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Figure Captions

Figure 1.
This pictures explains the setup for input-output fluxes. Carriers and energy are added at $\omega _0$ at rates and $\omega _0 Q_0$ respectively. Energy and some carriers are dissipated at $\omega _R>\omega _0$ (an idealization) and carriers and some energy are absorbed by the laser at $\omega _L$ . Finite flux stationary solutions are realized in the windows $(\omega _L,\omega _0)$ and $(\omega _0,\omega _R)$ although in practice there will be some losses through both of these regions.
Figure 2
(a) Numerical solution of (4.13). Initial conditions are $n_{\omega =0.1}=f_{\omega =0.1}$ , $n'_{\omega =0.1}=f'_{\omega =0.1}$ , where $f_\omega =1/(\exp{(7\omega -4)}+1)$ . The results are shown for . The dot size indicates the value of the flux, with larger dots corresponding to larger flux.
(b) Same as (a) but with (4.14) and $n_{\omega =0.3}=f_{\omega =0.3}, n^\prime_{\omega =0.3}=f^\prime_{\omega =0.3}$ . The results are shown for .
Figure 3.
(a) Time evolution of the distribution function as described by (4.9), with boundary conditions at both ends. The initial distribution (thin line) relaxes to a Fermi-Dirac state (thick line). Several intermediate states are shown by long-dashed and short-dashed lines.
(b) Same as (a), but for at both ends. The initial distribution function (thick line) relaxes to finite--equilibria as shown by the long-dashed line (only the final steady state is shown). Also shown are the results for the boundary conditions at both ends (short-dashed line) and for at both ends (dotted line).
Figure 4
Time dependence of distributions (a) and laser intensity (b) according to (5.15-5.18). Local-band pumping is modeled by specifying the carrier and energy flux rates and $P_L=-\omega _L Q_L$ at the right ( $\omega _0\simeq 200 {\rm meV}$ ) boundary. The initial distribution function (shown by a thin line in this and consequent figures) evolves through a number of intermediate states shown by dashed lines, until the laser switches on. The final (steady) distribution function is shown by a thick solid line (in this and subsequent figures). Time is given in units of the relaxation time $\tau _{\rm relax}=100fs$ on this and subsequent figures.
The laser fails to switch on in the broad-band pumping case for these levels of pumping.
Figure 5.
Same as in Figure 4 but for increased pump rate.
(a) Broad-band pumping (b) Narrow-band pumping with $\omega _0\simeq 200 {\rm meV}$ .

Next: Appendix. Diagrams Up: text Previous: Acknowledgment

Dr Yuri V Lvov 2007-01-31