Two unique phenomena in photonic crystals are presented. One is the Purcell effect, which essentially enhances the spontaneous emission rate. The other is the slow light which is flexibly controlled by the photonic band engineering.
We consider the one-dimensional problem of imperfections' influence on the Purcell effect in photonic crystal system. We demonstrate that the presence of disorder in a one-dimensional photonic crystal can lead to a modification of the spontaneous emission rate in the photonic band gap (PBG) frequency region. We show that the amount of disorder regulates two different scenarios of the Purcell effect modification. In the case of weak disorder, the Purcell enhancement of the spontaneous emission occurs at PBG edges, and, in the case of strong disorder, it occurs at PBG centre.
Was provided statistical analysis of Purcell effect dependence on emission frequency and emitter position in disordered structure. Fact that the presence of disorder in one-dimensional photonic crystals could lead to a modification of spontaneous emission rate in the frequency region corresponding to a photonic band gap (PBG) was demonstrated. Was shown, that amount of disorder regulates the two different regimes of the Purcell effect. In case of weak disorder Purcell enhancement of spontaneous emission occurs at PBG edges, and in case of strong disorder at PBG centre.
Photonic crystals are optical materials that have an intricate structure with length scales of the order of the wavelength of light. The flow of photons is controlled in a manner analogous to how electrons propagate through semiconductor crystals, i.e., by Bragg diffraction and the formation of band structures. If the interaction between light and matter is made strong, multiple diffraction and multiple scattering effects dominate. A main research goal is the realization of a "photonic band gap", that is, a frequency range for which no light can propagate in a crystal in any direction, which causes radical modifications of the density of radiative states. Important consequences of photonic band gaps are the complete control over spontaneous and stimulated emission of light, as well as over the propagation of light, in particular photon localization. This opens up the possibility to achieve a "cage for light": trap photons and do with them whatever one chooses. In this talk we will also review means for making such structures, and recent experimental advances in optical experiments.
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.
Spontaneous emission is one of the most fundamental out-of-equilibrium processes in which an excited quantum emitter relaxes to the ground state due to quantum fluctuations. In this process, a photon is emitted that can interact with other nearby emitters and establish quantum correlations between them, e.g., via super and subradiance effects. One way to modify these photon-mediated interactions is to alter the dipole radiation patterns of the emitter, e.g., by placing photonic crystals near them. One recent example is the generation of strong directional emission patterns - key to enhancing super and subradiance effects - in two dimensions by employing photonic crystals with band structures characterized by linear isofrequency contours and saddle points. However, these studies have predominantly used oversimplified toy models, overlooking the electromagnetic field's intricacies in actual materials, including aspects like geometrical dependencies, emitter positions, and polarization. Our study delves into the interaction between these directional emission patterns and the variables mentioned above, revealing the untapped potential to fine-tune collective quantum optical phenomena.