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The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size in terms of N1 smaller DFTs of sizes N2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below.
A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications.
Photonic-crystal fiber (PCF) is a class of optical fiber based on the properties of photonic crystals. It was first explored in 1996 at University of Bath, UK. Because of its ability to confine light in hollow cores or with confinement characteristics not possible in conventional optical fiber, PCF is now finding applications in fiber-optic communications, fiber lasers, nonlinear devices, high-power transmission, highly sensitive gas sensors, and other areas. More specific categories of PCF include photonic-bandgap fiber, holey fiber, hole-assisted fiber, and Bragg fiber. Photonic crystal fibers may be considered a subgroup of a more general class of microstructured optical fibers, where light is guided by structural modifications, and not only by refractive index differences. Hollow-core fibers (HCFs) are a related type of optical fiber which bears some resemblance to holey optical fiber, but may or may not be photonic depending on the fiber.
Finite-difference time-domain (FDTD) or Yee's method is a numerical analysis technique used for modeling computational electrodynamics. Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way.
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The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology.
Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment using computers.
A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially in the FDTD and FE methods. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed so that waves incident upon the PML from a non-PML medium do not reflect at the interface—this property allows the PML to strongly absorb outgoing waves from the interior of a computational region without reflecting them back into the interior.
Allen Taflove was a full professor in the Department of Electrical and Computer Engineering of Northwestern's McCormick School of Engineering, since 1988. Since 1972, he pioneered basic theoretical approaches, numerical algorithms, and applications of finite-difference time-domain (FDTD) computational solutions of Maxwell's equations. He coined the descriptors "finite difference time domain" and "FDTD" in the 1980 paper, "Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic penetration problems." In 1990, he was the first person to be named a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in the FDTD area. Taflove was the recipient of the 2014 IEEE Electromagnetics Award with the following citation: "For contributions to the development and application of finite-difference time-domain (FDTD) solutions of Maxwell's equations across the electromagnetic spectrum." He was a Life Fellow of the IEEE and a Fellow of the Optical Society (OSA). His OSA Fellow citation reads: "For creating the finite-difference time-domain method for the numerical solution of Maxwell's equations, with crucial application to the growth and current state of the field of photonics."
The finite-difference frequency-domain (FDFD) method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics, based on finite-difference approximations of the derivative operators in the differential equation being solved.
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The James H. Wilkinson Prize for Numerical Software is awarded every four years to honor outstanding contributions in the field of numerical software. The award is named to commemorate the outstanding contributions of James H. Wilkinson in the same field.
Coupled mode theory (CMT) is a perturbational approach for analyzing the coupling of vibrational systems in space or in time. Coupled mode theory allows a wide range of devices and systems to be modeled as one or more coupled resonators. In optics, such systems include laser cavities, photonic crystal slabs, metamaterials, and ring resonators.
A liquid-crystal laser is a laser that uses a liquid crystal as the resonator cavity, allowing selection of emission wavelength and polarization from the active laser medium. The lasing medium is usually a dye doped into the liquid crystal. Liquid-crystal lasers are comparable in size to diode lasers, but provide the continuous wide spectrum tunability of dye lasers while maintaining a large coherence area. The tuning range is typically several tens of nanometers. Self-organization at micrometer scales reduces manufacturing complexity compared to using layered photonic metamaterials. Operation may be either in continuous wave mode or in pulsed mode.
John D. Joannopoulos is an American physicist, focused in condensed matter theory. He is currently the Francis Wright Davis Professor of Physics at Massachusetts Institute of Technology, an Elected Member of the National Academy of Sciences (NAS), an Elected Member of the American Academy of Arts and Sciences (AAA&S), and an Elected Fellow of the American Association for the Advancement of Science (AAAS) and American Physical Society (APS).
Shanhui Fan is a Chinese-born American electrical engineer and physicist, with a focus on theoretical, computational and numerical aspects of photonics and electromagnetism. He is a professor of electrical engineering, and a professor of applied physics at Stanford University. He is the director of the Edward L. Ginzton Lab and Senior Fellow at the Precourt Institute for Energy.
Nanophotonic scintillators are scintillating materials or structures which possess improved properties due to the manipulation of the scintillated visible light using nanophotonics.
The Bailey's FFT is a high-performance algorithm for computing the fast Fourier transform (FFT). This variation of the Cooley–Tukey FFT algorithm was originally designed for systems with hierarchical memory common in modern computers. The algorithm treats the samples as a two dimensional matrix and executes short FFT operations on the columns and rows of the matrix, with a correction multiplication by "twiddle factors" in between.
Meep is a free and open-source software package for electromagnetic simulations, developed by ab initio research group at Massachusetts Institute of Technology in 2006. Operating under Unix-like systems, it uses finite-difference time-domain method with perfectly matched layer or periodic boundary conditions for field computation.
References
- ↑ "Steven Johnson | MIT Mathematics". math.mit.edu. Retrieved 27 February 2020.
- ↑ "Johnson, Steven G., 1973-". viaf.org. Retrieved 27 February 2020.
- 1 2 Frigo M, Johnson SG (February 2005). "The design and implementation of FFTW3" (PDF). Proceedings of the IEEE. 93 (2): 216–231. CiteSeerX 10.1.1.66.3097 . doi:10.1109/JPROC.2004.840301. S2CID 6644892.
- ↑ Frigo M, Johnson SG (1998). "FFTW: An adaptive software architecture for the FFT". Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181). Vol. 3. pp. 1381–1384. CiteSeerX 10.1.1.47.8661 . doi:10.1109/ICASSP.1998.681704. ISBN 978-0-7803-4428-0. S2CID 12560207.
- ↑ Johnson SG, Frigo M (September 2008). "ch.11: Implementing FFTs in practice". In C. S. Burrus (ed.). Fast Fourier Transforms. Houston TX: Connexions: Rice University.
- ↑ "Steven Johnson | MIT Mathematics". math.mit.edu. Retrieved 27 February 2020.
- ↑ Frigo M, Johnson SG (September 11, 1997). "The Fastest Fourier Transform in the West" (PDF). MIT Labroratory for Computer Science.
- ↑ "THE WILKINSON PRIZE FOR NUMERICAL SOFTWARE". Numerical Algorithms Group. Retrieved 22 November 2017.
- ↑ SIAM. "James H. Wilkinson Prize for Numerical Software". Society for Industrial and Applied Mathematics. Retrieved 22 November 2017.
- ↑ Steven G. Johnson, The NLopt nonlinear-optimization package, https://nlopt.readthedocs.io/en/latest/
- ↑ Oskooi, Ardavan F.; Roundy, David; Ibanescu, Mihai; Bermel, Peter; Joannopoulos, J.D.; Johnson, Steven G. (March 2010). "Meep: A flexible free-software package for electromagnetic simulations by the FDTD method". Computer Physics Communications . 181 (3): 687–702. doi:10.1016/j.cpc.2009.11.008. hdl: 1721.1/60946 .
- ↑ Johnson, Steven G.; Joannopoulos, J. D. (2001). "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis". Optics Express . 8 (3): 173–190. doi:10.1364/OE.8.000173.
- ↑ Herriman, Jane (29 March 2019). "Steven Johnson as a JuliaCon 2019 keynote speaker!". Julia Discourse. Retrieved 29 March 2019.
