Unveiling the complexity of Arnold's tongues in a breathing-soliton laser

Synchronization occurs ubiquitously in nature and science. The synchronization regions generally broaden monotonically with the strength of the forcing, thereby featuring a tongue-like shape in parameter space, known as Arnold's tongue. Such a shape is universal, prevailing in many diverse synchronized systems. Interestingly, theoretical studies suggest that under strong external forcing, the shape of the synchronization regions can change substantially and even holes can appear in the solid patterns. However, experimentally accessing these abnormal regimes is quite challenging, mainly because many real-world systems displaying synchronization become fragile under strong forcing. Here, we are able to observe these intriguing regimes in a breathing-soliton laser. Two types of abnormal synchronization regions are unveiled, namely, a leaf- and a ray-like shape. High-resolution control of the loss allows holes to be revealed in the synchronization regions. Our work opens the possibility to study intriguing synchronization dynamics using a simple breathing-soliton laser as a testbed.