We describe the theory and implementation of a multipole method for calculating the modes of microstructured optical fibers (MOFs). We develop tools for exploiting results obtained through the multipole method, including a discrete Bloch transform. Using the multipole method, we study in detail the physical nature of solid core MOF modes, and establish a distinction between localized defect modes and extended modes. Defect modes, including the fundamental mode, can undergo a localization transition we identify with the mode�s cutoff. We study numerically and theoretically the cutoff of the fundamental and the second mode extensively, and establish a cutoff diagram enabling us to predict with accuracy MOF properties, even for exotic MOF geometries. We study MOF dispersion and loss properties and develop unconventional MOF designs with low losses and ultra-flattened near-zero dispersion on a wide wavelength range. Using the cutoff-diagram we explain properties of these MOF designs.

This thesis consist of a theoretical study of propagation effects in optical waveguides, fibres and photonic crystals, with some comparison with experiment.¶ Chapter 1 gives a brief introduction with the current view of optical components in photonic integrated circuits and issues related to the loss mechanism.¶ In Chapter 2 the characteristics of single-mode propagation and transient effects in practical square- and rectangular-core buried channel planar waveguides are quantified, assuming a cladding which is unbounded in one transverse dimension and bounded in the other. The wavelength cut-off condition for the fundamental mode is determined when the cladding index is asymmetric and composed of step-wise, uniform index regions.¶ In Chapter 3, the application of segmented reflection gratings in planar devices that can function as either a single- or two-wavelength add/drop filter is investigated and a numerical technique developed in Chapter 2 is applied to the waveguides with high extinction ratio. The role of the segmented gratings is analogous to that of a blazed grating, but they can provide a higher reflectivity level at the Bragg wavelength, eliminate back reflection into the fundamental mode and provide arbitrarily small channel spacing in the two-wavelength case.¶ Chapters 4 address the problem of bend loss in a single-mode slab waveguide. A new theoretical strategy for reducing bend loss is presented and compared to existing designs. The results obtained in this chapter are the basis for the following two chapters.¶ Chapter 5 deals with bend loss in single-mode buried channel waveguides and demonstrates that the new strategy can lead to significant bend loss reduction when compared to other strategies, and, conversely, can be used to enhance bend loss for a fixed bend radius for application to devices such as optical attenuators.¶ In Chapter 6, a novel design of a variable optical attenuator based on a bent channel waveguide is proposed, realized by applying a new strategy for bend loss control in a polymer buried channel waveguide.¶ Chapter 7 investigates effects of the additional rings in a single mode step-index fibre on bend loss. It is supported with the experimental results of Ron Bailey from Optical the Fibre Technology Centre, University in Sydney.¶ In Chapter 8, bend loss of a one-dimensional photonic crystal is quantified and compared to bend loss of a standard single-mode slab waveguide and a bend-resistant waveguide.¶

<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>

<p>Photonic Crystal (PC) devices are the most exciting advancement in the field of photonics. The use of computational techniques has made considerable improvements in photonic crystals design. We present here an ultrahigh quality factor (Q) photonic crystal slab nanocavity formed by the local width modulation of a line defect. We show that only shifting two holes away from a line defect is enough to attain an ultrahigh Q value. We simulated this double heterostructure nano cavity by using Finite Difference Time Domain (FDTD) technique. We observed that photonic crystal cavities are very sensitive to the frequency, size and position of the source. So we must choose the right values for these parameters.</p>

We report on the process parameters of nanoimprint lithography (NIL) for the fabrication of two-dimensional (2-D) photonic crystals. The nickel mould with 2-D photonic crystal patterns covering the area up to 20mm² is produced by electron-beam lithography (EBL) and electroplating. Periodic pillars as high as 200nm to 250nm are produced on the mould with the diameters ranging from 180nm to 400nm. The mould is employed for nanoimprinting on the poly-methyl-methacrylate (PMMA) layer spin-coated on the silicon substrate. Periodic air holes are formed in PMMA above its glass-transition temperature and the patterns on the mould are well transferred. This nanometer-size structure provided by NIL is subjective to further pattern transfer. / Singapore-MIT Alliance (SMA)

Das Strahlungsfeld in einem absorbierenden, periodischen Dielektrikum ist kanonisch quantisiert worden. Dabei wurde ein eindimensionales Modell mit punktförmigen Streuern betrachtet, deren Polarisierbarkeit den Kramers-Kronig Relationen gehorcht. Es wurde ein Quantisierungsverfahren nach Knöll, Scheel und Welsch [1] verwendet, das als eine Ergänzung zum mikroskopischen Huttner-Barnett Schema [2] aufgefaßt werden kann und in dem auf der Basis der phänomenologischen Maxwell Gleichungen eine bosonische Rauschpolarisation als die Quelle des Feldes auftritt. Das Problem reduziert sich dabei auf die Bestimmung der klassischenGreens Funktion. Die Kramers-Kronig Relationen der komplexen Polarisierbarkeit der Punktstreuer sichert die korrekte Verknüpfung zwischen Dispersion und Absorption. Der Punktstreuer ist dabei ein idealisiertes Modell, um periodische Hintergrundmedien, denen das Strahlungsfeld ausgesetzt ist, zu beschreiben. Er bedarf jedoch eines Kompromisses, um die entsprechenden Rauschquellen zu konstruieren. Es konnte gezeigt werden, daß der Punktstreuer dasselbe Streuverhalten wie eine dünne Potentialschwelle besitzt und damit die technischen Schwierigkeiten für den Fall eines absorptiven Punktstreuers überwunden werden können. An Hand dieses Beispiels konnte das Quantisierungsschema nach Knöll, Scheel und Welsch auf periodische und absorbierende Strukturen angewendet werden. Es ist bekannt, daß die Bestimmung der Modenstruktur für den Fall der Modenzerlegung des Strahlungsfeldes ein rein klassisches Problem darstellt. Mit Ausnahme des Vakuums ist eine zweckmäßige Modenzerlegung nur dann durchführbar, wenn mit einer reellen Polarisierbarkeit die Absorption vernachlässigt werden kann. Aus den Kramers-Kronig Relationen wird klar, daß solch eine Annahme nur in bestimmten Intervallen des Frequenzspektrums gerechtfertigt werden kann. Es wurde gezeigt, daß auch das quantisierte Strahlungsfeld in Anwesenheit der Punktstreuer in eben solchen Intervallen in Quasimoden entwickelt werden kann, wenn man neue Quasioperatoren als Erzeuger und Vernichter einführt. Die bosonischen Vertauschungsrelationen dieser Operatoren konnten bestätigt werden. Die allgemeine Vertauschungsrelation kanonisch konjugierter Variablen im Sinne der kanonischen Quantisierung kann für das elektrische Feld und das Vektorpotential beibehalten werden. In der Greens Funktion sind sämtliche Informationen über die dispersiven und absorptiven Eigenschaften des Dielektrikums sowie über die räumliche Struktur enthalten. Die wesentlichen Merkmale werden dabei durch den Reflexionskoeffizienten nach Boedecker und Henkel [3] bestimmt, der das Reflexionsverhalten an einem unendlich ausgedehnten Halbraum aus periodisch angeordneten Punktstreuern beschreibt. Mit Hilfe des Transfermatrixformalismus war es möglich einen allgemeinen Zugang zum Reflexionsverhalten zunächst endlicher Strukturen zu erhalten. Die Ausdehnung auf den Halbraum mit Hilfe der Klassifizierung in Untergruppen der Transfermatrizen nach ermöglichte es, den Reflexionskoeffizienten nach Boedecker und Henkel [3] auch geometrisch plausibel zu machen. Ein wesentlicher Aspekt von periodischen Systemen ist die Translationssymmetrie, die im Fall unendlich ausgedehnter, verlustfreier Systeme auf eine ideale Bandstruktur führt. Mit Hilfe der Untergruppenklassifizierung kann im verlustfreien Fall die Geometrie der Anordnung indirekt mit der Bandstruktur verknüpft werden. Es konnte nachgewiesen werden, daß auch der einzelne Punktstreuer immer in einer dieser Untergruppen zu finden ist. Dabei besitzt die Bandstruktur der unendlich periodischen Anordnung dieser Streuer immer eine von der Polarisierbarkeit abhängige Bandkante und eine von der Polarisierbarkeit unabhängige Bandkante. Die Bandstruktur, die mit den verlustbehafteten Feldern einhergeht, ist eine doppelt komplexe. Alternativ zu dieser nur schwer zu interpretierenden Bandstruktur wurden die Feldfluktuationen selektiv nach reellen Frequenzen und Wellenzahlen sondiert. Es zeigt sich, daß Absorption besonders in der Nähe der Bandkanten die Bänder verbreitert. Die Ergebnisse, die mit Hilfe der lokalen Zustandsdichtefunktion gewonnen wurden, konnten dabei bestätigt werden. [1] S. Scheel, L. Knöll and D. G. Welsch, Phys.Rev. A 58, 700 (1998). [2] B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992). [3] G. Boedecker and C. Henkel, OPTICS EXPRESS 11, 1590 (2003). / A canonical scheme based on the phenomenological Maxwell equations in the presence of dielectric matter is used to quantize the electromagnetic field in a periodic and lossy linear dielectric. We focus on a one-dimensional model of point scatterers with given frequency-dependent complex permittivity, and construct an expansion of the field operators that is based on the Green function and preserves the canonical equal-time commutation relations. Translation symmetry is secured by working with an infinite lattice. The impact of absorption is examined using the local density of states and the decay rate of a phase-coherent dipole chain located inside the structure. Incidentally the model is used to bring about a geometrical interpretation of the reflection from multilayers

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.

This thesis is concerned with the fabrication methodology of polymeric photonic crystals operating in the visible to near infrared regions and the correlation between the chemical deposition morphologies and the resultant photonic stopband enhancements of photonic crystals. Multiphoton lithography (MPL) is a powerful approach to the fabrication of polymeric 3D micro- and nano-structures with a typical minimum feature size ~ 200 nm. The completely free-form 3D fabrication capability of MPL is very well suited to the formation of tailored photonic crystals (PCs), including structures containing well defined defects. Such structures are of considerable current interest as micro-optical devices for their filtering, stop-band, dispersion, resonator, or waveguiding properties. More specifically, the stop-band characteristics of polymer PCs can be finely controlled via nanoscale changes in rod spacings and the chemical functionalities at the polymer surface can be readily utilized to impart new optical properties. Nanoscale features as small as 65 ± 5 nm have been formed reproducibly by using 520 nm femtosecond pulsed excitation of a 4,4'-bis(di-n-butylamino)biphenyl chromophore to initiate crosslinking in a triacrylate blend. Dosimetry studies of the photoinduced polymerization were performed on chromophores with sizable two-photon absorption cross-sections at 520 and 730 nm. These studies show that sub-diffraction limited line widths are obtained in both cases with the lines written at 520 nm being smaller. Three-dimensional multiphoton lithography at 520 nm has been used to fabricate polymeric woodpile photonic crystal structures that show stop bands in the visible to near-infrared spectral region. 85 ± 4 nm features were formed using swollen gel photoresist by 730 nm excitation MPL. An index matching oil was used to induce chemical swelling of gel resists prior to MPL fabrication. When swollen matrices were subjected to multiphoton excitation, a similar excitation volume is achieved as in normal unswollen resins. However, upon deswelling of the photoresist following development a substantial reduction in feature size was obtained. PCs with high structural fidelity across 100 µm × 100 µm × 32 layers exhibited strong reflectivity (>60% compared to a gold mirror) in the near infrared region. The positions of the stop-bands were tuned by varying the swelling time, the exposure power (which modifies the feature sizes), and the layer spacing between rods. Silver coatings have been applied to PCs with a range of coverage densities and thicknesses using electroless deposition. Sparse coatings resulted in enhanced reflectivity for the stop band located at ~5 µm, suggesting improved interface reflectivity inside the photonic crystal due to the Ag coating. Thick coatings resulted in plasmonic bandgap behavior with broadband reflectivity enhancement and PC lattice related bandedge at 1.75 µm. Conformal titania coatings were grown onto the PCs via a surface sol-gel method. Uniform and smooth titania coatings were achieved, resulting in systematically red-shifted stopbands from their initial positions with increasing thicknesses, corresponding to the increased effective refractive index of the PC. High quality titania shell structures with modest stopbands were obtained after polymer removal. Gold replica structures were obtained by electroless deposition on the silica cell walls of naturally occurring diatoms and the subsequent silica removal. The micron-scaled periodic hole lattice originated from the diatom resulted in surface plasmon interferences when excited by infrared frequencies. The hole patterns were characterized and compared with hexagonal hole arrays fabricated by focused ion beam etching of similarly gold plated substrate. Modeling of the hole arrays concluded that while diatom replicas lack long-ranged periodicity, the local hole to hole spacings were sufficient to generate enhanced transmission of 13% at 4.2 µm. The work presented herein is a step towards the development of PCs with new optical and chemical functionalities. The ability to rapidly prototype polymeric PCs of various lattice parameters using MPL combined with facile coating chemistries to create structures with the desired optical properties offers a powerful means to produce tailored high performance photonic crystal devices.

We report on the combination of slow light propagation with the resonance properties of a photonic crystal (PhC) cavity and with the slow mode of a PhC waveguide. We demonstrate theoretically and experimentally that slow light induced by the Coherent Population Oscillation (CPO) effect enables to have small-size and ultrahigh quality (Q) factor cavity, regardless of the technological and design issues. The experimental proof is performed in a L3 2D PhC cavity with semiconductor quantum wells as active, medium in which the CPO effect is induced. We achieve a cavity Q-factor of 520000, which corresponds to an enhancement by a factor 138 in comparison with the original Q-factor of the cavity. We present a theoretical approach to the combination of CPO-based slow light and slow mode in PhC waveguides, showing that the total group index is a multiplication of the group indices associated respectively to the CPO slow light and to the waveguide slow mode. We also set the basis for the experimental demonstration by designing and fabricating samples in the clean room facilities of LPN and addressing the challenging issue of coupling and extracting light in and from the waveguides. A particular design of the PhC in the waveguide is issued as a grating that allows to couple light perpendicularly to the plane of the PhC from free space. The vertical coupler has also been designed and fabricated along the waveguide and has been experimentally characterized. Slow light based on CPO effect in the PhC waveguides is always under experimental investigation.

Photonic Crystal (PC) devices are the most exciting advancement in the field of photonics. The use of computational techniques has made considerable improvements in photonic crystals design. We present here an ultrahigh quality factor (Q) photonic crystal slab nanocavity formed by the local width modulation of a line defect. We show that only shifting two holes away from a line defect is enough to attain an ultrahigh Q value. We simulated this double heterostructure nano cavity by using Finite Difference Time Domain (FDTD) technique. We observed that photonic crystal cavities are very sensitive to the frequency, size and position of the source. So we must choose the right values for these parameters.