Abstract: In this work we present a new combined analytical and numerical method to obtain the turn-on delay time probability distribution P($tau@) of single-mode semiconductor lasers under pseudorandom work modulation (PRWM) of the injection current. The laser is descried by stochastic rate equations that include the effect of the spontaneous emission noise. The method allows the calculation of P($tau@) for lasers biased below and above threshold, and for different modulation frequencies. For bias currents below threshold the method is based on the same assumptions that the theory already developed for the periodic modulation regime. When the laser is biased above threshold a new method is introduced to obtain P($tau@) in the periodic modulation case. Under PRWM the turn-on time probability distribution is shown to satisfy an integral equation, and the kernel is obtained by numerical integration of the deterministic laser rate equations. In this way the numerical simulations of the stochastic rate equations is avoided. Then large computational times are not necessary to obtain P($tau@). The results obtained with this method are in good agreement with the numerical simulations of the stochastic rate equations. These results show, in agreement with previous numerical results, that turn-on time statistics for laser diodes modulated in the GHz range is very different under periodic and PRWM regimes. In the periodic regime timing jitter is rather independent of the bias current. Under PRWM timing jitter becomes larger when biasing above threshold that when biasing below threshold. This large jitter is related to a bimodal P($tau@) due to pattern effects. A bias slightly below threshold suppresses these patterns effects making the laser response almost independent of previous input bits. The method developed in this work can be used to obtain the bit error rate as a function of the transmission distance for different bias currents and bit rates. !42
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机译：摘要：在这项工作中，我们提出了一种新的分析和数值相结合的新方法，用于在注入电流的伪随机功调制（PRWM）下获得单模半导体激光器的开启延迟时间概率分布P（$ tau @）。随机速率方程式描述了激光器，其中包括自发发射噪声的影响。该方法允许针对偏置低于和高于阈值的激光器以及不同的调制频率计算P（$ tau @）。对于低于阈值的偏置电流，该方法基于与已经针对周期性调制机制开发的理论相同的假设。当激光器被偏置到阈值以上时，在周期调制的情况下，一种新的方法被引入以获得P（$ tau @）。在PRWM下，打开时间概率分布显示为满足一个积分方程，并且通过对确定性激光速率方程进行数值积分来获得内核。这样，避免了随机速率方程的数值模拟。然后，不需要大量的计算时间即可获得P（$ tau @）。用这种方法获得的结果与随机速率方程的数值模拟非常吻合。这些结果表明，与以前的数值结果相一致，在周期性和PRWM机制下，在GHz范围内调制的激光二极管的开启时间统计信息非常不同。在周期性状态下，时序抖动与偏置电流无关。在PRWM下，偏置高于阈值时的时序抖动会大于偏置低于阈值时的时序抖动。由于模式效应，这种较大的抖动与双峰P（$ tau @）有关。略低于阈值的偏置会抑制这些图案效应，从而使激光响应几乎独立于先前的输入位。在这项工作中开发的方法可用于获得针对不同偏置电流和比特率的，作为传输距离的函数的误码率。 ！42
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