VCSEL Equivalent Circuits and Silicon Photonics Integration

The vertical-cavity surface-emitting laser (VCSEL) is a light source of great importance for numerous industrial and consumer products. The main application areas are datacom and sensing. The datacom industry uses GaAs-based VCSELs for optical interconnects, the short-reach fiber optical communication links used to transfer large amounts of data at high rates between units within data centers and supercomputers. In the area of sensing, VCSELs are largely used in consumer products such as smart phones (e.g. face ID and camera auto focus), computer mice, and automobiles (e.g. gesture recognition and LIDAR for autonomous driving).In this work, an advanced physics-based equivalent circuit model for datacom VCSELs has been developed. The model lends itself to co-design and co-optimization with driver and receiver ICs, thereby enabling higher data rate transceivers with bandwidth limited VCSELs and photodiodes. The model also facilitates an understanding of how each physical process within the VCSEL affects the VCSEL static and dynamic performance. It has been applied to study the impact of carrier transport and capture on VCSEL dynamics.The work also includes micro-transfer-printing of GaAs-based single-mode VCSELs on silicon nitride photonic integrated circuits (PICs). Such PICs are increasingly used for e.g. compact and highly functional bio-photonic sensors. Transfer printing of VCSELs enables the much-needed on-PIC integration of power efficient light sources. The bottom-emitting VCSELs are printed above grating couplers on the PIC and optical feedback is used to control the polarization for efficient coupling to the silicon nitride waveguide. Wavelength tuning, as required by the bio-sensing application, is achieved by direct current modulation

Large-Signal Equivalent Circuit for Datacom VCSELs – Including Intensity Noise

Optical interconnects (OIs) continue to require more and more sophisticated driver and receiver electronics as higher baud rates are pushed in datacom, mainly due to the bandwidth stagnation of the optoelectronic components such as the vertical-cavity surface-emitting laser (VCSEL) in the transmitter as well as the photodetector (PD) in the receiver. Another important focus is maintaining high energy efficiency for the OIs. For both cases, a reliable equivalent circuit model for high-speed VCSELs is required for link optimization. This work is an extension of our previously presented large-signal VCSEL equivalent circuit model, where noise is added to the physical processes that the VCSEL model is based on. Thus, a new step is taken in the strive of developing an even more accurate physics-based large-signal VCSEL equivalent circuit model for datacom applications. Following a detailed description of the VCSEL noise modelling, a presentation is given on simulated results of VCSEL relative intensity noise (RIN) spectrum and eye diagrams under 28 Gbaud on-off keying (OOK) and pulse-amplitude 4 (PAM4) modulation, and that are compared with corresponding measurement results. Good agreement is found over a wide range of VCSEL driving conditions and temperatures. A 28-GHz-bandwidth VCSEL is applied for the demonstration, and the presented noise extended VCSEL equivalent circuit model was implemented in Verilog-A, and the simulations were performed using Cadence Spectre

Ab initio vibrational free energies including anharmonicity for multicomponent alloys

A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy

Effects of Detuning on Wide-Temperature Behavior of 25 Gbaud 850 nm VCSELs

Emerging markets for optical interconnects with VCSEL-based transceivers require VCSELs with superior wide temperature performance. One of the prime parameters controlling the temperature dependence of VCSEL performance is wavelength detuning. We study the impact of detuning on the performance of 25 Gbaud class 850 nm VCSELs over a temperature range of -40 to 125\ub0C, as applicable to e.g. automotive optical networking. Two VCSELs with different detuning, but otherwise identical, are compared. Basic static and dynamic performance parameters and their temperature dependencies are extracted. The results show that with appropriate detuning, sufficient performance at the temperature extremes and improved tolerance to temperature variations can be achieved. Excessive detuning to meet the more challenging high temperature performance requirements leads to insufficient low temperature performance

Beyond Normal: On the Evaluation of Mutual Information Estimators

Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically evaluated on simple families of probability distributions, namely multivariate normal distribution and selected distributions with one-dimensional random variables. In this paper, we show how to construct a diverse family of distributions with known ground-truth mutual information and propose a language-independent benchmarking platform for mutual information estimators. We discuss the general applicability and limitations of classical and neural estimators in settings involving high dimensions, sparse interactions, long-tailed distributions, and high mutual information. Finally, we provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered and issues one needs to consider when applying an estimator to a new data set.Comment: Accepted at NeurIPS 2023. Code available at https://github.com/cbg-ethz/bm

Formally Real Fields

Summary We extend the algebraic theory of ordered fields [7, 6] in Mizar [1, 2, 3]: we show that every preordering can be extended into an ordering, i.e. that formally real and ordered fields coincide.We further prove some characterizations of formally real fields, in particular the one by Artin and Schreier using sums of squares [4]. In the second part of the article we define absolute values and the square root function [5].Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdansk Wita Stwosza 57, 80-308 Gdansk, PolandGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-8 17.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015. doi: 10.1007/s10817-015-9345-1.Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Infor mation Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363-371, 2016. doi: 10.15439/2016F520.Nathan Jacobson. Lecture Notes in Abstract Algebra, III. Theory of Fields and Galois Theory. Springer-Verlag, 1964.Manfred Knebusch and Claus Scheiderer. Einf¨uhrung in die reelle Algebra. Vieweg-Verlag, 1989.Alexander Prestel. Lectures on Formally Real Fields. Springer-Verlag, 1984.Knut Radbruch. Geordnete K¨orper. Lecture Notes, University of Kaiserslautern, Germany, 1991.Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.Christoph Schwarzweller. Ordered rings and fields. Formalized Mathematics, 25(1):63-72, 2017. doi: 10.1515/forma-2017-0006.Christoph Schwarzweller. On roots of polynomials and algebraically closed fields. Formalized Mathematics, 25(3):185-195, 2017. doi: 10.1515/forma-2017-0018.Christoph Schwarzweller and Artur Korniłowicz. Characteristic of rings. Prime fields. Formalized Mathematics, 23(4):333-349, 2015. doi: 10.1515/forma-2015-0027.25424925

Enabling VCSEL-on-silicon nitride photonic integrated circuits with micro-transfer-printing

New wavelength domains have become accessible for photonic integrated circuits (PICs) with the development of silicon nitride PICs. In particular, the visible and near-infrared wavelength range is of interest for a range of sensing and communication applications. The integration of energy-efficient III-V lasers, such as vertical-cavity surface-emitting lasers (VCSELs), is important for expanding the application portfolio of such PICs. However, most of the demonstrated integration approaches are not easily scalable towards low-cost and large-volume production. In this work, we demonstrate the micro-transfer-printing of bottom-emitting VCSELs on silicon nitride PICs as a path to achieve this. The demonstrated 850 nm lasers show waveguide-coupled powers exceeding 100 mu W, with sub-mA lasing thresholds and mW-level power consumption. A single-mode laser with a side-mode suppression ratio over 45 dB and a tuning range of 5 nm is demonstrated. Combining micro-transfer-printing integration with the extended-cavity VCSEL design developed in this work provides the silicon nitride PIC industry with a great tool to integrate energy-efficient VCSELs onto silicon nitride PICs