution is obtained for this case. We also show that a laser operating in direct modulation exhibits an inertia in switching between the optical and electrical fields which introduces a corresponding loss in the modulating current. The output photon density and the input carrier density depend directly on this loss. For the systems with a minimal and maximal loss, the output photon density can be obtained analytically.
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ABSTRACT: We studied the rate equations of direct modulation laser and showed that it may be reduced to the special case when spontaneous carrier decay rate is equal to the photon decay rate. The solution in this case is unique. For the general case, we investigated the vector field of the differential system of the rate equations and pointed out the basic stability problems of this system when the modulation current was required to change.
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ABSTRACT: A memory diagram, i.e., regions where pattern effects appear at the output of the laser, in the bias-current-versus-modulation-period plane is obtained, both by numerical simulation of the rate equations and by using an analytical approach. A simple method, based on the superposition of the turn-on time probability distribution for the periodic sequence . . .1111. . . of input bits and the turn-on time probability distribution obtained for repetitive gain switching, is used to describe the response of the laser to a pseudorandom word modulation of the injection currentIEEE Journal of Quantum Electronics 07/1993; 29(6-29):1624 - 1630. DOI:10.1109/3.234414 · 2.11 Impact Factor
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