The history of resonance photonic crystals started with the pursuit for control over spontaneous decay in a photonic bandgap structure. Initiated by Bykov in optics, it was however implemented for the first time in the microwave domain by Yablonovitch et al. in 1991. This prediction of suppression of spontaneous emission of photons by a two-level atom turned into enhancement of optical nonlinearities, optical soliton generation and transport, and addressable light localization that is due to both structure and optically active defect created inside the crystal. This article reviews both fundamental theoretical ideas in the resonance photonic crystal with defect inside and selected experimental developments in the sense that reflects interests and expertise of the author.
The history of resonance photonic crystals started with the pursuit for control over spontaneous decay in a photonic bandgap structure. Initiated by Bykov in optics, it was however implemented for the first time in the microwave domain by Yablonovitch et al. in 1991. This prediction of suppression of spontaneous emission of photons by a two-level atom turned into enhancement of optical nonlinearities, optical soliton generation and transport, and addressable light localization that is due to both structure and optically active defect created inside the crystal. This article reviews both fundamental theoretical ideas in the resonance photonic crystal with defect inside and selected experimental developments in the sense that reflects interests and expertise of the author.
Optical phenomena in materials with a space modulation of dielectric constant at distances close to the light wavelengths (so called photonic band-gap structures or photonic crystals) are of a great interest now because of the existence of band gaps in their photonic band structure (Bykov, 1972; Yablonovitch, 1987; John, 1987). These band gaps represent frequency regions where electromagnetic waves are forbidden, irrespective of the spatial propagation directions. Inside the band gaps, the photon density of states is equal to zero and so the emission of light sources embedded in these crystals should be inhibited in these spectral regions (Vats et al., 2002). Since the time the effect is predicted, many experiments have been devoted to studies of spontaneous emission of molecules embedded in photonic crystals (Gaponenko et al., 1999; Gorelik, 2007). Typical structures of photonic crystals and calculations of corresponding photonic band structures are presented in a book by Prof. Joannopoulos (Joannopoulos et al., 2008). Besides the emission inhibition effect, a number of new optical phenomena in 3D photonic crystals, interesting from the applied point of view, are under intensive study now. The main research directions are the following: Effects of light localisation (John, 1987; Kaliteevskii et al., 2005; Vignolini et al., 2008). Radiation of photonic crystals filled with organic (rhodamine 6G, 1,8-naphthoylene1’,2’-benzimidazole, stilbene) and inorganic (ZnO, ZnS, rare-earth ions Eu3+, Tb3+, Er3+) luminophores near by the edges of photonic band-gap (Gaponenko et al., 1999; Aliev et al., 2002; Emel’chenko et al., 2005; Li et al., 2007). Radiation of CdTe, CdSe/ZnS quantum dots in photonic crystal volume (Gruzintsev et al., 2009; Ambrozevich et al., 2009). Quantum optics phenomena in nano-structured materials based on photonic crystals and nonlinear optical substances (Lin & Vuckovic, 2010). Effects of the radiation field amplification in photonic crystals (Lin & Vuckovic, 2010). Increase of solar cells efficiency with the use of photonic crystals (Florescu et al., 2007).
We demonstrate interesting and previously unforeseen properties of a pair of gap solitons in a resonant photonic crystal which can be predicted and explained in a physically transparent form using both analytical and numerical methods. The most important result is the fact that we are able to show that the oscillating gap soliton created by the presence of an inversion inside the crystal can be manipulated by means of a proper choice of bit rate, phase and amplitude modulation. Using this approach, we were able to obtain qualitatively different regimes of the resonant photonic crystal operation. A noticeable observation is that both the delay time and amplitude difference must exceed a certain level to ensure effective control over soliton dynamics. The modification of the defect that accomplishes the soliton trapping can make the dynamics of N soliton trains in the resonant photonic crystal with defects even more interesting and is a subject of the future work.
In the first part of this introductory review we outline the developments in photonic band gap materials from the physics of photonic band gap formation to the fabrication and potential applications of photonic crystals. We briefly describe the analogies between electron and photon localization, present a simple model of a band structure calculation and describe some of the techniques used for fabricating photonic crystals. Also some applications in the field of photonics and optical circuitry are briefly presented. In the second part, we discuss the consequences for the interaction between an atom and the light field when the former is embedded in photonic crystals of a specific type, exhibiting a specific form of a gap in the density of states. We first briefly review the standard treatment (Weisskopf – Wigner theory) in describing the dynamics of spontaneous emission in free space from first principles, and then proceed by explaining the alterations needed to properly treat the case of a two-level atom embedded in a photonic band gap material.
Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.
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.
Focus Serial: Frontiers of Nonlinear Optics Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.