In this thesis I consider tuning of the optical response of a one-dimensional\nphotonic crystal. The optical response is represented by (a) re\nectance and\n(b) spontaneous emission. In both cases the photonic crystal is constituted\nfrom alternating silicon (Si) and silica (SiO2) layers. The density of free\ncarriers in the Si layers is modulated at a level of 1019=cm3, the wavelength\nof light being xed at 1:54m.\n(a) I calculate the tuning of re\nectance of a one-dimensional photonic\ncrystal (PC) by means of charge injection. The PC is constituted from highly\ndoped Si layers alternating with SiO2 layers. The wavelength of the light is\nassumed to be the important communications wavelength of 1:54m. A\nrealistic calculation shows that sensitive tuning, and switching as well, can\nbe achieved for an impurity density 1019=cm3 even for superlattices (SLs)\nonly a few periods long. The re\nectance results are satisfactorily interpreted\nin terms of photonic band (PB) structure calculations.\n(b) If the modal density available to an excited atom is varied on the time\nscale of its lifetime, then we can expect the natural process of spontaneous\nemission (SE) to become dynamically manipulable. I consider various experimental\npossibilities and focus on an atom embedded in a PC designed to\nhave a band edge in the vicinity of the frequency of the emitted light. Specifically,\nI calculate the rate of SE by erbium ions (radiating at the wavelength\n1:54m) implanted in a one-dimensional Si/SiO2 PC. The semiconductor\nlayers are assumed to be strongly doped; by tuning the impurity density the\nfree carrier concentration changes and the PBs shift. As a result, the SE rate\nexhibits signicant dependency on the level of charge injection. The body of\nthe thesis consists of two papers, corresponding to (a) and (b) above.\nOne of these has been already accepted for publication, while the other\nhas been submitted for publication. Their preprints are enclosed at the end\nof the thesis.
In this thesis I consider tuning of the optical response of a one-dimensional\nphotonic crystal. The optical response is represented by (a) re\nectance and\n(b) spontaneous emission. In both cases the photonic crystal is constituted\nfrom alternating silicon (Si) and silica (SiO2) layers. The density of free\ncarriers in the Si layers is modulated at a level of 1019=cm3, the wavelength\nof light being xed at 1:54m.\n(a) I calculate the tuning of re\nectance of a one-dimensional photonic\ncrystal (PC) by means of charge injection. The PC is constituted from highly\ndoped Si layers alternating with SiO2 layers. The wavelength of the light is\nassumed to be the important communications wavelength of 1:54m. A\nrealistic calculation shows that sensitive tuning, and switching as well, can\nbe achieved for an impurity density 1019=cm3 even for superlattices (SLs)\nonly a few periods long. The re\nectance results are satisfactorily interpreted\nin terms of photonic band (PB) structure calculations.\n(b) If the modal density available to an excited atom is varied on the time\nscale of its lifetime, then we can expect the natural process of spontaneous\nemission (SE) to become dynamically manipulable. I consider various experimental\npossibilities and focus on an atom embedded in a PC designed to\nhave a band edge in the vicinity of the frequency of the emitted light. Specifically,\nI calculate the rate of SE by erbium ions (radiating at the wavelength\n1:54m) implanted in a one-dimensional Si/SiO2 PC. The semiconductor\nlayers are assumed to be strongly doped; by tuning the impurity density the\nfree carrier concentration changes and the PBs shift. As a result, the SE rate\nexhibits signicant dependency on the level of charge injection. The body of\nthe thesis consists of two papers, corresponding to (a) and (b) above.\nOne of these has been already accepted for publication, while the other\nhas been submitted for publication. Their preprints are enclosed at the end\nof the thesis.
Photonic crystals, i.e. materials that have a periodic variation in refractive index, form an interesting new class of materials that can be used to modify spontaneous emission and manipulate optical modes in ways that were impossible so far. This thesis is divided in three parts. \nPart I discusses the design and fabrication of two-dimensional photonic crystals in silicon using deep anisotropic etching with a SF6/O2 plasma. The etching process was optimized for the fabrication of two-dimensional photonic crystals by tuning the main parameters of the etching process, i.e. temperature, bias voltage and O2 flow. Vertical confinement in these structures is provided by integrating the structures in a dielectric waveguide. For this purpose, amorphous silicon, silicon-on-insulator and SiGe structures were considered. Fabrication of structures in both amorphous silicon and silicon-on-insulator was successfully demonstrated. The incorporation of luminescent species, such as laser dyes, was demonstrated using a new wet chemical coating technique that forms thin silica layers on a substrate.\nPart II discusses the modification of spontaneous emission in one dimensional systems by studying the decay rate of luminescing Cr ions close to a dielectric interface. The decay rate of the Cr ions can be changed by bringing the samples into contact with a range of liquids with different refractive indices. The change in radiative decay rate can be calculated by calculating the local density of states. To explain the experimental results additional non-radiative decay channels have to be introduced and yields a quantum efficiency of ~50% for the Cr R-line luminescence. This concept was further extended to a thin silica layer on silicon implanted with erbium ions and resulted in the radiative rate of erbium in pure silica: 54 s-1. This number was used to analyze the decay rate of erbium ions in silica colloidal spheres that can be used as building block for three-dimensional photonic crystals by self-assembly.\nFinally, Part III discusses the optical properties and modified spontaneous emission from a three-dimensional silicon photonic crystal of finite (5-layers) thickness. The crystals are made in a layer-by-layer approach using lithographic tools and show near 100% reflection in the 1.4-1.7 mu m wavelength range indicative of a photonic stopgap. A direct comparison with the calculated reflectivity reveals that some features in the reflectivity can be ascribed to the finite thickness of the crystal, while other features can be explained in terms of a superstructure that leads to zone folding of the photonic bandstructure. The collected spontaneous emission from erbium implanted crystals is strongly reduced for wavelengths in the stopgap from 1.4-1.7 mu m. The changes in collected luminescence intensity are explained in terms of a rate equation model that takes into account the effect of Bragg scattering, the local density of states and the quantum efficiency of the emitters inside the crystal. Using this model a spectral attenuation of 5 dB per unit cell at 1.539 mu m wavelength is obtained from the experimental data, which is in perfect agreement with existing theory and transmission data.
Chapter 1 IntroductionUltimate inhibition of spontaneous emission can be achieved in artificial periodic structures with tailor-made forbidden frequency bands [5].These periodic structures known as photonic crystals consist of different dielectric materials, where the index of refraction varies on length scales comparable to the wavelength of light.Therefore, the periodicity of photonic crystals is about 1000 times as large as that of atomic crystals.Light with specific frequencies is forbidden to propagate along certain directions by wave interference, similarly to Bragg diffraction of x-rays in atomic crystals.Such forbidden frequency ranges are called stopgaps.The larger the contrast of the refractive index between the two materials of a photonic crystal, the more strongly light is influenced, and the broader the stopgaps become.It was predicted in 1987 that an extreme situation may be feasible when light cannot propagate along any direction [6, 7].This situation is called a photonic bandgap.Spontaneous emission is completely inhibited for frequencies inside such a bandgap and, conversely, strongly enhanced for frequencies outside the bandgap.Photonic crystals, therefore, provide an ultimate tool for manipulating with light, which is of extreme interest for scientists and engineers [8, 9].Recent advances in nanotechnology have resulted in ability to synthesize semiconductor structures with dimensions of a few nanometers.Due to the finite sizes, electron-hole pairs (excitons) can be confined in these nanostructures, which leads to discrete excitonic energy levels.The nanocrystals that confine excitons in spherical or circular spaces are known as quantum dots.The discrete structure of the energy levels results in advantageous optical properties of these nanocrystals: narrow and tunable emission spectra.The emission frequencies can be tuned by varying the nanocrystal size: the smaller the size, the higher the emission frequency.These properties make the nanocrystals very promising elementary emitters for new experiments and devices [10, 11]. Outline of the thesisThis thesis describes time-and angle-resolved experiments, in which effects of threedimensional (3D) photonic crystals on spontaneous emission of embedded light sources (quantum dots and dye molecules) were studied.The thesis is organized as follows:In Chapter 2 we review the theoretical basics of the interaction between light and matter.We discuss the factors triggering the process of spontaneous emission and consider in detail the time evolution of the excited state of the emitter that interacts with the quantized 1.
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
Erbium is a rare-earth metal that, when incorporated in a solid, can emit light at a wavelength of 1.5 μm. It plays a key role in current day telecommunication technology as the principle ingredient of optical fiber amplifiers. In this thesis the control of the Er spontaneous emission in three different types of microphotonic materials is described. Part I of this thesis focuses on the effect of a metallo-dielectric interface on the spontaneous emission of optical emitters in silica glass. It is shown that Er ions near a Ag interface can couple to surface plasmons (SPs) via a near-field interaction. By coupling SPs out into the far field, large changes in the Er photoluminescence emission distribution, spectra, and polarization can be observed. The excitation of SPs also results in an increase of the Er photoluminescence decay rate. The observed decay rates are in good agreement with calculations based on a classical dipole oscillator model. From the change in photoluminescence decay rate of Si nanocrystals near a Ag interface it is shown that Si nanocrystals can efficiently excite SPs and have an internal quantum efficiency of 77 %. Part II focuses on the effect of a microcavity on the spontaneous emission of Er and describes how ion implantation can be used to dope dielectric microresonators with optically active Er ions. The fabrication and characterization of an Er ion-implanted silica microsphere resonator is described that shows lasing at 1.5 μm when pumped above its lasing threshold. Ion implantation is also used to dope toroidal microcavities on a Si chip with Er. The microtoroids are doped by either pre-implantation into the SiO2 base material, or by post-implantation in a fully fabricated microtoroid. The optical activation of Er ions in the microtoroid is investigated and Er lasing at 1.5 μm is observed for both types of microcavities with the lowest threshold (4.5 μW) for the pre-implanted microtoroids. Part III describes the fabrication of an Er-doped Si-inverse opal photonic crystal. These photonic crystals can potentially have a photonic bandgap that can fully inhibit the spontaneous emission of on optical emitter. Fabrication criteria are derived for such a photonic crystal, based on the lattice parameter, filling fraction, and Si refractive index. In the opal photonic crystal composed of both Si and SiO2 we show that Er ions can be selectively excited in both the Si and SiO2 part of the photonic crystal by changing the excitation wavelength and/or the measurement temperature.
In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.
The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.