Complex Optical Networks based on Vertical-Cavity Surface-Emitting Lasers (VCSELs)

Pflüger, Moritz
PhD Thesis (2023)

This thesis is centered around the experimental realization of networks of optically coupled vertical-cavity surface-emitting lasers (VCSELs) that are arranged in square-lattice arrays, using diffraction in an external cavity. After successfully implementing the diffractive coupling scheme, we experimentally study qualitatively and quantitatively the coupling of VCSEL pairs and of an entire VCSEL array, as well as simultaneous optical injection into all the VCSELs. Finally, we evaluate the established network's potential for brain-inspired information processing.

Very few networks containing more than twenty optically coupled semiconductor lasers (SLs) have so far been implemented, although they are interesting for various reasons. From a fundamental research point of view, they allow studying the dynamics of real-world complex networks at high speed. From an application-oriented perspective, they are promising hardware substrates for neuro-inspired computing.

We first characterize the individual VCSELs. After that, we study the behaviour of coupled VCSEL pairs, mainly by analyzing their optical and radio-frequency (RF) spectra. In the RF spectra of the central VCSEL of the array, we find signatures for coupling with every individual non-central VCSEL. Analyzing the optical spectra, we find optical locking of the central VCSEL with two thirds of the individual non-central VCSELs. For entire-array coupling, we also find a clear transition in both optical and RF spectra of the central VCSEL upon incrementing the common wavelength of the ensemble of the non-central VCSELs. We interpret this as a transition from entire-array locking to unlocking. Furthermore, we achieve simultaneous optical injection locking of 22 out of 25 VCSELs to an external drive laser, and analyze the dynamic response of the VCSELs to intensity-modulated injection.

Having characterized coupling and injection, we evaluate the experimental setup's capacity to be utilized as a reservoir computer. We test our experimental system's computing capability on the four basic benchmark tasks memory capacity, exclusive or, header recognition, and digital-to-analog conversion. We observe that the system has good one-step-memory, which then decays rapidly to close to zero for five steps. For the other tasks, we observe that the performance depends crucially on the complexity of the task, with low errors for the 2-bit versions of the tasks, but with substantial decreases in precision for every additional bit. Investigating the output configuration, we find that the change in computing performance upon connecting a reservoir node to the output layer varies greatly from node to node, which means that not all nodes in the output layer are equally important. However, we could not identify reliable indicators of a node's contribution to the computing performance.

In summary, we have experimentally established a diffractively coupled VCSEL network, characterized the coupling and injection, and evaluated the information-processing properties of the network. We have therefore demonstrated one of the first experimental realizations in which tens of SLs are optically coupled within a scalable approach. These results are of interest for the study of complex systems and for photonic reservoir computing.

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