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Light propagation in finite and infinite photonic crystals: The recursive Greens function technique
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 15, p. 155117-Article in journal (Refereed) Published
Abstract [en]

We report a computational method based on the recursive Green’s function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference time domain (FDTD) technique is that it computes Green’s function of the photonic structure recursively by adding slice by slice on the basis of Dyson’s equation. This eliminates the need for storage of the wave function in the whole structure, which obviously strongly relaxes the memory requirements and enhances the computational speed. The second advantage of this method is that it can easily account for the infinite extension of the structure both into air and into the space occupied by the photonic crystal by making use of the so-called “surface Green’s functions.” This eliminates the spurious solutions (often present in the conventional FDTD methods) related to, e.g., waves reflected from the boundaries defining the computational domain. The developed method has been applied to study scattering and propagation of the electromagnetic waves in the photonic band-gap structures including cavities and waveguides. Particular attention has been paid to surface modes residing on a termination of a semi-infinite photonic crystal. We demonstrate that coupling of the surface states with incoming radiation may result in enhanced intensity of an electromagnetic field on the surface and very high Q factor of the surface state. This effect can be employed as an operational principle for surface-mode lasers and sensors.

Place, publisher, year, edition, pages
2005. Vol. 72, no 15, p. 155117-
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-14030DOI: 10.1103/PhysRevB.72.155117OAI: oai:DiVA.org:liu-14030DiVA, id: diva2:22490
Available from: 2006-10-03 Created: 2006-10-03 Last updated: 2017-12-13
In thesis
1. Theoretical studies of microcavities and photonic crystals for lasing and waveguiding applications
Open this publication in new window or tab >>Theoretical studies of microcavities and photonic crystals for lasing and waveguiding applications
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes.

The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations.

Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications.

Place, publisher, year, edition, pages
Institutionen för teknik och naturvetenskap, 2006. p. 43
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1224
Keywords
photonic crystals, microcavities, microlasers, scattering matrix, Green's function
National Category
Telecommunications
Identifiers
urn:nbn:se:liu:diva-7482 (URN)91-85457-99-X (ISBN)
Presentation
2006-01-20, K3, Kåkenhus, Campus Norrköping, Norrköping, 13:15 (English)
Opponent
Supervisors
Note
Report code: LIU-TEK-LIC 2006:5Available from: 2006-10-03 Created: 2006-10-03 Last updated: 2009-03-09
2. Theoretical studies of light propagation in photonic and plasmonic devices
Open this publication in new window or tab >>Theoretical studies of light propagation in photonic and plasmonic devices
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Photonics nowadays is one of the most rapidly developing areas of modern physics. Photonic chips are considered to be promising candidates for a new generation of high-performance systems for informational technology, as the photonic devices provide much higher information capacity in comparison to conventional electronics. They also offer the possibility of integration with electronic components to provide increased functionality. Photonics has also found numerous applications in various fields including signal processing, computing, sensing, printing, and others.

Photonics, which traditionally covers lasing cavities, waveguides, and photonic crystals, is now expanding to new research directions such as plasmonics and nanophotonics. Plasmonic structures, namely nanoparticles, metallic and dielectric waveguides and gratings, possess unprecedented potential to guide and manipulate light at nanoscale.

This Thesis presents the results of theoretical studies of light propagation in photonic and plasmonic structures, namely lasing disk microcavities, photonic crystals, metallic gratings and nanoparticle arrays. A special emphasis has been made on development of high-performance techniques for studies of photonic devices.

The following papers are included:

In the first two papers (Paper I and Paper II) we developed a novel scattering matrix technique for calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refraction index. The results demonstrate that the surface imperfections represent the crucial factor determining the $Q$ factor of the cavity.

A generalization of the scattering-matrix technique to the quantum-mecha\-nical electron scattering has been made in Paper III. This has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and has provided a new insight and interpretation of the experimental observations.

Papers IV and V present a novel effective Green's function technique for studying light propagation in photonic crystals. Using this technique we have analyzed surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications.

In Paper VI the propagation of light in nanorod arrays has been studied. We have demonstrated that the simple Maxwell Garnett effective-medium theory cannot properly describe the coupling and clustering effects of nanorods. We have demonstrated the possibility of using nanorod arrays as high-quality polarizers.

In Paper VII we modeled the plasmon-enhanced absorption in polymeric solar cells. In order to excite a plasmon we utilized a grated aluminum substrate. The increased absorption has been verified experimentally and good agreement with our theoretical data has been achieved.

Place, publisher, year, edition, pages
Universitetsbibliotek, 2007. p. 68
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1115
Keywords
microcavities, photonic crystals, plasmonics, nanoparticles, scattering matrix technique, Green's function technique
National Category
Telecommunications
Identifiers
urn:nbn:se:liu:diva-9585 (URN)978-91-85831-45-6 (ISBN)
Public defence
2007-08-30, K3, Kåkenhus, Campus Norrköping, Linköpings universitet, Norrköping, 00:00 (English)
Opponent
Supervisors
Available from: 2007-08-30 Created: 2007-08-30 Last updated: 2009-05-12

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Rahachou, AliaksandrZozoulenko, Igor

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