A multi-layered periodic structure is investigated for optimal shape design in diffraction gratings. A periodic dielectric material is used as the scattering profile for a planar incident wave. Designing optimal profiles for scattering is a type of inverse problem. The ability to fabricate such materials on the order of the wavelength of the incoming light is key for design strategies. We compute a finite element approximation on a variational setup of the forward problem. On the inverse and optimal design problem, we discuss the stability of the designs and develop computational strategies based on a level-set evolutionary approach.

Numerical analysis of the electromagnetic fields in large, complex structures is very challenging due to the high computational overhead. Recently, it has been shown that a new method called Trefftz-FLAME ( Flexible Local Approximation MEthod) is suitable for problems where there exist a large number of similar structures. / This thesis develops Trefftz-FLAME in two areas. First, a novel 2D Trefftz-FLAME method incorporates the modal analysis and port boundary condition that are essential to an accurate calculation of reflection and transmission coefficients for photonic crystal devices. The new technique outperforms existing methods in both accuracy and computational cost. / The second area pertains to the 3D, vector problem of electromagnetic wave scattering by aggregates of identical dielectric particles. A methodology for the development of local basis functions is introduced, applicable to particles of any shape and composition. Boundary conditions on the surface of the finite FLAME domain are described, capable of representing the incident wave and absorbing the outgoing radiation. A series of problems involving dielectric spheres is solved to validate the new method. Comparison with exact solutions is possible in some cases and shows that the method is able to produce accurate near-field results even when the computational grid spacing is equal to the radius of the spheres.

Paskutiniais dešimtmečiais puslaidininkių fizika vaidino svarbų vaidmenį beveik kiekvienoje šiuolaikinių technologijų srityje. Šiame greitai besikeičiančiame pasaulyje mūsų jau nebetenkina supantys buities ir darbo prietaisai, valdomi naudojantis elektronais. Mums reikalingas didesnis kompiuterių operatyvumas, didesnė atminties talpa, greitesnis telekomunikacinis ryšys, ir todėl reikalingos naujos technologijos bei sprendimai. Naujas žingsnis fotoninės struktūros. Žinių ir technologijų pasiekimai leidžia fotoninių sturktūrų savybes taikyti šviesos valdymui. Dabartiniame optinės fizikos tyrinėjimų etape šviesos sąveika su medžiaga labai aktuali: ji gali atrodyti universali ir invariantiška, kadangi šviesa jau kontroliuojama pasitelkus hibridinius fotoninius kristalus. Šių darinių tyrimai patrauklūs tiek fundamentaliam, tiek taikomajam mokslui. Į opalą infiltravę skystąjį kristalą, gauname hibridinį fotoninį kristalą. Jo optines savybes galima keisti priklausomai nuo infiltruotos medžiagos lūžio rodiklio. Fotoniniai kristalai, reikia tikėtis, bus taikomi ateities fotoniniuose įrenginiuose, telekomunikacijoje. Su šia sritimi siejamos tokios pat ar net didesnės viltys, kokios buvo siejamos su prieš 50 metų išrastu puslaidininkiniu tranzistoriumi, pakeitusiu techniką ir davusiu impulsą naujoms mokslo kryptims. Teoriškai fotoninių kristalų egzistavimą nepriklausomai vienas nuo kito 1987 metais pirmieji aprašė E.Jablonovičius ir S. Johnas. Tačiau prireikė dar dešimt metų, kol buvo... [toliau žr. visą tekstą] / We live in the rapidly developing technological world. However, fields of communication, computer memory, and data processing require considerable improvements. The speed of data transportation is acceptable but capacity is low. There is a growing need for new technologies that rapidly detect and treat diseases at an early stage or even pre-stage. When we get accustomed to the advance, we demand more compact, energy-efficient, rapidly-responding and environmentally-safe technologies. During the last century this problem was solved by switching to transportation of electronic data, which connected people around the world. This approach had changed our lives, but about twenty years ago this technology reached its limits, while need for an even higher transportation capacity increases. Now we need faster computers and other state-of-the-art technological solutions: electrons are too slow and we have to use photons. Over the last decade, the steady progress regarding ability to fabricate hybrid photonic nanostructures led to a rich variety of different one-, two-, and three-dimensional dielectric/organic and/or metallic periodic structures. They demonstrate qualitatively new and fascinating linear-optical, nonlinear-optical, and quantum-optical features which provide an unprecedented control of light propagation and light-matter interaction. Photonic-based technology, coupled with nanotechnology, can meet many of these challenges. In this work fabrication of hybrid photonic... [to full text]

The byproducts of human engineered energy production are increasing atmospheric CO2 concentrations well above their natural levels and accompanied continual decline in the natural reserves of fossil fuels, necessitates the development of green energy alternatives. Solar energy is attractive because it is abundant, can be produced in remote locations and consumed on site. Specifically, thin-film silicon-based photovoltaic (PV) solar cells have numerous inherent advantages including their availability, non-toxicity, and they are relatively inexpensive. However, their low-cost and electrical performance depends on reducing their thickness to as great an extent as possible. This is problematic because their thickness is much less than their absorption length. Consequently, enhanced light trapping schemes must be incorporated into these devices. Herein, a transparent and conducting photonic crystal (PC) intermediate reflector (IR), integrated into the rear side of the cell and serving the dual function as a back-reflector and a spectral splitter, is identified as a promising method of boosting the performance of thin-film silicon-based PV. To this end a novel class of PCs, namely selectively transparent and conducting photonic crystals (STCPC), is invented. These STCPCs are a significant advance over existing 1D PCs because they combine intense wavelength selective broadband reflectance with the transmissive and conductive properties of sputtered ITO. For example, STCPCs are made to exhibit Bragg-reflectance peaks in the visible spectrum of 95% reflectivity and have a full width at half maximum that is greater than 200nm. At the same time, the average transmittance of these STCPCs is greater than 80% over the visible spectrum that is outside their stop-gap. Using wave-optics analysis, it is shown that STCPC intermediate reflectors increase the current generated in micromorph cells by 18%. In comparison, the more conventional IR comprised of a single homogeneous transparent conducting oxide film increases the current generated in the same cell by just 8%. Moreover, the benefit of using STCPC IRs in building integrated photovoltaics is also presented.

This work describes the functionalization and testing of Si$_3$N$_4$-based photonic crystal slabs (PCS) for label-free biosensing. PCS support optical resonance modes that are sensitive to the local refractive index. Knowing that surface binding events change the local RI, analyte binding to the activated sensor can be detected. Various functionalization recipes were tried, and one was preferred for the biosensing experiments due to its higher yield and uniformity. Additionally, thickness of the topmost sensor layer was studied to assess biosensor performance quantified through sensitivity metrics. On the systems level, a reusable clamping system and customized microfluidic channels were designed, fabricated, and implemented on the PCS biosensors to enable device refurbishment. Proof-of-principle biodetection experiments were carried out using the established functionalization protocol on the in-house fabricated PCS. Conjugation of streptavidin and bovine serum albumin to the sensor surface was observed through wavelength shifts of the resonant modes.

The byproducts of human engineered energy production are increasing atmospheric CO2 concentrations well above their natural levels and accompanied continual decline in the natural reserves of fossil fuels, necessitates the development of green energy alternatives. Solar energy is attractive because it is abundant, can be produced in remote locations and consumed on site. Specifically, thin-film silicon-based photovoltaic (PV) solar cells have numerous inherent advantages including their availability, non-toxicity, and they are relatively inexpensive. However, their low-cost and electrical performance depends on reducing their thickness to as great an extent as possible. This is problematic because their thickness is much less than their absorption length. Consequently, enhanced light trapping schemes must be incorporated into these devices. Herein, a transparent and conducting photonic crystal (PC) intermediate reflector (IR), integrated into the rear side of the cell and serving the dual function as a back-reflector and a spectral splitter, is identified as a promising method of boosting the performance of thin-film silicon-based PV. To this end a novel class of PCs, namely selectively transparent and conducting photonic crystals (STCPC), is invented. These STCPCs are a significant advance over existing 1D PCs because they combine intense wavelength selective broadband reflectance with the transmissive and conductive properties of sputtered ITO. For example, STCPCs are made to exhibit Bragg-reflectance peaks in the visible spectrum of 95% reflectivity and have a full width at half maximum that is greater than 200nm. At the same time, the average transmittance of these STCPCs is greater than 80% over the visible spectrum that is outside their stop-gap. Using wave-optics analysis, it is shown that STCPC intermediate reflectors increase the current generated in micromorph cells by 18%. In comparison, the more conventional IR comprised of a single homogeneous transparent conducting oxide film increases the current generated in the same cell by just 8%. Moreover, the benefit of using STCPC IRs in building integrated photovoltaics is also presented.

This work describes the functionalization and testing of Si$_3$N$_4$-based photonic crystal slabs (PCS) for label-free biosensing. PCS support optical resonance modes that are sensitive to the local refractive index. Knowing that surface binding events change the local RI, analyte binding to the activated sensor can be detected. Various functionalization recipes were tried, and one was preferred for the biosensing experiments due to its higher yield and uniformity. Additionally, thickness of the topmost sensor layer was studied to assess biosensor performance quantified through sensitivity metrics. On the systems level, a reusable clamping system and customized microfluidic channels were designed, fabricated, and implemented on the PCS biosensors to enable device refurbishment. Proof-of-principle biodetection experiments were carried out using the established functionalization protocol on the in-house fabricated PCS. Conjugation of streptavidin and bovine serum albumin to the sensor surface was observed through wavelength shifts of the resonant modes.

My research on the new concepts for spectrometer has been focused on the development of true multi-dimensional spectrometers, which use a multi-dimensional [two-dimensional (2D) or 3D] mapping of the spectral information into space. I showed that by combining a simple dispersive element (a volume hologram) formed in very inexpensive polymers with a basic Fabry-Perot interferometer, we can form a spectrometer with ultra-high resolution over a large spectral bandwidth, which surpasses all conventional spectrometers. I strongly believe that the extension of this mapping into three dimensions by using synthetic nanophotonic structures with engineered dispersion can further improve the performance and reduce the overall spectrometer size into the micron regime. The need for efficient modeling and simulation tools comes from the sophisticated nature of the new 3D nanophotonic structures, which makes their simple analysis using well-known simple formulas for the propagation of the electromagnetic fields in bulk materials impossible. In my Ph.D. research, I developed new approximate modeling tools for both the modeling of incoherent sources in nanophotonics, and for the propagation of such optical beams inside the 3D nanophotonic structures of interest with several orders of magnitude improvement in the simulation speed for practical size devices without sacrificing accuracy. To enable new dispersive properties using a single nanophotonic structure, I have focused in my Ph.D. research into polymer-based 3D photonic crystals, which can be engineered using their geometrical features to demonstrate unique dispersive properties in three dimensions that cannot be matched by any bulk material even with orders of magnitude larger sizes. I have demonstrated the possibilities of using a very compact structure for wavelength demultiplexing and also for spectroscopy without adding any other device.

The present thesis is devoted to theoretical studies of pulse propagation of light through linear and nonlinear media, and of light-induced nuclear dynamics. The first part of the thesis addresses propagation of light pulses in linear periodical media - photonic crystals. The main accent was put on studies of the angular properties of two qualitatively different types of photonic crystals: holographic photonic crystals, and impurity band based photonic crystals. The anisotropy of band structure, group velocity and pulse delay with respect to the light polarization are analyzed. In the second part of the thesis a strict theory of nonlinear propagation of a few strong interacting light beams is presented. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material. This technique is applied to studies of dynamics of cavityless lasing generated by ultra-fast multi-photon excitation. It is shown that interaction of co- and counter-propagating pulses of amplified spontaneous emission (ASE) affects the dynamics and efficiency of nonlinear conversion. Our dynamical theory allows to explain the asymmetric spectral properties of the forward and backward ASE pulses, which were observed in recent experiment with different dye molecules. It is shown that the ASE spectral profile changes drastically when the pump intensity approaches the threshold level. The effect of the temporal self-pulsation of ASE is studied in detail. The third part of the thesis is devoted to light-induced nuclear dynamics. Time- and frequency-resolved X-ray spectroscopy of molecules driven by strong and coherent infrared (IR) pulses shows that the phase of the IR field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. Such a dependence arises due to the interference of one (X-ray) and two-photon (X-ray + IR) excitation channels. The phase of the light influences the dynamics also when the Rabi frequency approaches the vibrational frequency, breaking down the rotating-wave approximation. The probe X-ray spectra are also sensitive to the delay time, the duration, and the shape of the pulses. The evolution of the nuclear wave packets in the dissociative core-excited state affects the dynamics of resonant Auger scattering from fixed-in-space molecules. One of the important dynamical effects is the atomic-like resonance which experiences electronic Doppler shift. We predict that the scattering of the Auger electrons by nearby atoms leads to new Doppler shifted resonances. These extra resonances show sharp maxima in the bond directions, which makes them very promising as probes for local molecular structure using energy and angular resolved electron-ion coincidence techniques. Our theory provides prediction of several new effects, but also results that are in good agreement with the available experimental data. / QC 20100906

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.