Problem of spontaneous emission in photonic crystals

Adam Paweł Rudziński

Abstract

The subject of this thesis is modelling of the process of spontaneous emission occuring in a photonic crystal medium. To retain the possibility of analytic description of the structure,the investigation has been limited to one-dimensional photonic crystal, what allows to describe the phenomenon rigorously in every aspect. Therefore, general conclusions can be formulated,along with assumptions and restrictions they are amenable to. Because one-dimensional photonic crystal posseses the same features, as more complicated two- and three-dimensional structures, presented analysis and conclusions are applicable to these structures as well. In the thesis, there is presented an analytic model of electromagnetic field in the structure of one-dimensional photonic crystal – based on translation matrix method so-called effective resonator model, proposed and constructed by the author of the thesis. There has been given a physical interpretation of a parameter defined within the model, so-called mode spectrum, which allows an easy and clear analysis of modal structure and is directly related to spontaneous emission rate. Construction of basis of orthonormal modes has been shown and numerous mathematical properties of the model demonstrated. An expression based on the effective resonator model describing spontaneous emission rate has been derived for a single atom and for multiatomic case. This way, a description characterizing impact of one-dimensional photonic crystal on the spontaneous emission rate with the help of mode spectrum has been obtained. It has been show to be a convenient tool for design of multilayer structures and it constitutes an original contribution of the thesis’ author. Conducted calculations allowed to draw conclusions concerning impact of parameters and defects of structure on spontaneous emission, in particular it has been shown, that spontaneous emission into a defect mode becomes weaker with growing distance to the defected layer. On the base of results obtained for many atoms in defferent layers, a hypothesis was formed, stating,that collective emission by a pair of atoms, one of which is placed in environment strongly inhibiting spontaneous emission, may be a dominant emission channel.
Diploma typeDoctor of Philosophy
Author Adam Paweł Rudziński (FEIT / MO)
Adam Paweł Rudziński,,
- The Institute of Microelectronics and Optoelectronics
Title in EnglishProblem of spontaneous emission in photonic crystals
Languagepl polski
Certifying UnitFaculty of Electronics and Information Technology (FEIT)
Disciplineelectronics / (technology domain) / (technological sciences)
Start date23-01-2007
Defense Date15-06-2010
End date22-06-2010
Supervisor Paweł Szczepański (FEIT / MO)
Paweł Szczepański,,
- The Institute of Microelectronics and Optoelectronics

Internal reviewers Miroslaw A. Karpierz (FP / OPD)
Miroslaw A. Karpierz,,
- Optics and Photonics Division
External reviewers Maciej Bugajski
Maciej Bugajski,,
-
Pages102
Keywords in Englishphotonic crystal, spontaneous emission, effective resonator model, superradiance
Abstract in EnglishThe subject of this thesis is modelling of the process of spontaneous emission occuring in a photonic crystal medium. To retain the possibility of analytic description of the structure,the investigation has been limited to one-dimensional photonic crystal, what allows to describe the phenomenon rigorously in every aspect. Therefore, general conclusions can be formulated,along with assumptions and restrictions they are amenable to. Because one-dimensional photonic crystal posseses the same features, as more complicated two- and three-dimensional structures, presented analysis and conclusions are applicable to these structures as well. In the thesis, there is presented an analytic model of electromagnetic field in the structure of one-dimensional photonic crystal – based on translation matrix method so-called effective resonator model, proposed and constructed by the author of the thesis. There has been given a physical interpretation of a parameter defined within the model, so-called mode spectrum, which allows an easy and clear analysis of modal structure and is directly related to spontaneous emission rate. Construction of basis of orthonormal modes has been shown and numerous mathematical properties of the model demonstrated. An expression based on the effective resonator model describing spontaneous emission rate has been derived for a single atom and for multiatomic case. This way, a description characterizing impact of one-dimensional photonic crystal on the spontaneous emission rate with the help of mode spectrum has been obtained. It has been show to be a convenient tool for design of multilayer structures and it constitutes an original contribution of the thesis’ author. Conducted calculations allowed to draw conclusions concerning impact of parameters and defects of structure on spontaneous emission, in particular it has been shown, that spontaneous emission into a defect mode becomes weaker with growing distance to the defected layer. On the base of results obtained for many atoms in defferent layers, a hypothesis was formed, stating,that collective emission by a pair of atoms, one of which is placed in environment strongly inhibiting spontaneous emission, may be a dominant emission channel.
EU classification8030
Thesis file
Rudzinski.pdf 804.56 KB

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