Journal articles: 'Photonics Mathematics'

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Vial, Benjamin, and Yang Hao. "Open-Source Computational Photonics with Auto Differentiable Topology Optimization." Mathematics 10, no. 20 (October 21, 2022): 3912. http://dx.doi.org/10.3390/math10203912.

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In recent years, technological advances in nanofabrication have opened up new applications in the field of nanophotonics. To engineer and develop novel functionalities, rigorous and efficient numerical methods are required. In parallel, tremendous advances in algorithmic differentiation, in part pushed by the intensive development of machine learning and artificial intelligence, has made possible large-scale optimization of devices with a few extra modifications of the underlying code. We present here our development of three different software libraries for solving Maxwell’s equations in various contexts: a finite element code with a high-level interface for problems commonly encountered in photonics, an implementation of the Fourier modal method for multilayered bi-periodic metasurfaces and a plane wave expansion method for the calculation of band diagrams in two-dimensional photonic crystals. All of them are endowed with automatic differentiation capabilities and we present typical inverse design examples.

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King, F. Graham Smith and Terry A. "Optics and Photonics: An Introduction." Measurement Science and Technology 12, no. 1 (December 18, 2000): 117. http://dx.doi.org/10.1088/0957-0233/12/1/701.

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Tittel, Wolfgang, and Gregor Weihs. "Photonic entanglement for fundamental tests and quantum communication." Quantum Information and Computation 1, no. 2 (August 2001): 3–56. http://dx.doi.org/10.26421/qic1.2-2.

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Entanglement is at the heart of fundamental tests of quantum mechanics like tests of Bell-inequalities and, as discovered lately, of quantum computation and communication. Their technological advance made entangled photons play an outstanding role in entanglement physics. We give a generalized concept of qubit entanglement and review the state of the art of photonics experiments.

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Prudêncio, Filipa R., and Mário G. Silveirinha. "First Principles Calculation of the Topological Phases of the Photonic Haldane Model." Symmetry 13, no. 11 (November 22, 2021): 2229. http://dx.doi.org/10.3390/sym13112229.

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Photonic topological materials with a broken time-reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge-states when enclosed by an opaque-type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed-matter systems, as it unveiled that a broken time-reversal symmetry is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo-Tellegen coupling. Here, we use Green’s function method to determine from “first principles” the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo-Tellegen parameter.

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Voyles, Richard M., and Seth Hulst. "Micro/macro force-servoed gripper for precision photonics assembly and analysis." Robotica 23, no. 4 (June 14, 2005): 401–8. http://dx.doi.org/10.1017/s0263574704000839.

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Photonics is a field that straddles both the macro and micro worlds. It largely deals with macro-scale devices, but many of these require sub-micron-scale precision in assembly. This makes it a very interesting application domain. We describe a microgripper for microassembly of photonic devices and micro-exploration of the properties of sub-micron attachment means (such as solder and UV epoxy). The microgripper has multi-degree-of-freedom actuation and a unique micro/macro actuator on the gripping axis to facilitate human loading and unloading and also very precise accommodation. We demonstrate the force sensitivity and stiffness of approximately 20 mN and 70 mN/um, respectively to be sufficient for the intended tasks. Finally, we demonstrate the gripper accommodating forces of a large solder ball freezing and cooling as a prelude to our intended study of sub-millimeter solder balls in sub-second heating regimes.

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Parker, Andrew R. "A vision for natural photonics." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 362, no. 1825 (August 31, 2004): 2709–20. http://dx.doi.org/10.1098/rsta.2004.1458.

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Parker, Andrew R. "Natural photonics for industrial inspiration." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1894 (May 13, 2009): 1759–82. http://dx.doi.org/10.1098/rsta.2009.0016.

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There are two considerations for optical biomimetics: the diversity of submicrometre architectures found in the natural world, and the industrial manufacture of these. A review exists on the latter subject, where current engineering methods are considered along with those of the natural cells. Here, on the other hand, I will provide a modern review of the different categories of reflectors and antireflectors found in animals, including their optical characterization. The purpose of this is to inspire designers within the $2 billion annual optics industry.

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Muševič, I. "Nematic colloids, topology and photonics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1988 (April 13, 2013): 20120266. http://dx.doi.org/10.1098/rsta.2012.0266.

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We review and discuss recent progress in the field of nematic colloids, with an emphasis on possible future applications in photonics. The role of the topology is described, based on experimental manipulations of the topological defects in nematic colloids. The topology of the ordering field in nematics provides the forces between colloidal particles that are unique to these materials. We also discuss recent progress in the new field of active microphotonic devices based on liquid crystals (LCs), where chiral nematic microlasers and tuneable nematic microresonators are just two of the recently discovered examples. We conclude that the combination of topology and microphotonic devices based on LCs provides an interesting platform for future progress in the field of LCs.

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Yoon, Hosang, Kitty Y. M. Yeung, Philip Kim, and Donhee Ham. "Plasmonics with two-dimensional conductors." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2012 (March 28, 2014): 20130104. http://dx.doi.org/10.1098/rsta.2013.0104.

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A wealth of effort in photonics has been dedicated to the study and engineering of surface plasmonic waves in the skin of three-dimensional bulk metals, owing largely to their trait of subwavelength confinement. Plasmonic waves in two-dimensional conductors, such as semiconductor heterojunction and graphene, contrast the surface plasmonic waves on bulk metals, as the former emerge at gigahertz to terahertz and infrared frequencies well below the photonics regime and can exhibit far stronger subwavelength confinement. This review elucidates the machinery behind the unique behaviours of the two-dimensional plasmonic waves and discusses how they can be engineered to create ultra-subwavelength plasmonic circuits and metamaterials for infrared and gigahertz to terahertz integrated electronics.

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Palffy-Muhoray, Peter, Wenyi Cao, Michele Moreira, Bahman Taheri, and Antonio Munoz. "Photonics and lasing in liquid crystal materials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1847 (August 21, 2006): 2747–61. http://dx.doi.org/10.1098/rsta.2006.1851.

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Owing to fundamental reasons of symmetry, liquid crystals are soft materials. This softness allows long length-scales, large susceptibilities and the existence of modulated phases, which respond readily to external fields. Liquid crystals with such phases are tunable, self-assembled, photonic band gap materials; they offer exciting opportunities both in basic science and in technology. Since the density of photon states is suppressed in the stop band and is enhanced at the band edges, these materials may be used as switchable filters or as mirrorless lasers. Disordered periodic liquid crystal structures can show random lasing. We highlight recent advances in this rapidly growing area, and discuss future prospects in emerging liquid crystal materials. Liquid crystal elastomers and orientationally ordered nanoparticle assemblies are of particular interest.

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Soref, Richard. "Silicon-based silicon–germanium–tin heterostructure photonics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2012 (March 28, 2014): 20130113. http://dx.doi.org/10.1098/rsta.2013.0113.

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The wavelength range that extends from 1550 to 5000 nm is a new regime of operation for Si-based photonic and opto-electronic integrated circuits. To actualize the new chips, heterostructure active devices employing the ternary SiGeSn alloy are proposed in this paper. Foundry-based monolithic integration is described. Opportunities and challenges abound in creating laser diodes, optical amplifiers, light-emitting diodes, photodetectors, modulators, switches and a host of high-performance passive infrared waveguided components.

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Li, Shuang, Yewang Su, and Rui Li. "Splitting of the neutral mechanical plane depends on the length of the multi-layer structure of flexible electronics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2190 (June 2016): 20160087. http://dx.doi.org/10.1098/rspa.2016.0087.

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Multi-layer structures with soft (compliant) interlayers have been widely used in flexible electronics and photonics as an effective design for reducing interactions among the hard (stiff) layers and thus avoiding the premature failure of an entire device. The analytic model for bending of such a structure has not been well established due to its complex mechanical behaviour. Here, we present a rational analytic model, without any parameter fitting, to study the bending of a multi-layer structure on a cylinder, which is often regarded as an important approach to mechanical reliability testing of flexible electronics and photonics. For the first time, our model quantitatively reveals that, as the key for accurate strain control, the splitting of the neutral mechanical plane depends not only on the relative thickness of the middle layer, but also on the length-to-thickness ratio of the multi-layer structure. The model accurately captures the key quantities, including the axial strains in the top and bottom layers, the shear strain in the middle layer and the locations of the neutral mechanical planes of the top and bottom layers. The effects of the length of the multi-layer and the thickness of the middle layer are elaborated. This work is very useful for the design of multi-layer structure-based flexible electronics and photonics.

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Larger, Laurent. "Complexity in electro-optic delay dynamics: modelling, design and applications." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1999 (September 28, 2013): 20120464. http://dx.doi.org/10.1098/rsta.2012.0464.

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Nonlinear delay dynamics have found during the last 30 years a particularly prolific exploration area in the field of photonic systems. Besides the popular external cavity laser diode set-ups, we focus in this article on another experimental realization involving electro-optic (EO) feedback loops, with delay. This approach has strongly evolved with the important technological progress made on broadband photonic and optoelectronic devices dedicated to high-speed optical telecommunications. The complex dynamical systems performed by nonlinear delayed EO feedback loop architectures were designed and explored within a huge range of operating parameters. Thanks to the availability of high-performance photonic devices, these EO delay dynamics led also to many successful, efficient and diverse applications, beyond the many fundamental questions raised from the observation of experimental behaviours. Their chaotic motion allowed for a physical layer encryption method to secure optical data, with a demonstrated capability to operate at the typical speed of modern optical telecommunications. Microwave limit cycles generated in similar EO delay oscillators showed significantly improved spectral purity thanks to the use of a very long fibre delay line. Last but not least, a novel brain inspired computational principle has been recently implemented physically in photonics for the first time, again on the basis of an EO delay dynamical system. In this latter emerging application, the computed result is obtained by a proper ‘read-out’ of the complex nonlinear transients emerging from a fixed point, the transient being issued by the injection of the information signal to be processed.

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Faraj, Mustafa, and Catherine Gebotys. "Quiescent photonics side channel analysis: Low cost SRAM readout attack." Cryptography and Communications 13, no. 3 (January 19, 2021): 363–76. http://dx.doi.org/10.1007/s12095-020-00469-5.

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Sarrigan, G. V., K. A. Matori, I. S. Amiri, H. Ahmad, and F. Fadaeifard. "Dual-Wavelength Generation with Terahertz Spacing Using GaAs–AlGaAs Microring Resonator Waveguides." Journal of Computational and Theoretical Nanoscience 14, no. 1 (January 1, 2017): 330–34. http://dx.doi.org/10.1166/jctn.2017.6324.

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In this research, we present the demonstration of GaAs–AlGaAs waveguide resonators. Two microring resonators (MRRs) have the same radius of 6.36 μm are coupled and used to generate dual-wavelength with terahertz (THz) spacing. We have shown that such resonators can be used to generate ultra-wide free spectral range (FSR) pulses with THz spacing, providing THz photonics communication signals. A Gaussian laser beam with power of 1 W is used as input. The MRRs are modeled by using GaAs–AlGaAs with GaAs core having refractive index of 3.368 surrounded by AlGaAs (n = 3.135). The drop port outputs of the MRRs system contains a dual-wavelength generated within 33 nm wavelength range, having a linewidth of 1.48 (185.320 GHz) and FSR of 3.95 nm (500 GHz) which varies slightly along the wavelength. Results were generated using the time-domain travelling wave (TDTW) method and capable of modeling both active and passive photonic circuits.

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Zhixun, Liang, Xu Chuanpei, Bi Lvqing, Shi Yunying, Yi Yunfei, and Hu Cong. "Modeling and Performance Analysis of a Fault-Tolerant 3D Photonic Network-on-Chip Based on Hybrid Photonics–Plasmonics." Computational Intelligence and Neuroscience 2022 (July 19, 2022): 1–24. http://dx.doi.org/10.1155/2022/9615610.

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The performance of electro-optic modulators and optical routers and their routing algorithms are the key factors affecting the performance of networks on optical chips. This paper improves the mesh 3-dimensional photonic network-on-chip (3D-PNoC) topology. An SPP hybrid silicon-based electro-optic modulator and an improved fault-tolerant SPP router are used to improve the performance of the network on an optical chip. SPP switching and SPP MRR are combined to form a fault-tolerant SPP router. On this basis, an improved genetic optimization routing algorithm is implemented on the improved mesh 3D PNoC topology, which completes the data exchange of the IP core of the network on the optical chip. Compared with the case of traditional optoelectronic devices, the performance of on-chip optical networks can be improved effectively. The simulation results show that upon the application of the improved genetic optimization routing algorithm to the improved mesh 3D PNoC topology, the average end-to-end delay is reduced by 32.9%, the throughput rate is increased by 28.5%, and the system power consumption is reduced by 27.6%. On the other hand, the average insertion loss and noise of optical routers are increased by 2.94 dB and 2.95 dB, respectively.

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Chigrinov, Vladimir G. "54.4: Invited Paper: Photoaligned ferroelectric liquid crystals for displays and photonics: what next." SID Symposium Digest of Technical Papers 53, S1 (October 2022): 541. http://dx.doi.org/10.1002/sdtp.16016.

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Poulios, Costas, and Vassilios Constantoudis. "Mathematical Analysis of Nanostructured Surfaces: The Period-Scale Transform." Mathematical Problems in Engineering 2021 (June 21, 2021): 1–14. http://dx.doi.org/10.1155/2021/5533673.

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This work has been motivated by the urgent need for accurate and complete characterization of patterns consisting of almost periodic arrangements of specific features (trenches, bumps, holes, spikes, and so on) amply used in the industries of nanotechnology, microelectronics, and photonics. The quantitative characterization of such surface structures demands mathematical methods able to reveal both period- and feature-scale aspects. Given that the conventional approaches (Fourier or wavelet transform) are limited to either periodicity or feature-scale characterization, our work contributes with the proposal of a transformation which combines Fourier and wavelet merits to quantify simultaneously the period and feature scale of a periodic or almost periodic surface pattern. The output of our study has been (a) a detailed investigation of the mathematical properties of the proposed period-scale transform (PST) along with its relationship with other well-known transforms, (b) a presentation of some examples of PST of model 1D periodic surfaces to identify its benefits, and (c) first applications of PST in real profiles extracted from experimental polymer surfaces after plasma treatment.

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Ferreira de Lima, Thomas, Bhavin J. Shastri, Alexander N. Tait, Mitchell A. Nahmias, and Paul R. Prucnal. "Progress in neuromorphic photonics." Nanophotonics 6, no. 3 (March 11, 2017): 577–99. http://dx.doi.org/10.1515/nanoph-2016-0139.

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AbstractAs society’s appetite for information continues to grow, so does our need to process this information with increasing speed and versatility. Many believe that the one-size-fits-all solution of digital electronics is becoming a limiting factor in certain areas such as data links, cognitive radio, and ultrafast control. Analog photonic devices have found relatively simple signal processing niches where electronics can no longer provide sufficient speed and reconfigurability. Recently, the landscape for commercially manufacturable photonic chips has been changing rapidly and now promises to achieve economies of scale previously enjoyed solely by microelectronics. By bridging the mathematical prowess of artificial neural networks to the underlying physics of optoelectronic devices, neuromorphic photonics could breach new domains of information processing demanding significant complexity, low cost, and unmatched speed. In this article, we review the progress in neuromorphic photonics, focusing on photonic integrated devices. The challenges and design rules for optoelectronic instantiation of artificial neurons are presented. The proposed photonic architecture revolves around the processing network node composed of two parts: a nonlinear element and a network interface. We then survey excitable lasers in the recent literature as candidates for the nonlinear node and microring-resonator weight banks as the network interface. Finally, we compare metrics between neuromorphic electronics and neuromorphic photonics and discuss potential applications.

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Habuka, Hitoshi. "Main and side reaction design exceeding the theoretical upper limit of chemical vapor deposition rate." Impact 2020, no. 1 (February 27, 2020): 62–64. http://dx.doi.org/10.21820/23987073.2020.1.62.

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Chemical engineering is a branch of engineering that brings together the principles of chemistry, physics, mathematics and biology to use, produce, design and transform energy and materials. Chemical engineering expert Professor Hitoshi Habuka, who is based at the Faculty of Engineering, Division of Materials Science and Chemical Engineering, Yokohama National University in Japan, is leading a team which is interested in creating advanced semiconductor materials through reaction engineering. One of their focuses in recent years has been on exceeding the epitaxial growth rate limit. Epitaxy - which is an important technique to prepare a crystalline film on a single-crystalline substrate - is essential to the manufacturing of devices and circuits association with electronics and photonics.

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Chen, Zhaopin, Yongyao Li, and Boris A. Malomed. "𝒫𝒯-symmetric and antisymmetric nonlinear states in a split potential box." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170369. http://dx.doi.org/10.1098/rsta.2017.0369.

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We introduce a one-dimensional -symmetric system, which includes the cubic self-focusing, a double-well potential in the form of an infinitely deep potential box split in the middle by a delta-functional barrier of an effective height ε , and constant linear gain and loss, γ , in each half-box. The system may be readily realized in microwave photonics. Using numerical methods, we construct -symmetric and antisymmetric modes, which represent, respectively, the system’s ground state and first excited state, and identify their stability. Their instability mainly leads to blowup, except for the case of ε =0, when an unstable symmetric mode transforms into a weakly oscillating breather, and an unstable antisymmetric mode relaxes into a stable symmetric one. At ε >0, the stability area is much larger for the -antisymmetric state than for its symmetric counterpart. The stability areas shrink with increase of the total power, P . In the linear limit, which corresponds to , the stability boundary is found in an analytical form. The stability area of the antisymmetric state originally expands with the growth of γ , and then disappears at a critical value of γ . This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Oppo, Gian-Luca. "Formation and control of Turing patterns and phase fronts in photonics and chemistry." Journal of Mathematical Chemistry 45, no. 1 (May 6, 2008): 95–112. http://dx.doi.org/10.1007/s10910-008-9370-y.

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Li, Yuanyuan, Qiliang Fu, Xuan Yang, and Lars Berglund. "Transparent wood for functional and structural applications." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2112 (December 25, 2017): 20170182. http://dx.doi.org/10.1098/rsta.2017.0182.

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Optically transparent wood combines mechanical performance with optical functionalities is an emerging candidate for applications in smart buildings and structural optics and photonics. The present review summarizes transparent wood preparation methods, optical and mechanical performance, and functionalization routes, and discusses potential applications. The various challenges are discussed for the purpose of improved performance, scaled-up production and realization of advanced applications. This article is part of a discussion meeting issue ‘New horizons for cellulose nanotechnology’.

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Mora, Fernando, Pierre Coullet, Sergio Rica, and Enrique Tirapegui. "Numerical path integral calculation of the probability function and exit time: an application to non-gradient drift forces." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20180027. http://dx.doi.org/10.1098/rsta.2018.0027.

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We provide numerical solutions based on the path integral representation of stochastic processes for non-gradient drift Langevin forces in the presence of noise, to follow the temporal evolution of the probability density function and to compute exit times even for arbitrary noise. We compare the results with theoretical calculations, obtaining excellent agreement in the weak noise limit. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Karakus, Melike, Amirhossein Sajadi, and Peter Salamon. "Inter-continental summer school of liquid crystal physics, mathematics, photonics, electro-optics, and optomechanics: I-CAMP’13’s overview." Liquid Crystals Today 22, no. 3 (July 2013): 64–69. http://dx.doi.org/10.1080/1358314x.2013.850779.

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Xue, Zheng‐Yuan, and Yong Hu. "Topological Photonics on Superconducting Quantum Circuits with Parametric Couplings." Advanced Quantum Technologies 4, no. 9 (July 26, 2021): 2100017. http://dx.doi.org/10.1002/qute.202100017.

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Botchev, M. A. "A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling." Computers & Mathematics with Applications 80, no. 2 (July 2020): 295–304. http://dx.doi.org/10.1016/j.camwa.2019.08.010.

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Suhir, E. "Modeling of the Mechanical Behavior of Materials in “High-Tech” Systems: Attributes and Review." Journal of Electronic Packaging 121, no. 4 (December 1, 1999): 213–21. http://dx.doi.org/10.1115/1.2793843.

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We examine some attributes of modeling of the mechanical behavior of materials and structures in microelectronics and photonics (mainly fiber optics) engineering. The merits and shortcomings of experimental and theoretical modeling are addressed, as well as the interaction between different modeling approaches. The concepts discussed are illustrated by a brief review of the published work in the field. The review is based primarily on the author’s research conducted during his work at Bell Laboratories and reflects, to a great extent, the state-of-the-art in modeling of the mechanical behavior of “high-tech” materials and structures. “The only real voyage to discovery consists not in seeking new landscapes, but in having new eyes.” [Marcel Proust, French Writer] “The Practical value of mathematics is, in effect, a possibility to obtain, with its help, results simpler and faster.” [Andrey Kolmogorov, Russian Mathematician]

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Cheng, Wei, Junbo Feng, Yan Wang, Zheng Peng, Hao Cheng, Xiaodong Ren, Yubei Shuai, et al. "High precision reconstruction of silicon photonics chaos with stacked CNN-LSTM neural networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 5 (May 2022): 053112. http://dx.doi.org/10.1063/5.0082993.

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Silicon-based optical chaos has many advantages, such as compatibility with complementary metal oxide semiconductor (CMOS) integration processes, ultra-small size, and high bandwidth. Generally, it is challenging to reconstruct chaos accurately because of its initial sensitivity and high complexity. Here, a stacked convolutional neural network (CNN)-long short-term memory (LSTM) neural network model is proposed to reconstruct optical chaos with high accuracy. Our network model combines the advantages of both CNN and LSTM modules. Further, a theoretical model of integrated silicon photonics micro-cavity is introduced to generate chaotic time series for use in chaotic reconstruction experiments. Accordingly, we reconstructed the one-dimensional, two-dimensional, and three-dimensional chaos. The experimental results show that our model outperforms the LSTM, gated recurrent unit (GRU), and CNN models in terms of MSE, MAE, and R-squared metrics. For example, the proposed model has the best value of this metric, with a maximum improvement of 83.29% and 49.66%. Furthermore, 1D, 2D, and 3D chaos were all significantly improved with the reconstruction tasks.

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Burunkova, Yu É., I. Yu Denisyuk, N. N. Aref'eva, A. P. Litvin, and O. A. Minozhenko. "Polymeric electrooptic composite based on Disperse Red and its derivatives for use in photonics." Journal of Optical Technology 77, no. 10 (October 1, 2010): 643. http://dx.doi.org/10.1364/jot.77.000643.

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Bullara, D., Y. De Decker, and I. R. Epstein. "On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170374. http://dx.doi.org/10.1098/rsta.2017.0374.

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We derive general conditions for the emergence of sustained chemomechanical oscillations from a non-oscillatory adsorption/desorption reaction in a gas/solid porous medium. The oscillations arise from the nonlinear response of the solid matrix to the loading of the adsorbed species. More particularly, we prove that, in order for oscillations to occur, adsorption of the gas must in general cause a swelling of the solid matrix. We also investigate the prototypical case of Langmuir kinetics both numerically and analytically. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Belov, Aleksandr, and Zhanna Dombrovskaya. "The Optical Path Method for the Problem of Oblique Incidence of a Plane Electromagnetic Wave on a Plane-Parallel Scatterer." Mathematics 11, no. 2 (January 15, 2023): 466. http://dx.doi.org/10.3390/math11020466.

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A number of actual problems of integrated photonics are reduced to an oblique incidence of radiation on a plane-parallel scatterer. For such problems, an approximate method of integrating the Maxwell equations along the beam propagation direction is proposed. As a result, the original two-dimensional problem is reduced to a one-dimensional one, and recently proposed one-dimensional bicompact schemes are used to solve it. This approach provides a significant reduction of computational costs compared to traditional two-dimensional methods such as finite differences and finite elements. To verify the proposed method, calculations of test and applied problems with known exact reflection spectra are carried out.

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Ferreira de Lima, Thomas, Alexander N. Tait, Armin Mehrabian, Mitchell A. Nahmias, Chaoran Huang, Hsuan-Tung Peng, Bicky A. Marquez, et al. "Primer on silicon neuromorphic photonic processors: architecture and compiler." Nanophotonics 9, no. 13 (August 10, 2020): 4055–73. http://dx.doi.org/10.1515/nanoph-2020-0172.

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AbstractMicroelectronic computers have encountered challenges in meeting all of today’s demands for information processing. Meeting these demands will require the development of unconventional computers employing alternative processing models and new device physics. Neural network models have come to dominate modern machine learning algorithms, and specialized electronic hardware has been developed to implement them more efficiently. A silicon photonic integration industry promises to bring manufacturing ecosystems normally reserved for microelectronics to photonics. Photonic devices have already found simple analog signal processing niches where electronics cannot provide sufficient bandwidth and reconfigurability. In order to solve more complex information processing problems, they will have to adopt a processing model that generalizes and scales. Neuromorphic photonics aims to map physical models of optoelectronic systems to abstract models of neural networks. It represents a new opportunity for machine information processing on sub-nanosecond timescales, with application to mathematical programming, intelligent radio frequency signal processing, and real-time control. The strategy of neuromorphic engineering is to externalize the risk of developing computational theory alongside hardware. The strategy of remaining compatible with silicon photonics externalizes the risk of platform development. In this perspective article, we provide a rationale for a neuromorphic photonics processor, envisioning its architecture and a compiler. We also discuss how it can be interfaced with a general purpose computer, i.e. a CPU, as a coprocessor to target specific applications. This paper is intended for a wide audience and provides a roadmap for expanding research in the direction of transforming neuromorphic photonics into a viable and useful candidate for accelerating neuromorphic computing.

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Belyi, V. V. "Fluctuations out of equilibrium." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170383. http://dx.doi.org/10.1098/rsta.2017.0383.

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A generalized fluctuation–dissipation theorem involving slowly varying parameters is presented. Application of the Langevin method, the method of moments and of a multiscale technique reveal that not only dissipation but also dispersive contributions determine the spectral functions of fluctuations in arbitrary statistical systems. The non-Joule dispersive contribution is characterized by a novel non-local effect due to the additional phase shift between the force and the response of the system. This phase shift occurs as a result of parametric control to the system. The general formalism is illustrated by concrete examples and applications. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Poëtte, Gaël, Xavier Valentin, and Adrien Bernede. "Canceling Teleportation Error in Legacy IMC Code for Photonics (Without Tilts, With Simple Minimal Modifications)." Journal of Computational and Theoretical Transport 49, no. 4 (June 6, 2020): 162–94. http://dx.doi.org/10.1080/23324309.2020.1785893.

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Balakireva, Irina V., and Yanne K. Chembo. "A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170381. http://dx.doi.org/10.1098/rsta.2017.0381.

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In this paper, the research related to the formation of optical dissipative structures in Kerr-nonlinear whispering-gallery mode resonators pumped with continuous-wave lasers is reviewed. Pattern formation in these systems can be analysed using the paradigmatic Lugiato–Lefever model, which is a partial differential equation ruling the dynamics of the intra-cavity laser field. Various dissipative structures such as Turing rolls, solitons, breathers and spatio-temporal chaos can emerge in the resonator depending on the laser power and frequency. The bifurcation analysis enables a classification of these patterns, and also permits identification of their basins of attraction. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Antonakakis, T., R. V. Craster, S. Guenneau, and E. A. Skelton. "An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130467. http://dx.doi.org/10.1098/rspa.2013.0467.

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An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh–Bloch waves, but which also go under other names, for example, spoof surface plasmon polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered, and an implicit long-scale wavelength is identified and compared with full numerical simulations. We also investigate non-periodic situations where a long-scale geometrical variation in the structure is introduced and show that localized defect states emerge which the asymptotic theory explains.

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Gandhi, Punit, Yuval R. Zelnik, and Edgar Knobloch. "Spatially localized structures in the Gray–Scott model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170375. http://dx.doi.org/10.1098/rsta.2017.0375.

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Spatially localized structures in the one-dimensional Gray–Scott reaction–diffusion model are studied using a combination of numerical continuation techniques and weakly nonlinear theory, focusing on the regime in which the activator and substrate diffusivities are different but comparable. Localized states arise in three different ways: in a subcritical Turing instability present in this regime, and from folds in the branch of spatially periodic Turing states. They also arise from the fold of spatially uniform states. These three solution branches interconnect in complex ways. We use numerical continuation techniques to explore their global behaviour within a formulation of the model that has been used to describe dryland vegetation patterns on a flat terrain. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Kostet, B., M. Tlidi, F. Tabbert, T. Frohoff-Hülsmann, S. V. Gurevich, E. Averlant, R. Rojas, G. Sonnino, and K. Panajotov. "Stationary localized structures and the effect of the delayed feedback in the Brusselator model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170385. http://dx.doi.org/10.1098/rsta.2017.0385.

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The Brusselator reaction–diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Qiao, Weiguo, and Zhong’an Li. "Recent Progress of Squaraine-Based Fluorescent Materials and Their Biomedical Applications." Symmetry 14, no. 5 (May 9, 2022): 966. http://dx.doi.org/10.3390/sym14050966.

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Squaraines (SQs) are unusual cyanine dyes with a unique resonance-stabilized zwitterionic structure. These dyes have attracted significant attention in the fields of organic electronics and organic photonics, due to their facile synthesis, intense and narrow visible and near-infrared absorption/emission, high photostability, low biotoxicity, etc. In this review, we summarize the recent progress of SQ-based fluorescent materials and their biomedical applications. After a brief introduction to SQs, general synthetic routes and design principles of SQ-based fluorescent materials, as well as their aggregation-induced luminescence behaviors, are discussed. Subsequently, their biomedical applications for cell imaging and as fluorescent sensors and therapeutic agents are introduced. Finally, a summary and perspective are given for promoting the development of SQs-based fluorescent materials.

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Reddy, T. Narendra, S. N. Vithun, Prakash Vinod, Shrikantha S. Rao, and Mervin Herbert. "Development of High Bandwidth Flexure Based Stage for Nanopositioning Applications." Advanced Science Letters 24, no. 8 (August 1, 2018): 5989–93. http://dx.doi.org/10.1166/asl.2018.12232.

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Micro and Nanopositioning systems are widely used in semiconductor, optics, materials science, photonics packaging, optical focusing objectives etc. This paper is focused on development of high bandwidth flexure based stage for nanopositioning requirements. The speed, nano-metric motions and positioning accuracy are limited based on the structural vibrations of the flexure based nanopositioning, non-linear characteristics of the piezo-actuators and control system performance. The research work carried out includes design of complaint mechanisms, fabrication of flexure stages and implementation of closed loop systems to achieve high bandwidth positioning applications. The developed high speed and high bandwidth nanopositioning system are tested for accuracy, linearity and cross talk motions for Nanopositioning applications.

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You, Jian Wei, Jie You, Martin Weismann, and Nicolae C. Panoiu. "Double-resonant enhancement of third-harmonic generation in graphene nanostructures." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2090 (March 28, 2017): 20160313. http://dx.doi.org/10.1098/rsta.2016.0313.

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Intriguing and unusual physical properties of graphene offer remarkable potential for advanced, photonics-related technological applications, particularly in the area of nonlinear optics at the deep-subwavelength scale. In this study, we use a recently developed numerical method to illustrate an efficient mechanism that can lead to orders of magnitude enhancement of the third-harmonic generation in graphene diffraction gratings. In particular, we demonstrate that by taking advantage of the geometry dependence of the resonance wavelength of localized surface-plasmon polaritons of graphene ribbons and discs one can engineer the spectral response of graphene gratings so that strong plasmonic resonances exist at both the fundamental frequency and third-harmonic (TH). As a result of this double-resonant mechanism for optical near-field enhancement, the intensity of the TH can be increased by more than six orders of magnitude. This article is part of the themed issue ‘New horizons for nanophotonics’.

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Gunji, Yukio-Pegio, Hisashi Murakami, Takenori Tomaru, and Vasileios Basios. "Inverse Bayesian inference in swarming behaviour of soldier crabs." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170370. http://dx.doi.org/10.1098/rsta.2017.0370.

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Animals making a group sometimes approach and sometimes avoid a dense area of group mates, and that reveals the ambiguity of density preference. Although the ambiguity is not expressed by a simple deterministic local rule, it seems to be implemented by probabilistic inference that is based on Bayesian and inverse Bayesian inference. In particular, the inverse Bayesian process refers to perpetual changing of hypotheses. We here analyse a time series of swarming soldier crabs and show that they are employed to Bayesian and inverse Bayesian inference. Comparing simulation results with data of the real swarm, we show that the interpretation of the movement of soldier crabs which can be based on the inference can lead to the identification of a drastic phase shift-like transition of gathering and dispersing. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Tlidi, M., M. G. Clerc, D. Escaff, P. Couteron, M. Messaoudi, M. Khaffou, and A. Makhoute. "Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20180026. http://dx.doi.org/10.1098/rsta.2018.0026.

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We report for the first time on the formation of spirals like vegetation patterns in isotropic and uniform environmental conditions. The vegetation spirals are not waves and they do not rotate. They belong to the class of dissipative structures found out of equilibrium. Isolated or interacting spirals and arcs observed in South America (Bolivia) and North Africa (Morocco) are interpreted as a result of curvature instability that affects the circular shape of localized patches. The biomass exhibits a dynamical behaviour with arcs that transform into spirals. Interpretation of observations and of the predictions provided by the theory is illustrated by recent measurements of peculiar plant morphology (the alfa plant, or Stipa tenacissima L.) originated from northwestern Africa and the southern part of the Iberian Peninsula. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Veretenov, N. A., S. V. Fedorov, and N. N. Rosanov. "Topological three-dimensional dissipative optical solitons." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170367. http://dx.doi.org/10.1098/rsta.2017.0367.

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This article presents a review of recent investigations of topological three-dimensional (3D) dissipative optical solitons in homogeneous laser media with fast nonlinearity of amplification and absorption. The solitons are found numerically, with their formation, by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around a vortex straight line with their simultaneous twist. After a transient, the ‘hula-hoop’ solitons can form with a number of closed and unclosed infinite vortex lines, i.e. the solitons are tangles in topological notation. They are attractors and are characterized by extreme stability. The solitons presented here can be realized in lasers with fast saturable absorption and are promising for information applications. The tangle solitons of the type described present an example of self-organization that can be found not only in optics but also in various distributed dissipative systems of different types. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Li, Pengfei, Dumitru Mihalache, and Boris A. Malomed. "Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170378. http://dx.doi.org/10.1098/rsta.2017.0378.

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We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ( )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such -symmetric waveguides. The dependence of the propagation constant on the soliton’s power is presented for different strengths of the nonlinearity saturation, S . The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of S . This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Zykov, V. S. "Spiral wave initiation in excitable media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (November 12, 2018): 20170379. http://dx.doi.org/10.1098/rsta.2017.0379.

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Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

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Erneux, Thomas. "Early models of chemical oscillations failed to provide bounded solutions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20170380. http://dx.doi.org/10.1098/rsta.2017.0380.

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Before the development of the Brusselator, the Sel’kov and Turing models were considered as possible prototype models of chemical oscillations. We first analyse their Hopf bifurcation branches and show that they become vertical past a critical value of the control parameter. We explain this phenomenon by the emergence of canard orbits. Second, we analyse all solutions in the phase plane and show that some initial conditions lead to unbounded trajectories even if there exists a locally stable attractor. Our findings mathematically explain why these too simple two-variable models fail to account for the emergence of chemical oscillations. They support the conclusion that the Brusselator is the first minimal two-variable model explaining the onset of stable oscillations in a way fully compatible with thermodynamics and the law of mass action. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Akhmediev, N., J. M. Soto-Crespo, Peter Vouzas, N. Devine, and Wonkeun Chang. "Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2124 (June 11, 2018): 20180023. http://dx.doi.org/10.1098/rsta.2018.0023.

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Prigogine’s ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J. Chem. Phys. 48 , 1695–1700 ( doi:10.1063/1.1668896 ); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations . New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered—dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic–quintic Ginzburg–Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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Sachdeva, Geeta, Sumandeep Kaur, Ravindra Pandey, and Shashi P. Karna. "First-Principles Study of Linear and Nonlinear Optical Properties of Multi-Layered Borophene." Computation 9, no. 9 (September 18, 2021): 101. http://dx.doi.org/10.3390/computation9090101.

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Anisotropic materials are of great interest due to their unique direction-dependent optical properties. Borophene, the two-dimensional analog of graphene consisting of boron atoms, has attracted immense research interest due to its exciting anisotropic electronic and mechanical properties. Its synthesis in several structural polymorphic configurations has recently been reported. The present work reports the layer-dependent optical absorption and hyperpolarizabilities of the buckled borophene (δ6-borophene). The results, based on density functional theory, show that multilayer borophene is nearly transparent with only a weak absorbance in the visible region, reflecting its anisotropic structural characteristics. The static first-order hyperpolarizability significantly increases with the number of layers, due mainly to interactions among the frontier orbitals in multilayer borophene. Transparency in the visible region combined with enhanced nonlinear optical properties makes the multilayer borophene important for future photonics technologies.

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Journal articles on the topic 'Photonics Mathematics'

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