2162 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 11, NOVEMBER 1998 Effects of Carrier Cooling and Carrier Heating in Saturation Dynamics and Pulse Propagation Through Bulk Semiconductor Absorbers Alexander V. Uskov, Member, IEEE, J. R. Karin, John E. Bowers, Fellow, IEEE, John G. McInerney, Member, IEEE, and Jean Le Bihan, Member, IEEE Abstract—Numerical modeling has shown that carrier cooling and carrier heating strongly influence saturation dynamics and pulse shaping in bulk semiconductor absorbers. With no electric field in the absorbing region, carrier cooling leads to strong additional fast saturation of absorption. The saturation causes a substantial decrease in the saturation energies for subpicosecond pulses in comparison with picosecond pulses. Comparison of bulk and quantum-well absorbers shows that fast saturation can be stronger in a bulk absorber, so bulk saturable absorbers may be interesting for usage in mode-locked solid-state lasers. Applying a nonzero electric field to a bulk absorber leads to strong carrier heating, which in turn suppresses absorption saturation. In this case, transition to absorption saturation involves new mechanisms such as screening of the electric field by photogenerated carriers, as well as carrier cooling due to carrier–phonon interaction and by generated cold carriers. Carrier heating by the electric field causes the saturation energy of the absorber to increase with the applied electric field. The increased saturation energy allows one to shorten high-energy picosecond and subpicosecond pulses without increasing the length of the saturable absorber, which could be useful for the generation of high energy pulses with mode-locked and -switched semiconductor lasers. Index Terms— Carrier heating, intraband carrier dynamics, mode-locked lasers, saturable absorbers, semiconductor lasers. I. INTRODUCTION I NTRABAND carrier kinetics in semiconductors has at- tracted much attention because of their importance in defining and limiting high-speed laser performance. A great deal of attention has focused on the effects of intraband carrier kinetics, namely on spectral hole burning and carrier heating in semiconductor amplifying media (see, for instance, [1]–[15] and references therein). In passively mode-locked and - switched semiconductor [16]–[19] and solid-state [20]–[21] Manuscript received March 17, 1998; revised July 23, 1998. The work of A. V. Uskov was supported by Minist´ ere de l’Enseignement, de la Recherche et de la Technologie, and Centre International des Etudiants et Stagiaires. A. V. Uskov was with the Ecole Nationale d’Ingenieurs de Brest, Technopole Brest-Iroise-CP15, 29608 Brest Cedex, France, on leave from Lebedev Physical Institute, 117924 Moscow, Russia. J. R. Karin is with the Center for Quantized Electronic Structures, University of California, Santa Barbara, CA 93106-4170 USA. J. E. Bowers is with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9560 USA. J. G. McInerney is with the Department of Physics/Optronics Ireland, National University of Ireland, University College Cork, Cork, Ireland. J. Le Bihan is with Ecole Nationale d’Ingenieurs de Brest, Technopole Brest-Iroise-CP15, 29608 Brest Cedex, France. Publisher Item Identifier S 0018-9197(98)08082-8. lasers, semiconductor saturable absorbers play a principal role governing pulse generation. Intraband carrier kinetics in semiconductor absorbers can strongly influence the absorption saturation dynamics, defining, in fact, the scenario of mode- locking and pulse generation [20]–[23]. It explains why in the last few years the dynamics of saturation in semicon- ductor absorbers, particularly the effects of intraband carrier kinetics on absorption, have been studied [21], [24]–[29] in the same detail as gain dynamics in amplifiers. Complicated saturation dynamics based on intraband carrier kinetics have been demonstrated for both bulk [24]–[26] and quantum- well (QW) [21], [24], [27], [28] saturable absorbers. Those studies demonstrated that various mechanisms influence ab- sorption dynamics in semiconductors, including nonthermal energy distribution of photogenerated carriers (like spectral hole burning in amplifiers) [21], [24]–[27], carrier cooling and heating [24]–[27], quantum-confined Stark effect [28], and the dynamics of excitonic absorption [29]. All these mechanisms are related to intraband carrier kinetics—transport of carri- ers in both energy and real spaces within the same energy band—and their characteristic times are of picosecond and femtosecond time scales, much shorter than interband carrier relaxation times. Femtosecond pump-probe experiments on reverse-biased bulk PIN heterostructure waveguide saturable absorbers and modeling of these experiments are described in [24]–[26]. Those studies showed that carrier heating due to the electric field is significant in such absorbers, and this heating together with the dynamics of the electric field can have a dominant influence on the absorption saturation dynamics in bulk ab- sorbers. Carrier heating by the electric field is impossible in QW structures, where the electric field is normal to QW’s in which carriers are confined. Thus, electric field carrier heating principally distinguishes the saturation dynamics in bulk and QW absorbers. The temperature of the carriers in the QW, generated during absorption of light, is lower than lattice temperature; these “cold” carriers lead to “fast” saturation of absorption in addition to “slow” saturation [21]–[23], [27]. The fast saturation disappears on a picosecond time scale due to heating of the cold carriers to the lattice temperature. In bulk absorbers, carrier heating suppresses saturation of absorption [25], [26]. In this paper, we study theoretically the effects of carrier cooling and heating on the saturation dynamics and pulse 0018–9197/98$10.00  1998 IEEE