Piccardo Marco, Chevalier Paul, Schwarz Benedikt, Kazakov Dmitry, Wang Yongrui, Belyanin Alexey, Capasso Federico
Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Institute of Solid State Electronics, TU Wien, 1040 Vienna, Austria.
Phys Rev Lett. 2019 Jun 28;122(25):253901. doi: 10.1103/PhysRevLett.122.253901.
Laser dynamics encompasses universal phenomena that can be encountered in many areas of physics, such as bifurcation and chaos, mode competition, resonant nonlinearities, and synchronization-or locking-of oscillators. When a locking process occurs in a multimode laser, an optical frequency comb is produced, which is an optical spectrum consisting of equidistant modes with a fixed phase relationship. Describing the formation of self-starting frequency combs in terms of fundamental laser equations governing the field inside the cavity does not allow one, in general, to grasp how the laser synchronizes its modes. Our finding is that, in a particular class of lasers where the output is frequency modulated with small or negligible intensity modulation, a greatly simplified description of self-locking exists. We show that in quantum cascade lasers-solid-state representatives of these lasers characterized by an ultrashort carrier relaxation time-the frequency comb formation obeys a simple variational principle, which was postulated over 50 years ago and relies on the maximization of the laser output power. The conditions for the breakdown of this principle are also experimentally identified, shedding light on the behavior of many different types of lasers, such as dye, diode, and other cascade lasers. This discovery reveals that the formation of frequency-modulated combs is an elegant example of an optimization problem solved by a physical system.
激光动力学包含许多物理领域中都会出现的普遍现象，如分岔和混沌、模式竞争、共振非线性以及振荡器的同步或锁定。当多模激光器中发生锁定过程时，会产生一个光学频率梳，它是一种由具有固定相位关系的等距模式组成的光谱。一般来说，用描述腔内光场的基本激光方程来描述自启动频率梳的形成，无法让人理解激光器是如何使其模式同步的。我们的发现是，在一类特定的激光器中，其输出是频率调制的，而强度调制很小或可忽略不计，存在一种大大简化的自锁描述。我们表明，在量子级联激光器（这类激光器的固态代表具有极短的载流子弛豫时间）中，频率梳的形成遵循一个简单的变分原理，该原理在50多年前就已提出，它依赖于激光输出功率的最大化。我们还通过实验确定了这一原理失效的条件，并揭示了许多不同类型激光器（如染料激光器、二极管激光器和其他级联激光器）的行为。这一发现表明，调频梳的形成是物理系统解决优化问题的一个精妙范例。
