Access the full text.
Sign up today, get DeepDyve free for 14 days.
Yaxun Liu, C. Sarris (2006)
Fast time-domain simulation of optical waveguide structures with a multilevel dynamically adaptive mesh refinement FDTD approachJournal of Lightwave Technology, 24
L. Mandel, E. Wolf (1995)
Optical Coherence and Quantum Optics
Q. Cheng, T. Cui, Chao Zhang (2007)
Waves in planar waveguide containing chiral nihility metamaterialOptics Communications, 276
J. Harrison (2005)
A HOL Theory of Euclidean Space
M. Malak, N. Pavy, F. Marty, Y. Peter, A. Liu, T. Bourouina (2011)
Stable, high-Q fabry-perot resonators with long cavity based on curved, all-silicon, high reflectance mirrors2011 IEEE 24th International Conference on Micro Electro Mechanical Systems
U. Siddique, Vincent Aravantinos, S. Tahar (2012)
On the Formal Analysis of Geometrical Optics in HOL
Clifford Pollock (1994)
Fundamentals of Optoelectronics
(1990)
Spoelhof, Ch.P.: The Hubble Space Telescope Optical System Failure Report
(2014)
linalgeig1
P. Hayes, M. O'keefe, P. Woodward, A. Gopinath (1999)
Higher-order-compact time-domain numerical simulation of optical waveguidesOptical and Quantum Electronics, 31
M. Gordon, T. Melham (1993)
Introduction to HOL: a theorem proving environment for higher order logic
F. Wiedijk (2012)
A Synthesis of the Procedural and Declarative Styles of Interactive Theorem ProvingLog. Methods Comput. Sci., 8
C. Kaliszyk, F. Wiedijk (2007)
Certified Computer Algebra on Top of an Interactive Theorem Prover
Sandrine Blazy, Christine Paulin-Mohring, David Pichardie (2013)
Interactive Theorem Proving, 7998
R. Feynman (1999)
Simulating physics with computersInternational Journal of Theoretical Physics, 21
Maciej Bugajski, J. Muszalski, B. Mroziewicz, K. Reginski (1995)
Resonant cavity enhanced photonic devicesJournal of Applied Physics, 78
Aftab Naqvi (2011)
Comments on “Waves in planar waveguide containing chiral nihility metamaterial”Optics Communications, 284
U. Siddique, Vincent Aravantinos, S. Tahar (2013)
A new approach for the verification of optical systems, 8844
T. Ralph, A. Gilchrist, G. Milburn, W. Munro, S. Glancy (2002)
Quantum computation with optical coherent states
D.J. Griffiths (2005)
Introduction to Quantum Mechanics
R. Garg (2008)
Analytical and Computational Methods in Electromagnetics
(1997)
Theorem Proving in Higher Order Logics
M. Tan, A. Kasten, J. Sulkin, K. Choquette (2013)
Planar Photonic Crystal Vertical-Cavity Surface-Emitting LasersIEEE Journal of Selected Topics in Quantum Electronics, 19
Albert Fromhold (1981)
CHAPTER 1 – AN INTRODUCTION TO QUANTUM MECHANICS
J. Harrison (2007)
Formalizing Basic Complex Analysis
U. Siddique, Vincent Aravantinos, S. Tahar (2013)
Formal Stability Analysis of Optical Resonators
A.E. Siegman (1986)
Lasers
Binghua Su, Junwen Xue, Lu Sun, H. Zhao, Xuedan Pei (2011)
Generalised ABCD matrix treatment for laser resonators and beam propagationOptics and Laser Technology, 43
Steven Johnson, J. Joannopoulos (2001)
Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis.Optics express, 8 3
B. Saleh, M. Teich, R. Slusher (1991)
Fundamentals of Photonics
J. Harrison (1996)
HOL Light: A Tutorial Introduction
O. Caprotti, A. Cohen, Manfred Riem (2000)
JAVA Phrasebooks for computer algebra and automated deductionSIGSAM Bull., 34
M. Karimi, K. Abedi, M. Zavvari (2013)
Resonant cavity enhanced quantum ring photodetector at $$20\,\upmu $$20μm wavelengthOptical and Quantum Electronics, 45
B. Buchberger, A. Craciun, T. Jebelean, L. Kovács, Temur Kutsia, K. Nakagawa, Florina Piroi, Nikolaj Popov, Judit Robu, M. Rosenkranz, W. Windsteiger (2006)
Theorema: Towards computer-aided mathematical theory explorationJ. Appl. Log., 4
(2014)
A HOL-Light library for vectors of complex numbers
J. Heinbockel (2004)
Numerical Methods for Scientific Computing
T. Jennewein, M. Barbieri, A. White (2010)
Single-photon device requirements for operating linear optics quantum computing outside the post-selection basisJournal of Modern Optics, 58
Stephan Merz (2000)
Model Checking
L. Yin, W. Hong (1999)
Domain decomposition method: a direct solution of Maxwell equationsIEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010), 2
J. Harrison, L. Théry (1998)
A Skeptic's Approach to Combining HOL and MapleJournal of Automated Reasoning, 21
Manuel Kauers, Manfred Kerber, Robert Miner, W. Windsteiger (2007)
Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
R. Hadfield (2009)
Single-photon detectors for optical quantum information applicationsNature Photonics, 3
MA PhD (1998)
Theorem Proving with the Real Numbers
J. Hölzl, Fabian Immler, B. Huffman (2013)
Type Classes and Filters for Mathematical Analysis in Isabelle/HOL
J. Harrison (2009)
HOL Light: An Overview
D. Griffiths (2017)
Introduction to Electrodynamics
J. Harrison (2009)
Handbook of Practical Logic and Automated Reasoning
K.J. Chen, H.C. Chen, K.A. Tsai, al. et. (2012)
Light-emitting devices: resonant-enhanced full-color emission of quantum-dot-based display technology using a pulsed spray methodAdv. Funct. Mater., 22
P. Dirac (1925)
The fundamental equations of quantum mechanicsProceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 109
Wuzhou Song, Xuming Zhang, A. Liu, C. Lim, P. Yap, H. Hosseini (2006)
Refractive index measurement of single living cells using on-chip Fabry-Pérot cavityApplied Physics Letters, 89
S. Mookherjea, A. Yariv (2001)
Analysis of optical pulse propagation with two-by-two (ABCD) matrices.Physical review. E, Statistical, nonlinear, and soft matter physics, 64 1 Pt 2
B. Saadany, M. Malak, M. Kubota, F. Marty, Y. Mita, D. Khalil, T. Bourouina (2006)
Free-Space Tunable and Drop Optical Filters Using Vertical Bragg Mirrors on SiliconIEEE Journal of Selected Topics in Quantum Electronics, 12
M. Nakazawa, H. Kubota, A. Sahara, K. Tamura (1998)
Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmissionIEEE Journal of Quantum Electronics, 34
O. Caprotti, A. Cohen (1999)
Connecting Proof Checkers and Computer Algebra Using OpenMath
S. Tan (1999)
A computational toolbox for quantum and atomic opticsJournal of Optics-nouvelle Revue D Optique
H. Prieto, Stéphane Dalmas, Y. Papegay (2000)
Mathematica as an OpenMath applicationSIGSAM Bull., 34
Alexsandro Pereira, F. Ostermann, C. Cavalcanti (2009)
On the use of a virtual Mach–Zehnder interferometer in the teaching of quantum mechanicsPhysics Education, 44
B. Lounis, M. Orrit (2005)
Single-photon sourcesReports on Progress in Physics, 68
C. Ballarin, K. Homann, J. Calmet (1995)
Theorems and algorithms: an interface between Isabelle and Maple
Max Born (1999)
Principles of optics - electromagnetic theory of propagation, interference and diffraction of light (7. ed.)
S.M. Tan (1999)
A computational toolbox for quantum and atomic opticsJ. Opt. B: Quantum Semiclass. Opt., 1
W. Wilson, G. Atkinson (2013)
Moems Modeling Using the Geometrical Matrix Toolbox
G. M.
The Collected Mathematical Papers of James Joseph SylvesterNature, 79
T. Hales (2005)
Introduction to the Flyspeck Project
M. Baaske, F. Vollmer (2012)
Optical resonator biosensors: molecular diagnostic and nanoparticle detection on an integrated platform.Chemphyschem : a European journal of chemical physics and physical chemistry, 13 2
U. Leonhardt (2003)
Quantum physics of simple optical instrumentsReports on Progress in Physics, 66
M. Mahmoud, Vincent Aravantinos, S. Tahar (2013)
Formalization of Infinite Dimension Linear Spaces with Application to Quantum Theory
Kuo‐Ju Chen, H. Chen, K. Tsai, C. Lin, H. Tsai, S. Chien, B. Cheng, Y. Hsu, M. Shih, Chih‐Hao Tsai, H. Shih, H. Kuo (2012)
Resonant‐Enhanced Full‐Color Emission of Quantum‐Dot‐Based Display Technology Using a Pulsed Spray MethodAdvanced Functional Materials, 22
H. Kogelnik, T. Li (1966)
Laser beams and resonatorsAppl. Opt., 5
O. Hasan, S. Afshar, S. Tahar (2009)
Formal Analysis of Optical Waveguides in HOL
Optical systems are becoming increasingly important by resolving many bottlenecks in today’s communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical system models using traditional paper-and-pencil and computer simulation approaches sets limits especially in safety-critical applications. In order to overcome these limitations, we propose to employ higher-order-logic theorem proving as a complement to computational and numerical approaches to improve optical model analysis in a comprehensive framework. The proposed framework allows formal analysis of optical systems at four abstraction levels, i.e., ray, wave, electromagnetic, and quantum.
Mathematics in Computer Science – Springer Journals
Published: May 1, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.