Abstract
Photonic signal processing is an emerging area of research, which provides unique prospects to build high-speed communication systems. Recent advancements in fabrication technology allow on-chip manufacturing of signal processing devices. This fact has lead to the widespread use of photonics in industrial critical applications such as telecommunication, biophotonics and aerospace. One the most challenging aspects in the photonics industry is the accurate modeling and analysis of photonic devices due to the complex nature of light and optical components. In this paper, we propose to use higher-order-logic theorem proving to improve the analysis accuracy by overcoming the known limitations of incompleteness and soundness of existing approaches (e.g., paper-and-pencil based proofs and simulation). In particular, we formalize the notion of transfer function using the signal-flow-graph theory which is the most fundamental step to model photonic circuits. Consequently, we formalize and verify the important properties of the stability and the resonance of photonic systems. In order to demonstrate the effectiveness of the proposed infrastructure, we present the formal analysis of a widely used double-coupler double-ring (DCDR) photonic processor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
IBM: Silicon photonics (2015), http://www.zurich.ibm.com/st/photonics/silicon.html
Intel-based Optical PCI Express (2015), http://www.intel.com/content/www/us/en/research/intel-labs-silicon-photonics-optical-pci-express-server.html
Beillahi, S.M., Siddique, U.: Formal Analysis of Photonic Signal Processing Systems (2015), http://hvg.ece.concordia.ca/projects/optics/psp.html
Beillahi, S.M., Siddique, U., Tahar, S.: On the Formalization of Signal-Flow-Graphs in HOL. Technical report, Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada (November 2014)
Binh, L.N.: Photonic Signal Processing: Techniques and Applications. Optical Science and Engineering. Taylor & Francis (2010)
Harvey, D., Millar, C.A., Urquhart, P.: Fibre Reflection Mach-Zehnder Interferometer. Optics Communcation 70, 304–308 (1989)
MIT’s CTR (2015), https://mphotonics.mit.edu/ctr-documents
Dey, S.B., Mandal, S., Jana, N.N.: Quadruple Optical Ring Resonator based Filter on Silicon-on-insulator. Optik - International Journal for Light and Electron Optics 124(17), 2920–2927 (2013)
Emelett, S., Soref, R.: Synthesis of Dual-Microring-Resonator Cross-Connect Filters. Optics Express 13(12), 4439–4456 (2005)
Driessen, A., et al.: Microresonators as Building Blocks for VLSI Photonics. AIP Conference Proceedings 709(1), 1–18 (2004)
Signal Flow Graph Simplification Program for MATLAB (2015), http://www.mathworks.com/matlabcentral/fileexchange/22-mason-m
Harrison, J.: HOL Light: A Tutorial Introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)
Hasan, O., Khan Afshar, S., Tahar, S.: Formal Analysis of Optical Waveguides in HOL. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 228–243. Springer, Heidelberg (2009)
Ladkin, P.B.: An Overview of IEC 61508 on EEPE Functional Safety (2008)
Yousri Mahmoud, M., Tahar, S.: On the Quantum Formalization of Coherent Light in HOL. In: Badger, J.M., Rozier, K.Y. (eds.) NFM 2014. LNCS, vol. 8430, pp. 128–142. Springer, Heidelberg (2014)
Mason, S.J.: Feedback Theory, Further Properties of Signal Flow Graphs. In: Proceeding of IRE, vol. 44, pp. 920–926 (July 1956)
Mason, S.J.: Feedback Theory, Some Properties of Signal Flow Graphs. In: Proceeding of IRE, vol. 41, pp. 1144–1156 (September 1953)
RTCA/DO-178B: Software Considerations in Airborne Systems and Equipment Certification (1992)
Rumley, S., Glick, M., Dutt, R., Bergman, K.: Impact of Photonic Switch Radix on Realizing Optical Interconnection Networks for Exascale Systems. In: IEEE Optical Interconnects Conference, pp. 98–99 (2014)
Siddique, U., Aravantinos, V., Tahar, S.: Formal Stability Analysis of Optical Resonators. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 368–382. Springer, Heidelberg (2013)
Siddique, U., Mahmoud, M.Y., Tahar, S.: On the Formalization of Z-Transform in HOL. In: Klein, G., Gamboa, R. (eds.) ITP 2014. LNCS, vol. 8558, pp. 483–498. Springer, Heidelberg (2014)
Siddique, U., Tahar, S.: Towards the Formal Analysis of Microresonators Based Photonic Systems. In: IEEE/ACM Design Automation and Test in Europe, pp. 1–6 (2014)
Taqdees, S.H., Hasan, O.: Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 744–758. Springer, Heidelberg (2013)
Tiernan, J.C.: An Efficient Search Algorithm to Find the Elementary Circuits of a Graph. Communnications of the ACM 13(12), 722–726 (1970)
Weaver, T.: High-Flying Photonics. SPIE OE Magazine (2004), http://spie.org/x17123.xml
Yupapin, P.P., Li, C., Saeung, P.: Characteristics of Complementary Ring-Resonator Add/Drop Filters Modeling by Using Graphical Approach. Optics Communications 272(1), 81–86 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Siddique, U., Beillahi, S.M., Tahar, S. (2015). On the Formal Analysis of Photonic Signal Processing Systems. In: Núñez, M., Güdemann, M. (eds) Formal Methods for Industrial Critical Systems. FMICS 2015. Lecture Notes in Computer Science(), vol 9128. Springer, Cham. https://doi.org/10.1007/978-3-319-19458-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-19458-5_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19457-8
Online ISBN: 978-3-319-19458-5
eBook Packages: Computer ScienceComputer Science (R0)