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Transient Electromagnetic Waves in Nonlinear Media

Sjöberg, Daniel LU (2001) 23.
Abstract (Swedish)
Popular Abstract in Swedish

Denna avhandling behandlar hur elektromagnetiska vågor utbreder sig i olika material. Vanligtvis antar man i elektromagnetiska problem att materialen är linjära, det vill säga om man vet att man får en viss utsignal från materialet vid en given insignal, så förväntar man sig att få två gånger så stor utsignal om man fördubblar insignalen. I avhandlingen försöker vi klara oss utan denna egenskap, och utvecklar metoder som inte behöver linjäritet för att behandla vågutbredning. Detta kan behövas för att beskriva fenomen där man använder mycket stora energier, och vi ger ett antal olika exempel på sådana situationer i den allmänna inledningen, som föregår de fem vetenskapliga artiklar som utgör... (More)
Popular Abstract in Swedish

Denna avhandling behandlar hur elektromagnetiska vågor utbreder sig i olika material. Vanligtvis antar man i elektromagnetiska problem att materialen är linjära, det vill säga om man vet att man får en viss utsignal från materialet vid en given insignal, så förväntar man sig att få två gånger så stor utsignal om man fördubblar insignalen. I avhandlingen försöker vi klara oss utan denna egenskap, och utvecklar metoder som inte behöver linjäritet för att behandla vågutbredning. Detta kan behövas för att beskriva fenomen där man använder mycket stora energier, och vi ger ett antal olika exempel på sådana situationer i den allmänna inledningen, som föregår de fem vetenskapliga artiklar som utgör huvuddelen av avhandlingen.



Olika problem som behandlas i detta verk är hur man kan tolka mätningar utförda på olinjära material, och hur vågutbredningen i materialen kan beskrivas. Vi undersöker dels material som har samma egenskaper i alla riktningar, så kallade isotropa material, som material som har särskilda egenskaper i någon riktning, så kallade anisotropa material. Det visar sig att man vanligtvis har två olika vågutbredningshastigheter i ett olinjärt material. Dessa hastigheter kallas karakteristiska hastigheter, som dessutom visar sig bero på hur starka vågor vi försöker skicka genom materialet.



Ett typiskt fenomen som inträffar med vågutbredning i olinjära material är så kallade chockvågor. Detta är vågor som kan börja som lugna och mjuka vågor, men efter en viss ändlig tids utbredning börjar de kantra och blir skarpare och skarpare. Ett typiskt exempel på detta är vattenvågor som kommer in mot en grund strand; då avståndet mellan vattenytan och botten minskar, kommer toppen av vågen att färdas snabbare än resten, varpå vågen till slut bryts och vi får de typiska bränningar som kan iakttas vid en strand. Det visar sig att det finns tre sorters elektromagnetiska chockvågor, som skiljer sig åt beroende på hur snabbt de utbreder sig i förhållande till de två karakteristiska hastigheterna som vi nämnde i förra stycket: de snabba, långsamma eller mellanliggande chockvågorna. (Less)
Abstract
This thesis is concerned with the propagation of transient electromagnetic waves in nonlinear media. It consists of a General Introduction and five scientific papers.



The General Introduction gives a broad overview of nonlinear electromagnetic phenomena. The emphasis is on the representation of the constitutive functional modeling the material's response to electromagnetic excitation, and the methods employed to analyze the combination of the constitutive functional and the Maxwell equations. Some applications of nonlinear electromagnetics are also discussed.



Paper I treats the inverse scattering problem for an isotropic, homogeneous, nonlinear slab, subjected to a normally incident field. It is shown... (More)
This thesis is concerned with the propagation of transient electromagnetic waves in nonlinear media. It consists of a General Introduction and five scientific papers.



The General Introduction gives a broad overview of nonlinear electromagnetic phenomena. The emphasis is on the representation of the constitutive functional modeling the material's response to electromagnetic excitation, and the methods employed to analyze the combination of the constitutive functional and the Maxwell equations. Some applications of nonlinear electromagnetics are also discussed.



Paper I treats the inverse scattering problem for an isotropic, homogeneous, nonlinear slab, subjected to a normally incident field. It is shown that when both reflected and transmitted fields are measured, we can reconstruct both the nonlinear permittivity and permeability. When one of these functions is known, reflection data is sufficient to obtain the other.



Paper II gives a formulation of transient electromagnetic fields, that can be used to analyze wave propagation in homogeneous media. The source free Maxwell equations are treated as an eigenvalue problem, from which we deduce the propagating waves and their wave speeds. The analysis is applied to the case of obliquely incident waves on a semi-infinite, bianisotropic, nonlinear medium.



Paper III analyzes the propagation of electromagnetic waves in a waveguide filled with an isotropic, nonlinear material. The equations governing each waveguide mode are derived, and it is shown that the different modes couple to each other. This coupling is quantified, and a growth estimates is given for the induced modes.



Paper IV deals with discontinuous electromagnetic waves, shock waves. It is shown that in order for these waves to be stable, they must satisfy a number of conditions, similar to Lax's classical shock conditions. These conditions permit us to classify electromagnetic shock waves as slow, fast or intermediate shock waves.



Finally, Paper V investigates the uniqueness and continuous dependence on data for solutions of the quasi-linear Maxwell equations, when we also require them to satisfy an entropy condition. This condition is related to the second law of thermodynamics, that the energy that is not described by our model must be dissipated. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Prof. Wall, David J.N.
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Signal processing, nonlinear materials, Electromagnetic waves, instantaneous response, waveguides, shock waves, entropy condition, Elektronik och elektroteknik, Electronics and Electrical technology, Signalbehandling, Electromagnetism, optics, acoustics, Elektromagnetism, optik, akustik
volume
23
pages
150 pages
publisher
Department of Electroscience, Lund University
defense location
Lund Institute of Technology, E:1406
defense date
2001-04-27 10:15
ISSN
1402-8662
ISBN
91-7874-132-7
language
English
LU publication?
yes
id
ce37f89e-e4b3-4ff8-9ed4-0256e0f559be (old id 41572)
date added to LUP
2007-08-01 11:43:51
date last changed
2018-05-29 10:39:42
@phdthesis{ce37f89e-e4b3-4ff8-9ed4-0256e0f559be,
  abstract     = {This thesis is concerned with the propagation of transient electromagnetic waves in nonlinear media. It consists of a General Introduction and five scientific papers.<br/><br>
<br/><br>
The General Introduction gives a broad overview of nonlinear electromagnetic phenomena. The emphasis is on the representation of the constitutive functional modeling the material's response to electromagnetic excitation, and the methods employed to analyze the combination of the constitutive functional and the Maxwell equations. Some applications of nonlinear electromagnetics are also discussed.<br/><br>
<br/><br>
Paper I treats the inverse scattering problem for an isotropic, homogeneous, nonlinear slab, subjected to a normally incident field. It is shown that when both reflected and transmitted fields are measured, we can reconstruct both the nonlinear permittivity and permeability. When one of these functions is known, reflection data is sufficient to obtain the other.<br/><br>
<br/><br>
Paper II gives a formulation of transient electromagnetic fields, that can be used to analyze wave propagation in homogeneous media. The source free Maxwell equations are treated as an eigenvalue problem, from which we deduce the propagating waves and their wave speeds. The analysis is applied to the case of obliquely incident waves on a semi-infinite, bianisotropic, nonlinear medium.<br/><br>
<br/><br>
Paper III analyzes the propagation of electromagnetic waves in a waveguide filled with an isotropic, nonlinear material. The equations governing each waveguide mode are derived, and it is shown that the different modes couple to each other. This coupling is quantified, and a growth estimates is given for the induced modes.<br/><br>
<br/><br>
Paper IV deals with discontinuous electromagnetic waves, shock waves. It is shown that in order for these waves to be stable, they must satisfy a number of conditions, similar to Lax's classical shock conditions. These conditions permit us to classify electromagnetic shock waves as slow, fast or intermediate shock waves.<br/><br>
<br/><br>
Finally, Paper V investigates the uniqueness and continuous dependence on data for solutions of the quasi-linear Maxwell equations, when we also require them to satisfy an entropy condition. This condition is related to the second law of thermodynamics, that the energy that is not described by our model must be dissipated.},
  author       = {Sjöberg, Daniel},
  isbn         = {91-7874-132-7},
  issn         = {1402-8662},
  keyword      = {Signal processing,nonlinear materials,Electromagnetic waves,instantaneous response,waveguides,shock waves,entropy condition,Elektronik och elektroteknik,Electronics and Electrical technology,Signalbehandling,Electromagnetism,optics,acoustics,Elektromagnetism,optik,akustik},
  language     = {eng},
  pages        = {150},
  publisher    = {Department of Electroscience, Lund University},
  school       = {Lund University},
  title        = {Transient Electromagnetic Waves in Nonlinear Media},
  volume       = {23},
  year         = {2001},
}