<p>Photonic crystals are periodic structures that offers the possibility to control the propagation of light.</p><p>The revised plane wave method has been implemented in order to compute band structures for photonic crystals. The main advantage of the revised plane wave method is that it can handle lossless dispersive materials. This can not be done with a conventional plane wave method. The computational challenge is comparable to the conventional plane wave method.</p><p>Band structures have been calculated for a square lattice of cylinders with different parameters. Both dispersive and non-dispersive materials have been studied as well as the influence of a surface roughness.</p><p>A small surface roughness does not affect the band structure, whereas larger inhomogeneities affect the higher bands by lowering their frequencies.</p>

Photonic crystals are periodic structures that offers the possibility to control the propagation of light. The revised plane wave method has been implemented in order to compute band structures for photonic crystals. The main advantage of the revised plane wave method is that it can handle lossless dispersive materials. This can not be done with a conventional plane wave method. The computational challenge is comparable to the conventional plane wave method. Band structures have been calculated for a square lattice of cylinders with different parameters. Both dispersive and non-dispersive materials have been studied as well as the influence of a surface roughness. A small surface roughness does not affect the band structure, whereas larger inhomogeneities affect the higher bands by lowering their frequencies.

Carbon nanotubes have extraordinary mechanical, electrical, thermal andoptical properties. They are harder than diamond yet exible, have betterelectrical conductor than copper, but can also be a semiconductor or evenan insulator. These ranges of properties of course make carbon nanotubeshighly interesting for many applications. Carbon nanotubes are already usedin products as hockey sticks and tennis rackets for improving strength and exibility. Soon there are mobile phones with exible screens made fromcarbon nanotubes. Also, car- and airplane bodies will probably be mademuch lighter and stronger, if carbon nanotubes are included in the construction.However, the real game changers are; nanoelectromechanical systems(NEMS) and computer processors based on graphene and carbon nanotubes.In this work, we study Young's modulus in the axial direction of carbonnanotubes. This has been done by performing density functional theorycalculations. The unit cell has been chosen as to accommodate for tubes ofdierent radii. This allows for modelling the eect of bending of the bondsbetween the carbon atoms in the carbon nanotubes of dierent radii. Theresults show that Young's modulus decreases as the radius decreases. Ineect, the Young's modulus declines from 1 to 0.8 TPa. This eect can beunderstood because the bending diminishes the pure sp^2 character of thebonds.These results are important and useful in construction, not only when usingcarbon nanotubes but also when using graphene. Our results point towardsa Young's modulus that is a material constant and, above a certain criticalvalue, only weakly dependent on the radius of the carbon nanotube.Graphene can be seen as a carbon nanotube with innite radius.

The absence of appropriate media to cultivate photons efficiently at the micro or nano scale has hindered taking the full advantage of processing information with light. The proposal of such a medium for light, known as photonic crystals (PCs)--multi-dimensional artificially periodic dielectric media--brings the possibility of a revolution in communications and sensing much closer. In such media, one can manipulate light at a scale on the order of the wavelength or even shorter. Applications of PCs other than in communication include bio-sensing because of the peculiar properties of PCs such as the capability of enhance field-matter interaction and control over the group velocity. As a result, PC waveguide (PCW) structures are of interest and it is expected that PC sensors offer the feasibility of multi-analyte and compact sensing schemes as well as the ability of the detection of small absolute analyte quantities (nanoliters) and low-concentration samples (picomoles), which may be advantages over conventional approaches such as fiber optic and slab waveguide sensors. Depending on the nature of the analyte, either dispersive or absorptive sensing schemes may be implemented. Light propagation is controlled fully only with 3D PCs. One of the problems arising due to reducing the dimension to 2D is that PCs become strongly polarization sensitive. In many cases, one wants to implement polarization insensitive devices such that the PC provides a full band gap for all polarizations. To address this problem, a novel type of PC called annular PC is proposed and analyzed. The capability of tuning the TE and TM polarizations independently within the same structure provides great flexibility to produce polarization-independent or polarization-dependent devices as desired. PCW bends are expected to be the essential building blocks of photonic integrated circuits. Sharp corners having small radii of curvature can be obtained. To enhance the low-loss and narrow-band transmission through these bends, PC heterostructures waveguide concept is introduced. We show that in PCWs formed by joining different types of PCs in a single structure, light can flow around extremely sharp bends in ways that are not possible using conventional PCWs based on a single type of PC.

The dispersion property of periodic structures is a hot research topic in the last decade. By exploiting dispersion properties, one can manipulate the propagation of electromagnetic waves, and produce effects that do not exist in conventional materials. This thesis is devoted to two important dispersion effects: negative refraction and designed surface plasmons. First, we introduce negative refraction and designed surface plasmons, including a historical perspective, main areas for applications and current trends. Several numerical methods are implemented to analyze electromagnetic effects. We apply the layer-KKR method to calculate the electromagnetic wave through a slab of photonic crystals. By implementing the refraction matrix for semi-infinite photonic crystals, the layer-KKR method is modified to compute the coupling coefficient between plane waves and Bloch modes in photonic crystals. The plane wave method is applied to obtain the band structure and the equal-frequency contours in two-dimensional regular photonic crystals. The finite-difference time-domain method is widely used in our works, but we briefly discuss two calculation recipes in this thesis: how to deal with the surface termination of a perfect conductor and how to calculate the frequency response of high-Q cavities more efficiently using the Pad\`{e} approximation method. We discuss a photonic crystal that exhibits negative refraction characterized by an effective negative index, and systematically analyze the coupling coefficients between plane waves in air and Bloch waves in the photonic crystal. We find and explain that the coupling coefficients are strong-angularly dependent. We first propose an open-cavity structure formed by a negative-refraction photonic crystal. To illuminate the physical mechanism of the subwavelength imaging, we analyze both intensity and phase spectrum of the transmission through a slab of photonic crystals with all-angle negative refraction. It is shown that the focusing properties of the photonic crystal slab are mainly due to the negative refraction effect, rather than the self-collimation effect. As to designed surface plasmons, we design a structured perfectly conducting surface to achieve the negative refraction of surface waves. By the average field method, we obtain the effective permittivity and permeability of a perfectly conducting surface drilled with one-dimensional periodic rectangle holes, and propose this structure as a designed surface plasmon waveguide. By the analogy between designed surface plasmons and surface plasmon polaritons, we show that two different resonances contribute to the enhanced transmission through a metallic film with an array of subwavelength holes, and explain that the shape effect is attributed to localized waveguide resonances. / QC 20100817