Abstract

The noise properties of semiconductor lasers are studied by using the equations for the photon and carrier number fluctuations originally introduced in [1] and extended in [2] to include the blocking of the injected carriers induced by the Pauli principle Here F^fld, F^pol, F^spo, and F^cir are the operators corresponding to field noise, polarization noise, spontaneous emission noise, and thermal noise in the driving circuit resistance, respectively. The time rates γ_sti, γ_blk, γ_spo and γ_cir take into account the carrier fluctuation damping by stimulated recombinations, pump-blocking, spontaneous recombinations, and injection from the circuit, respectively. Pump-blocking damps the carrier fluctuations because if N rises above its stationary value, more of the injected carriers will find their quantum states already occupied, and therefore less of them will be allowed into the active layer, thus contributing to restore the stationary value of N The fluctuation in the output photon flux is δI^out = 2κδi – F^fld, κ being the field decay rate. The analytical expression of the outside intensity noise spectrum is given by the thick lines in Fig. (1) for two values of the pumping The thin lines represents the numerically-derived spectra, obtained by Fourier transforming the time-dependent solutions of Eqs. (1). In the higher-pump case we have represented with the full and the dashed lines respectively the cases in which pump-blocking is taken into account and artificially set equal to zero A sample of the corresponding dynamical solutions is represented in Fig. (2) and Fig (3). Both the carrier and the photon number fluctuations have an oscillating behavior, whose frequency$v_{osc}=\sqrt{2{\text{κγ}}_{sti}}/2\text{π}$ corresponds to the relaxation oscillation. When δN is positive δI increases, meaning that the probability of a photon emission event increases, so that a process of “regularization” of the stimulated emission takes place, which is more and more effective as the amplitude of the δI oscillations increases We have verified that this amplitude increases as the pump rises, and from Fig. (1) we deduce that correspondingly the low-frequency noise spectrum diminishes and goes below the shot noise level (normalized to 1), thus exhibiting intensity squeezing. By comparing Fig (2) and Fig (3) we see that pump blocking reduces the amplitude of the oscillations of δN and consequently of δI Correspondingly, Fig. (1) shows that in the presence of pump-blocking the low-frequency intensity noise increases and squeezing is hindered.

© 2000 IEEE