Synchronization and Clustering in a Multimode Quantum Dot Laser

Abstract

We analyze experimentally the intensity oscillations of the longitudinal modes of quantum dot semiconductor lasers. We show that the modal intensities can oscillate chaotically with different average frequencies, but obey a highly organized antiphase dynamics leading to a constant total output power. The fluctuations are in the MHz range. We report the first experimental observation of frequency clustering associated with synchronization. We also observe the propagation of perturbations across the optical spectrum from blue to red. DOI: 10.1103/PhysRevLett.96.053902 PACS numbers: 42.65.Sf, 05.40.Ca, 05.45.ÿa, 42.65.Pc Coupled oscillators exhibit many interesting features that appear naturally in everyday life [1,2]. Such systems can be broadly divided into either globally coupled, where each oscillator is directly influenced by each of the other oscillators, or locally coupled, where nearest-neighbor interactions dominate. Synchronization occurs in both types of systems. The appearance of one or more clusters, where each cluster consists of a subset of synchronized oscillators, was predicted for globally coupled systems in the framework of the Kuramoto model [3]. In lasers, synchronization has been harnessed to achieve phase locked arrays of lasers which deliver high brightness outputs (local coupling) [4] and mode-locked lasers resulting in very short optical pulses (global coupling). Fundamental studies of chaotic state locking have also been examined in multimode lasers; e.g., two coupled modes of a ring laser can exhibit chaotic phase synchronization [5]. Globally coupled multimode lasers also exhibit antiphase dynamics [6,7]. Antiphase dynamics was studied theoretically and experimentally in diverse globally coupled systems such as Josephson junctions [8], chemical oscillators [9], and olfactory systems [10].The aim of this Letter is to report the first experimental evidence, to our best knowledge, of clustering effects associated with synchronization. This was achieved by analyzing the intensity oscillations of the longitudinal modes of quantum dot semiconductor lasers. Each laser has up to 40 longitudinal modes where each lasing mode displays large amplitude chaotic fluctuations although the total laser output power remains almost constant. The fluctuations measured in each mode occur at frequencies of tens of MHz, which is much smaller than the frequency difference between two consecutive modes (25 GHz) and the laser's relaxation oscillation frequency (>1 GHz). Modal fluctuations in quantum well lasers at similar frequencies, known as mode partition, have previously been interpreted as a noise induced phenomenon [11]. However, our measurements indicate several deterministic features which cannot be accounted for by such a description. We observe that groups of modes may have the same frequency indicating the appearance of clustering. We also observe the propagation of perturbations across the optical spectrum from blue to red similar to those observed in quantum well semiconductor lasers [12]. Transi...

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