**Quantum noise and coherence**
Progress
in integrated optoelectronics technologies has reduced the laser device
dimensions to an order of a single wavelength in size. As a consequence,
the quantum fluctuations in the light field become increasingly important. Therefore,
a comprehensive model of the quantum noise effects is indispensable for the
correct simulation of the optical field evolution. We exploit the
quantum-classical correspondence in the presence of the quantum noise by
formulating stochastic equations. Within this framework the quantum noise due
to the spontaneous emission is simulated by adding random Langevin noise terms
to the deterministic evolution of the optical field and to the medium
polarisation through the Maxwell’s equations. This term generates the
statistical fluctuations of the laser field, which in turn, induce fluctuations
in the population inversion, thus modifying the equations of motion of the
quantum system. Using the extended Maxwell-Bloch equations, we have numerically
demonstrated the intracavity electric field build up with time (Fig. 11 **click on figure to see a movie**)*Fig. 11. **Spatially resolved
dynamics of the electric field build-up within the cavity due solely to the
noise background as a function of time elapsed (initial population profile r*_{30}=1
within the cavity, providing gain)
The corresponding population inversion dynamics (Fig. 12 **click on figure to see evolution**) results in the
coherent oscillations build-up with the time at the output laser facet of a
semiconductor microcavity (Fig. 13) identifying the lasing threshold and in ultrafast
relaxation behaviour of the electric field envelope until the settlement of the
steady-state emission. *Fig. 12.** Time evolution of
the intracavity electric field and the population inversion*
*Fig.13. **Build up of coherent
self-sustained oscillations at the output facet of a semiconductor microcavity
filled with initially inverted gain medium (a) electric field; (b) Expanded
view of the fast single mode oscillations in the steady-state(gain saturation)
region*
The simulations predict ultrafast relaxation behaviour that
is not present in the usual rotating wave and slowly-varying envelope
approximations. The simulations provide an estimate for the coherence time of
the laser emission and allow us to infer and subsequently optimize important
emission characteristics, such as the spontaneous emission rate, the laser line
shape, and the relaxation oscillation frequencies and decay rates. |