Analytical and computational study of self-induced transparency mode locking in quantum cascade lasers
Analytical and computational study of self-induced transparency mode locking in quantum cascade lasers
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DOI：
10.1103/physreva.79.063841
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发表时间：
2009-06
影响因子：
2.9
通讯作者：
M. A. Talukder;C. Menyuk
中科院分区：
文献类型：
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作者：
M. A. Talukder;C. Menyuk
利用自诱导透明效应实现激光锁模的可能性从20世纪60年代末就开始讨论，但从未被观察到。在之前的工作中，我们提出量子级联激光器是实现自诱导透明锁模的理想工具，因为它们具有快速的增益恢复时间和相对较长的相干时间，并且因为它可以交错增益和吸收周期。在这里，我们提出的量子级联激光器的设计，满足要求的自诱导透明锁模在8和12米，这表明它是可以满足这些要求在很宽的波长范围内。描述具有增益和吸收周期的量子级联激光器动力学的耦合Maxwell-Bloch方程已被解析和计算求解。分析锁模的解决方案以前已经发现的条件下，没有频率失谐，吸收周期的偶极矩的增益周期的两倍，输入脉冲是在增益介质中的脉冲，增益和吸收周期的增益恢复时间比相干时间T2长得多，是短的往返时间相比。结果表明，锁模脉冲的持续时间是T2的数量级，这通常是约100 fs的量子级联激光器。在这项工作中，这些分析结果进行审查和扩展，包括部分反转的增益和吸收周期和频率失谐的影响。导出了长相干时间极限下的能量定理。Maxwell-Bloch方程已经被计算求解，以确定当存在频率失谐时锁模解的鲁棒性，吸收周期的偶极矩不同于增益周期的偶极矩的两倍，增益弛豫时间是1-10 ps的量级，如通常在量子级联激光器中获得的，并且初始脉冲不是增益介质中的脉冲。我们发现，锁模的解决方案存在于一个广泛的参数范围。我们还研究了初始脉冲的演化，初始脉冲比最终的锁模脉冲宽得多。只要初始脉冲持续时间为T1量级或更短，并且具有足够的能量在介质中产生脉冲，则最终将形成持续时间为T2量级的锁模脉冲。
The possibility of using the self-induced transparency effect to achieve laser mode locking has been discussed since the late 1960s but has never been observed. In prior work, we proposed that quantum cascade lasers are the ideal tool to realize self-induced transparency mode locking due to their rapid gain recovery times and relatively long coherence times, and because it is possible to interleave gain and absorbing periods. Here, we present designs of quantum cascade lasers that satisfy the requirements for self-induced transparency mode locking at both 8 and 12 m, indicating that it is possible to satisfy these requirements over a wide wavelength range. The coupled Maxwell-Bloch equations that define the dynamics in quantum cascade lasers that have both gain and absorbing periods have been solved both analytically and computationally. Analytical modelocked solutions have previously been found under the conditions that there is no frequency detuning, the absorbing periods have a dipole moment twice that of the gain periods, the input pulse is a pulse in the gain medium, and the gain recovery times in the gain and absorbing periods are much longer than the coherence time T2 and are short compared to the round-trip time. It was shown that the mode-locked pulse durations are on the order of T2, which is typically about 100 fs in quantum cascade lasers. In this work, these analytical results are reviewed and extended to include the effects of partial inversion in the gain and absorbing periods and of frequency detuning. An energy theorem in the limit of long coherence times is derived. The MaxwellBloch equations have been solved computationally to determine the robustness of the mode-locked solutions when frequency detuning is present, the dipole moment of the absorbing periods differs from twice that of the gain periods, the gain relaxation time is on the order of 1–10 ps, as is typically obtained in quantum cascade lasers, and the initial pulse is not a pulse in the gain medium. We find that mode-locked solutions exist over a broad parameter range. We have also investigated the evolution of initial pulses that are initially much broader than the final mode-locked pulses. As long as the initial pulse duration is on the order of T1 or shorter and has enough energy to create a pulse in the medium, a mode-locked pulse with a duration on the order of T2 will ultimately form.