The circular birefringence of artificial chiral crystals at microwave frequencies

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dc.contributor.advisorCloete, J. H.en_ZA
dc.contributor.authorTheron, Isak Petrusen_ZA
dc.contributor.otherStellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.en_ZA
dc.date.accessioned2012-08-27T11:36:46Zen_ZA
dc.date.available2012-08-27T11:36:46Zen_ZA
dc.date.issued1995en_ZA
dc.descriptionDissertation (Ph.D.) -- University of Stellenbosch, 1995.en_ZA
dc.description.abstractENGLISH ABSTRACT: The current interest of the electromagnetic engineering community in chiral media was stimulated by Jaggard et al. [11] through the publication of their paper in 1979. They used approximate electric and magnetic dipole moments to analyse a material composed of single turn helices randomly distributed and oriented in vacuum. Recently there has been a growing interest in anisotropic media, for which the constitutive relations are generalised by using second rank tensors. For anisotropic media the electric and magnetic dipole moments are, however, not sufficient. Constitutive relations which include electric quadrupole terms, in addition to electric and magnetic dipole terms, are therefore used to predict the circular birefringence experienced by an electromagnetic wave propagating in an artificial uniaxial chiral crystal which is non-magnetic. The multipole theory is mostly used by physicists and chemists to study optical activity. Due to the complexity of the chiral molecules interacting with the incident light, it is very difficult to accurately find the charge distribution in the molecule. Thus it is not easy to compute the multipole moments of a single molecule and the multipole moment tensors are mostly found experimentally. However, at microwave frequencies it is possible to construct a physical structure that can also be analysed theoretically. The first part of this research concerns the choice of a chiral element and the most efficient way to analyse it. The polarizability tensors which determine circular birefringence are computed symbolically from the single element multipole moments which are computed numerically. This requires careful treatment of the relationship between the applied field and the local field in the crystal. A study of crystallography was done to determine the best crystal lattice for manufacturing such a uniaxial chiral crystal and careful attention was given to the calculation of the single element multipole moments. The formulation is independent of the origin chosen for the computation of the multipole moments. Numerical values are presented, in the long wavelength regime, for the rotatory dispersion as a result of circular birefringence. It is quantitatively demonstrated that neglect of the electric quadrupole contribution would lead to a serious error in the predicted value for the rotation angle of the polarization plane in the case of a uniaxial crystal geometry. In fact, the contribution of the electric quadrupole moments to optical activity is comparable to that of the magnetic dipole moments. The numerical predictions were verified by measurements on a 2 m long artificial crystal. The geometry, dimensions and spacing of the chiral elements were chosen for relative ease of fabrication of the crystal as well as allowing experimentation at frequencies where microwave instrumentation is readily available. An S-band (2 to 4 GHz) waveguide was constructed to measure the rotation of the E-field polarization of a wave propagating down the guide. The rotation was found to be less than expected, but within 13% of the predicted value using electric quadrupole moments. The error is more or less to be expected when considered in the light of uncertainties in the construction and calculations. If the quadrupole term is ignored in the modelling, the measured value is 70% greater than predicted. This proves beyond doubt that the electric quadrupole term must be included when modelling anisotropic chiral media. The time convention e+jwt is used throughout this dissertation.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Die elektromagnetiese ingenieurswese gemeenskap se huidige belangstelling in chirale media is veroorsaak deur Jaggard et al. se publikasie in 1979 [11]. Hulle het elektriese en magnetiese dipole gebruik om die parameters van 'n lukrake samestelling van enkeldraai helikse te bepaal. Onlangs het die belangstelling in anisotropiese materiale egter begin toeneem. Die parameters word veralgemeen deur die skalare te vervang met tweede rang tensors. In hierdie geval is die elektriese en magnetiese dipole egter nie meer genoeg om die materiaal te beskryf nie en dus is 'n uitbreiding van die samestellingsparameters gedoen om elektriese kwadrupole in te sluit. Hierdie parameters word dan gebruik om die verskil in voortplantingskonstantes vir links en regs sirkulêr gepolariseerde golwe in die medium te voorspel. Hierdie multipool teorie is hoofsaaklik gebruik deur fisici wat optiese aktiwiteit ondersoek. By optiese frekwensies maak die kompleksiteit van die molekules wat met die invallende lig reageer, dit baie moeilik om hierdie parameters teoreties te bepaal en word dit gewoonlik deur eksperimentering vasgestel. Dit is egter wel moontlik om by mikrogolf-frekwensies 'n kunsmatige kristal te bou wat beide gemeet en relatief maklik teoreties geanaliseer kan word. Hierdie navorsing behels eerstens die keuse van 'n chirale element en die effektiewe analise daarvan. Die multipool-tensors word simbolies bereken vanaf die multipoolmomente van 'n enkele struktuur. Hiervoor word die verwantskap tussen die plaaslike en die gemiddelde veld ondersoek en word gebruik gemaak van kristallografie om te bepaal wat die beste rooster is waarvolgens die strukture georienteer moet word. Die multipool momente van 'n enkele struktuur word numeries bereken met 'n dundraad formulering wat versigtig aangepas is om korterige drade te kan hanteer. Die formulering is onafhanklik van die oorsprong wat gebruik word om die multipool momente te bereken. Numeriese waardes word bereken wat aantoon dat, vir 'n uniaksiale medium in die lae frekwensie gebied, die elektriese kwadrupool 'n baie belangrike bydrae lewer tot die waarneembare rotasie. Die bydrae is, om die waarheid te sê, omtrent net so groot as die van die magnetiese dipool dus sal dit lei tot groot foute as dit geignoreer word. Die teoretiese voorspellings is ook prakties bevestig deur 'n 2 m lang kunsmatige kristal te bou en in 'n golfleier te toets. Die afmetings en spasiering van die chirale strukture is versigtig gekies om eksperimente in die S-band (2 tot 4 GHz) moontlik te maak. Dit is gevind dat die meetings omtrent 13% laer as die teoretiese voorspellings is. Daar is verskeie voorspelbare faktore wat tot hierdie verskil bydra. Dit kan dus onomwonde gestel word dat die elektriese kwadrupool se bydrae nie geignoreer kan word wanneer anisotropiese materiale beskou word nie.af_ZA
dc.description.versionMastersen_ZA
dc.format.extent100 pages : ill.en_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/54869en_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshCrystal opticsen_ZA
dc.subject.lcshCrystallographyen_ZA
dc.subject.lcshPhysical opticsen_ZA
dc.subject.lcshChiralityen_ZA
dc.subject.lcshElectromagnetismen_ZA
dc.subject.lcshMicrowave antennasen_ZA
dc.subject.lcshElectromagnetic wavesen_ZA
dc.subject.lcshDissertations -- Engineeringen_ZA
dc.titleThe circular birefringence of artificial chiral crystals at microwave frequenciesen_ZA
dc.typeThesisen_ZA
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