Abstract
Quantum mechanics is playing an intriguing role in the area of nanotechnology, from atomic level to solid state systems. It is leading to new multidisciplinary research directions and, as a result, new devices and breakthroughs in the fields of engineering and biosciences. The concepts of quantum mechanics have been proven theoretically, numerically and experimentally. Schrödinger equation is one of the fundamental equations to model and simulate the quantum effects. It is a well established fact that Maxwell equations have been proven to be robust, accurate and efficient when modeling and simulating micro- and macro-devices. In this chapter, we first show how time-dependent Schrödinger equation can be coupled with time-dependent Maxwell equations to account for quantum effects that can embellish the classical electromagnetic phenomena. Following this, we apply different numerical methods to solve the above coupled equations to simulate problems associated with different applications in different domains.
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
References
Swanson DG, Hoefer WJR (2003) Microwave circuit modeling using electromagnetic field simulation. Artech House, Norwood
Lee KH, Ahmed I, Goh RSM, Khoo EH, Li EP, Hung TGG (2011) Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications. PIERS 116:441–456
Mitin VV, Sementsov DI, Vagidov NZ (2010) Quantum mechanics for nanostructures. Cambridge University Press, Cambridge, NY
Tsukerman I (2008) Computational methods for nanoscale applications, particles, plasmons and waves. Springer, New York
Taflove A (2005) Computational electrodynamics. Artech House, Norwood
Ahmed I, Khoo EH, Li EP, Mittra R (2010) A hybrid approach for solving coupled Maxwell and Schrodinger equations arising in the simulation of nano-devices. IEEE Antenna Wireless Propag Lett 9:914–917
Pierantoni L, Mencarelli D, Rozzi T (2008) A new 3-D transmission line matrix scheme for the combined Schrödinger-Maxwell problem in the electronic/electromagnetic characterization of nanodevices. IEEE Transact Micro Theo Tech 56(3):654–662
Esteban R, Borisov AG, Nordlander P, Aizpurua J (2012) Bridging quantum and classical plasmonics with a quantum-corrected model. Nat Commun 3:825
Lorin E, Chelkowski S, Bandrauk A (2007) A numerical Maxwell–Schrödinger model for intense laser–matter interaction and propagation. Comput Phys Commun 177:908–932
Shibayama J, Muraki M, Yamauchi J, Nakano H (2005) Efficient implicit FDTD algorithm based on locally one-dimensional scheme. Electron Lett 41(19):1046–1047
Ahmed I, Chua EK, Li EP, Chen Z (2008) Development of the three dimensional unconditionally stable LOD–FDTD method. IEEE Trans Ante Propag 56(11):3596–3600
Ahmed I, Li EP, Khoo EH (2009) Coupling of Maxwell’s and Schrodinger’s equations for plasmonics applications. In the digest of Nanometa 2009, Austria
Ahmed I, Li EP (2012) Simulation of plasmonics nanodevices using coupled Maxwell and Schrödinger equations using the FDTD method. J Adv Electromag 1(1):76–83
Soriano A, Navarro EA, Portì JA, Such V (2004) Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices. J Appl Phys 95(12):8011–8018
Sullivan DM (2000) Electromagnetic simulation using the FDTD method. IEEE Press, New York
Ahmed I, Khoo EH, Li EP (2010) Development of the CPML for three-dimensional unconditionally sable LOD-FDTD method. IEEE Trans Ante Propagate 58(3):832–837
Ahmed I, Chen Z (2004) A hybrid ADI-FDTD subgridding scheme for efficient electromagnetic computation. Int J Numer Model Electron Netw Devices Fields 17:237–249
Maier SA (2007) Plasmonics: fundamentals and applications. Springer, New York
Brongersma ML, Kik PG (2007) Surface plasmon nanophotonics. Springer, The Netherlands
Shalaev VM, Kawata S (2007) Nanophotonics with surface plasmons. Elsevier, Amsterdam
Zia R, Brongersma ML (2007) Surface plasmon polariton analogue to Young’s double-slit experiment. Nat Nanotech 2:426–429
Khoo EH, Ahmed I, Li EP (2010) Investigation of the light energy extraction efficiency using surface modes in electrically pumped semiconductor microcavity. Proc SPIE 7764:77640B
Ahmed I, Khoo EH, Kurniawan O, Li EP (2011) Modeling and simulation of active plasmonics with the FDTD method by using solid state and Lorentz–Drude dispersive model. J Opt Soc B 28(3):352–359
Kurniawan O, Ahmed I, Li EP (2011) Development of a palsmonics source based on nano-antenna concept for nano-photonics applications. IEEE Photonic J 3:344–352
MacDonald KF, Samson ZL, Stockman MI, Zheludev NI (2009) Ultrafast active plasmonics. Nat Photonic 3:55–58
Dionne JA, Diest K, Sweatlock LA, Atwater HA (2009) Plas-MOStor: a metal-oxide-Si field effect plasmonic modulator. Nano Lett 9:897–902
Krasavin AV, Zayats AV (2008) Three-dimensional numerical modeling of photonics integration with dielectric loaded SPP waveguides. Phys Rev B 78:045425–045428
Naik G, Boltasseva A (2012) Plasmonics and metamaterials: looking beyond gold and silver. SPIE, Newsroom 1–3
Rakic D, Djurisic AB, Elazar JM, Majewski ML (1998) Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Optics 37:5271–5283
Sullivan DM (2000) Electromagnetic simulation using the FDTD method. Wiley-IEEE Press, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ahmed, I., Li, E. (2014). Modeling the Quantum Effects in Electromagnetic Devices. In: Mittra, R. (eds) Computational Electromagnetics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4382-7_18
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4382-7_18
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4381-0
Online ISBN: 978-1-4614-4382-7
eBook Packages: EngineeringEngineering (R0)