The radiation dynamics of a magnetic dipole located inside a photonic crystal has been considered as an analogue for optical emission of a point-like emitter in such a crystal. We have experimentally realized this situation by fixing a single crystal yttrium iron garnet (YIG) sphere of 1.7 mm diameter inside a photonic crystal consisting of dielectric alumina rods. These rods form a woodpile structure of size 16 × 6 × 6 cm3 . The photonic crystal shows a band gap at microwave frequencies between 12.9 and 14.3 GHz as calculated and verified from the transmission characteristics of the crystal. The radiation feedback of the YIG sphere was probed by ferromagnetic resonance experiments covering a large frequency range from 8 to 17 GHz. Whereas outside the band gap the radiation-induced linewidth amounts up to 30 Oe, it is almost completely suppressed inside the gap. From the full analysis of linewidth and resonance shift, we could clearly prove the non-Markovian character of the radiation dynamics at the edges of the gap as expected from theory. The experimental control of spontaneous emission, as realized in our experiment, is a very promising step towards future optical applications in low threshold lasers, highly efficient light emitting diodes or photovoltaic solar modules.
The radiation dynamics of a magnetic dipole located inside a photonic crystal has been considered as an analogue for optical emission of a point-like emitter in such a crystal. We have experimentally realized this situation by fixing a single crystal yttrium iron garnet (YIG) sphere of 1.7 mm diameter inside a photonic crystal consisting of dielectric alumina rods. These rods form a woodpile structure of size 16 × 6 × 6 cm3 . The photonic crystal shows a band gap at microwave frequencies between 12.9 and 14.3 GHz as calculated and verified from the transmission characteristics of the crystal. The radiation feedback of the YIG sphere was probed by ferromagnetic resonance experiments covering a large frequency range from 8 to 17 GHz. Whereas outside the band gap the radiation-induced linewidth amounts up to 30 Oe, it is almost completely suppressed inside the gap. From the full analysis of linewidth and resonance shift, we could clearly prove the non-Markovian character of the radiation dynamics at the edges of the gap as expected from theory. The experimental control of spontaneous emission, as realized in our experiment, is a very promising step towards future optical applications in low threshold lasers, highly efficient light emitting diodes or photovoltaic solar modules.
The attempt to control spontaneous emission via modifications of the photonic environment using dielectric or plasmonic nanostructures has been a very active field of research for several decades. In particular the prospect of inhibiting fluorescence altogether by means of a photonic band gap has attracted great interest. In a recent paper, we have fully characterized the full non-Markovian radiation dynamics of a microwave spin system in a woodpile photonic crystal with a complete band gap near 14 GHz and found excellent agreement with ab-initio numerics. Here, we report on numerical details of this work.
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.
We study the control of spontaneous emission in a three-level V-type atom that is coupled by a static magnetic field in photonic crystals. We find that by changing the position of the upper band edge and Larmor frequency of the magnetic field, control of the steady-state behavior of spontaneous emission can be achieved. As the transition frequencies move from outside the band gap to inside, the structure of the spectral line changes from a two-peak structure to a single-peak structure, and then to a non-Lorentzian shape. With the increase of the Larmor frequency of the magnetic field, when both transition frequencies are outside the photonic band gap, the partial spectral line disappears; however, when both frequencies are inside the band gap, the non-Lorentzian shape is replaced by a Lorentzian shape. These phenomena arise from the fact that the corresponding transition frequency is pushed into or out of the band gap.
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.
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.
The fluorescence of emitters embedded in a photonic crystal is known to be inhibited by the presence of a photonic pseudo-gap acting in their emission range. Here we present a comparative study of the influence of the pseudo-gap on the fluorescence emission of either organic dyes or nanocrystals embedded within a photonic crystal. Our results clearly show that the optical properties of the emitters are primarily controlled by the presence of a pseudo-gap which causes inhibition of the emission in both cases, regardless of the differences in chemical composition. These findings are mainly attributed to a decrease of the number of available photonic modes for radiative decay of the emitter in a photonic crystal compared to the effective homogeneous medium. Furthermore, we show that a photonic crystal can be used to control the fluorescence energy transfer (FRET) between donor-acceptor (D-A) pairs of dyes. Finally, we show that the application of an external magnetic field can finely tune the emission characteristics of emitters with a permanent magnetic moment.