PHOTONIC RESERVOIR COMPUTING BASED ON OPTOELECTRONIC OSCILLATORS

Abstract

Optoelectronic Oscillator (OEO) is a device widely used in modern electronic and photonic systems. Its applications include but not limited to chaos communication systems, random number generation, chaotic radar and lidar, ultra-pure microwave generation, and sensing systems. Moreover, it has rich nonlinear dynamics suitable for studying phenomena like period-one (P1) oscillation, period doubling (P2), and chaos.Reservoir computing (RC) is a machine learning (ML) algorithm that breaks the traditional von Neumann computational paradigm. It is able to learn directly from data and perform both the regression and the classification tasks. Comparing to other machine learning algorithms like recurrent neural network (RNN), it has a much simpler structure that allows it to avoid computationally expensive back -propagation (BP) algorithm while maintains a competitive performance. Recently, as an intrinsic time-delay system, optoelectronic oscillator has been introduced as a machine learning platform to perform reservoir computing. Its ability to accept both the radio-frequency (RF) signal and the optical signal make it an ideal machine learning platform for optical fiber communication systems and radio-frequency communication systems. In Ch. 1, we start the thesis with a general review of the history of artificial intelligence (AI) and the recent development of microwave photonics. Then, we discuss the most recent advances that use photonic devices for machine learning (ML) - one of the most important branches in the field of photonic AI research. In Ch. 2, we introduce different types of OEOs, namely the broadband OEO and narrowband OEO, and how to mathematically model them. Specifically, we will derive the time-delayed equations that govern their behaviors. For the narrowband OEO, we introduce the derivation of an envelope equation which is suitable for the numerical simulations. Following the introduction of mathematical models of OEOs, we delve into our research work of the narrowband OEO-based RC, which is the first time a narrowband OEO is introduced into the field of machine learning for a time-delay reservoir computer implementation in Ch. 3. In this chapter, we develop the mathematical model required for studying the narrowband OEO-based RCs and introduce the concepts of OEO-based RCs. We also numerically simulate this narrowband OEO-based RC and demonstrate its suitability for processing IQ-modulated signals. Lastly, we train and test the narrowband OEO-based on IQ-modulation classification tasks, which reaches state-of-the-art performance with a reduced training set size. In Ch. 4, we further extend the narrowband OEO-based RC to the field of RF fingerprinting - a technology that is widely used to identify RF transmitters. In this chapter, we thoroughly evaluate the performance of the narrowband OEO-based RC across a wide range of benchmark datasets. Our simulation results demonstrate the suitability of the narrowband OEO-based RC for RF fingerprinting. Moreover, we once again show that the narrowband OEO not only requires significantly less training data for the IQ modulation classification task, as presented in Ch. 3, but also maintains excellent performance under limited-resource conditions, extending its effectiveness to RF fingerprinting. In Ch. 5, we further push the narrowband OEO-based RC to an extreme by further limiting its computational source and training data size. We experimentally test the narrowband OEO-based RC’s ability in such scenarios. Meanwhile, we propose a new metric named NET to measure ML platforms’ performances across different algorithms that takes into account the complexity of the algorithm, the performance, and data size required for training. Lastly, we also show that this metric is useful to quantitatively analyze the diminished returns of scaling the number of parameters in machine learning algorithms. It is known that nearly all OEO-based RCs require an expensive and bulky external modulator, which poses a significant obstacle to their practical applications. To resolve this issue, in Ch. 6, we, for the first time, introduce the concept of the directly laser-modulated OEOs for RCs (DL-OEO based RC). In our proposed scheme, we cancel the external modulator and replace it by directly modulating the laser, which not only significantly reduces the system size, but also the total budget for implementation an OEO-based RCs. This implementation makes our DL-OEO based RC one of the simplest OEO-based RCs ever known. First, we start by deriving mathematical models for this proposed scheme. Then, we show our numerical results of using the DL-OEOs for reservoir computing. Lastly, we discuss the usefulness of the nonlinearity introduced by the DL-OEO and how it could contribute a significant improvement in performance in comparison with traditional OEO-based RCs. In Appx. I, we revisit the concepts of time-division multiplexing, time-delay differential equation, and how to use them to numerically simulate the OEO-based RC. In Appx. II, for the first time, we show the relationship between the number of cavity modes N_CM supported by OEO and the total number of virtual nodes N required by OEO-based RCs. We conduct extensive simulations of both types of OEO-based RCs (including narrowband and wideband configurations) across a diverse set of datasets. Our simulation shows that the total number of virtual nodes N required for sufficiently good performance of OEO-based RC can be as less as the total number of cavity modes N_CM.