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Computational methods for the analysis and design of photonic bandgap structures
KTH, Superseded Departments, Signals, Sensors and Systems.
2000 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In the present thesis, computational methods for theanalysis and design of photonic bandgap structure areconsidered. Many numerical methods have been used to study suchstructures. Among them, the plane wave expansion method is veryoften used. Using this method, we show that inclusions ofelliptic air holes can be used effectively to obtain a largercomplete band gap for two-dimensional (2D) photonic crystals.An optimal design of a 2D photonic crystal is also consideredin the thesis using a combination of the plane wave expansionmethod and the conjugate gradient method. We find that amaximum complete 2D band gap can be obtained by connectingdielectric rods with veins for a photonic crystal with a squarelattice of air holes in GaAs.

For some problems, such as defect modes, the plane waveexpansion method is extremely time-consuming. It seems that thefinite-difference time-domain (FDTD) method is promising, sincethe computational time is proportional to the number of thediscretization points in the computation domain (i.e., it is oforderN). A FDTD scheme in a nonorthogonal coordinate systemis presented in the thesis to calculate the band structure of a2D photonic crystal consisting of askew lattice. The algorithmcan easily be used for any complicated inclusion configuration,which can have both the dielectric and metallic constituents.The FDTD method is also applied to calculate the off-plane bandstructures of 2D photonic crystals in the present thesis. Wealso propose a numerical method for computing defect modes in2D crystals (with dielectric or metallic inclusions). Comparedto the FDTD transmission spectra method, our method reduces thecomputation time and memory significantly, and finds as manydefect modes as possible, including those that are not excitedby an incident plane wave in the FDTD transmission spectramethod. The FDTD method has also been applied to calculateguided modes and surface modes in 2D photonic crystals using acombination of the periodic boundary condition and theperfectly matched layer for the boundary treatment. Anefficient FDTD method, in which only real variables are used,is also proposed for the full-wave analysis of guided modes inphotonic crystal fibers.

Place, publisher, year, edition, pages
Stockholm: KTH , 2000. , 33 p.
Keyword [en]
Photonic crystal, Photonic bandgap, Numerical analysis, Optimal design, Finite-difference time-domain method, Plane wave expansion method
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-3037ISBN: 91-7170-640-2 (print)OAI: oai:DiVA.org:kth-3037DiVA: diva2:8786
Public defence
2000-11-22, 00:00
Note
QC 20100629Available from: 2000-11-13 Created: 2000-11-13 Last updated: 2010-06-29Bibliographically approved
List of papers
1. Large complete band gap in two-dimensional photonic crystals with elliptic air holes
Open this publication in new window or tab >>Large complete band gap in two-dimensional photonic crystals with elliptic air holes
1999 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 60, no 15, 10610-10612 p.Article in journal (Refereed) Published
Abstract [en]

It is shown that elliptic air heres can be used effectively as inclusions to obtain a large complete band gap for two-dimensional photonic crystals. An instructive procedure of how one quickly finds the optimal configuration which gives the maximum complete band gap is described.

Keyword
LATTICE, FIBER
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13811 (URN)000083427600013 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
2. Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap
Open this publication in new window or tab >>Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap
2000 (English)In: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 17, no 6, 1027-1030 p.Article in journal (Refereed) Published
Abstract [en]

Optimal design of a two-dimensional photonic crystal with a square lattice of air holes in GaAs is considered. It is shown how a maximum complete two-dimensional band gap is obtained by optimally connecting the dielectric rods with veins. The complete two-dimensional bandgap of our optimal design reaches Delta omega = 0.0762(2 pi c/a) (a is the lattice constant).

Keyword
periodic dielectric structures, gaps
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13812 (URN)10.1364/JOSAB.17.001027 (DOI)000087534900020 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
3. A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions
Open this publication in new window or tab >>A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions
2000 (English)In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 87, no 12, 8268-8275 p.Article in journal (Refereed) Published
Abstract [en]

A finite-difference time-domain scheme in a nonorthogonal coordinate system is presented to calculate the band structure of a two-dimensional photonic crystal consisting of a skew lattice. The method can be used for a photonic crystal of complicated configuration, such as a photonic crystal with both dielectric and metallic inclusions. The method is verified by comparing with the results obtained by other methods for some special cases. The band structure of a photonic crystal with a dielectric layer coated on a metallic cylinder as an inclusion is studied. For such a case, it is noticed that both the dielectric and metallic characteristics of the band structure are inherited.

Keyword
electromagnetic-waves, 2-dimensional systems, maxwell equations, gap materials, scattering, propagation, dispersion, arrays, media
Identifiers
urn:nbn:se:kth:diva-13813 (URN)10.1063/1.373537 (DOI)000087346400005 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
4. FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions
Open this publication in new window or tab >>FDTD algorithm for computing the off-plane band structure in a two-dimensional photonic crystal with dielectric or metallic inclusions
2001 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 278, no 6, 348-354 p.Article in journal (Refereed) Published
Abstract [en]

An effective numerical method based on the finite-difference time-domain scheme for computing the off-plane band structure of a two-dimensional photonic crystal is presented. The method is an order N method, and requires only a two-dimensional discretization mesh for a given off-plant wave number k(z) although thr off-plane propagation is a three-dimensional problem. The computation time and memory required is thus reduced significantly. The present method can be used for any type of inclusions and no additional effort is needed for metallic inclusions. The off-plane band structures of a square lattice of metallic rods in the air are studied, and a complete bandgap for some nonzero off-plane wave number k(z) is found.

Keyword
gap, propagation
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13814 (URN)10.1016/S0375-9601(00)00795-7 (DOI)000166726200008 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
5. Numerical method for computing defect modes in two-dimensional photonic crystals with dielectric or metallic inclusions
Open this publication in new window or tab >>Numerical method for computing defect modes in two-dimensional photonic crystals with dielectric or metallic inclusions
2000 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 61, no 19, 12871-12876 p.Article in journal (Refereed) Published
Abstract [en]

A numerical method based on the finite-difference time-domain (FDTD) scheme for computing defect modes in two-dimensional photonic crystals (with dielectric or metallic inclusions) is presented. Compared to the FDTD transmission spectra method, the present method reduces the computation domain significantly. By means of it one can find as many defect modes as possible, including those that are inactive to the incident plane wave in the FDTD transmission spectra method. The calculated eigenfrequencies and field patterns for a defect in a square array of dielectric rods are consistent with those obtained by the plane wave expansion method. Modes for a defect in a square array of copper rods are also studied, and the calculated eigenfrequencies are in a very good agreement with experimental results.

Keyword
band-gap materials, propagation, lattices
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13815 (URN)10.1103/PhysRevB.61.12871 (DOI)000087159100065 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
6. Guided modes in a two-dimensional metallic photonic crystal waveguide
Open this publication in new window or tab >>Guided modes in a two-dimensional metallic photonic crystal waveguide
2000 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 266, no 4-6, 425-429 p.Article in journal (Refereed) Published
Abstract [en]

Guided modes in a two-dimensional metallic photonic crystal waveguide are studied. The guided modes in the photonic crystal waveguide are related to those in a conventional metallic waveguide. There exists a cutoff frequency and consequently a mode gap at low frequencies (starting from zero frequency) in the photonic crystal metallic waveguide.

Keyword
electromagnetic-waves, bends
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13816 (URN)10.1016/S0375-9601(00)00049-9 (DOI)000085767700032 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
7. Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study
Open this publication in new window or tab >>Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study
2001 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 282, no 1-2, 85-91 p.Article in journal (Refereed) Published
Abstract [en]

In the present Letter, surface modes in two-dimensional dielectric and metallic photonic crystals are studied by a finite-difference time-domain method. The existence of surface modes in metallic photonic crystals is examined. The influence of surface waves on dielectric photonic crystal antennas is also studied.

Keyword
electromagnetic-waves, crystals, states
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13817 (URN)10.1016/S0375-9601(01)00156-6 (DOI)000168163300012 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved
8. Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method
Open this publication in new window or tab >>Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method
2001 (English)In: Microwave and optical technology letters (Print), ISSN 0895-2477, E-ISSN 1098-2760, Vol. 30, no 5, 327-330 p.Article in journal (Refereed) Published
Abstract [en]

An efficient finite-difference time-domain method is proposed for the full-wave analysis of guided modes in photonic crystal fibers. The three-dimensional hybrid guided modes can be calculated by a two-dimensional mesh, if one assumes that the propagation constant along the z-direction (propagation direction) is fixed. Furthermore, only real variables are used in the present method. Therefore, the computation time and computer memory are significantly reduced. The results for a honeycomb-based silica-air photonic crystal fiber are in very good agreement with the results from the plane-wave expansion method.

National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-13818 (URN)10.1002/mop.1304 (DOI)000170191600011 ()
Note
QC 20100629Available from: 2010-06-29 Created: 2010-06-29 Last updated: 2017-12-12Bibliographically approved

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