Noise Properties of Injection Locked Semiconductor Lasers: Application to Optically Driven Phased Array Antennas.

A novel optically driven phased array antenna system is proposed. The proposed system utilizes heterodyne techniques to generate the microwave carrier frequency and phases. The heterodyning at each antenna element requires three injection locked lasers. The effects on the antenna performance due to the noise properties of injection locked lasers is investigated. A deterministic analysis of semiconductor laser injection locking based on the rate equations is presented. Included in the rate equations are the effects of amplitude-phase coupling, carrier dynamics, and gain saturation. We find that the steady state locking condition is not significantly affected by gain saturation. We also determine that the the rise (fall) time of the injected signal reduces the excitation of relaxation oscillations in the injection locking transients. We show that this reduction directly affects the bandwidth of antenna. It is possible to achieve a bandwidth which is roughly 10% of the laser relaxation frequency. The noise properties of injection locked semiconductor lasers are analyzed by including Langevin noise sources in the rate equations. We show for the weak injection limit, and with a nonzero injection rise time, that the carrier dynamics may be adiabatically eliminated from the rate equations. We make use of the Fokker-Planck equation to describe the statistics of the steady state locking condition. We also include the effects of finite detector bandwidth on the statistics. In addition, we show that the steady state locked condition corresponds to a particle in a potential well which has a finite probability to escape. Using the mean escape time, we point out the differences between the deterministic and noise locking properties. We also discuss the effects of noise on the locking time. We present experimental results which show the locking time of semiconductor lasers is dependent on the free running frequency difference and the locking bandwidth of the master and slave laser. The trends observed experimentally were the same as predicted by the analysis. Finally, we apply the knowledge of the noise properties of injection locked semiconductor lasers to the proposed antenna system. We examine the effect of noise on the gain, signal to noise ratio, and the bandwidth of the antenna system. We show that the performance degradation of the system, due to the noise in the lasers, is minimal, and therefore the bandwidth promise of optical drive could well be achieved with the use of heterodyne laser locking techniques.