A new theory for the low coherence laser amplification in rare ions doped glass has been proposed. Based on one-dimensional continuous energy level assumption and independent response assumption, the theory can describe the amplification of low coherence laser pulses with any time scale and any bandwidth. By the new theory, McCumber formula can be obtained, and a complete low coherence optical pulse amplification model in neodymium glass is established. Computation shows that at high fluences, inhomogeneous broadening will severely limit energy extraction of narrowband high coherence laser, therefore the extraction of broadband low coherence laser will exceed that of narrowband high coherence laser. In addition, the portion of long-wave of the output spectrum is slightly larger than that predicted by the homogeneous model. The new theory could be beneficial for the studies of low coherence pulse amplification in rare earth doped medium and other laser mediums.
A new theory for the low coherence laser amplification in rare ions doped glass has been proposed. Based on one-dimensional continuous energy level assumption and independent response assumption, the theory can describe the amplification of low coherence laser pulses with any time scale and any bandwidth. By the new theory, McCumber formula can be obtained, and a complete low coherence optical pulse amplification model in neodymium glass is established. Computation shows that at high fluences, inhomogeneous broadening will severely limit energy extraction of narrowband high coherence laser, therefore the extraction of broadband low coherence laser will exceed that of narrowband high coherence laser. In addition, the portion of long-wave of the output spectrum is slightly larger than that predicted by the homogeneous model. The new theory could be beneficial for the studies of low coherence pulse amplification in rare earth doped medium and other laser mediums.
The relation between absorption and emission spectra in a rare-earth doped solid is explored analytically and through numerical simulations on a model system. It is found that the widely used theory of McCumber [D. E. McCumber, Phys. Rev. 136, A954 (1964)] is strictly valid only when the linewidth of each individual transition between Stark levels is ≪kBT. When this assumption is relaxed, deviations between actual simulated spectra and McCumber-calculated spectra are found for both homogeneous and inhomogeneous broadening. The McCumber transform introduces a characteristic distortion of each component transition, in which the low-energy side of the spectrum is increased, and the high-energy side is decreased. The average degree of distortion for the model system is calculated to be 5% for a homogeneous width of 50 cm−1 at room temperature, but only 1% for a purely inhomogeneous width of 50 cm−1. For both homogeneous and inhomogeneous spectra, the distortion varies with the linewidth Δν as (Δν)3/2. The dependence of the distortion on temperature is different for the two types of line shapes, however: ∼T2 for homogeneous and ∼T−1 for inhomogeneous broadening. For most rare-earth doped glasses and crystals at room temperature, the average degree of distortion is expected to be on the order of 5% or less, although the actual discrepancy in the spectral wings can be much larger. The effects described here are likely to be of importance when using McCumber’s theory to obtain accurate cross section values in the spectral wings of rare-earth transitions.
When doped into solid state transparent crystals, rare-earth ions can have optically excited states with milliseconds coherence time and up to six hours coherence time for hyperfine levels after being cooled down to liquid helium temperature. This long coherence property makes them unique as solid state material and attractive for quantum information applications.The rare-earth ions have narrow homogeneous linewidths on the order of ~ kHz. When doped into a crystal, the lattice structure is slightly distorted due to the size mismatch between the dopant and the host ions, resulting in slight differences in the local crystal fields at the dopant sites. Therefore, the resonance frequencies of the rare-earth ions are shifted relatively, resulting in an inhomogeneously broadened absorption profile, typically on the order of a few GHz. This provides the possibility of addressing each group of ions individually and engineering the absorption profile for different purposes by optical pumping using a narrow linewidth laser, and makes rare-earth-ion-doped crystals suitable for ensemble based quantum memories.Quantum memories are vital components for developing longdistance quantum communication. Part of this thesis project focused on making quantum memories with high efficiency and long storage time, especially using materials with low optical depth. To achieve this goal, a low finesse, unsymmetrical cavity was employed and experiments were carried out at (or close to) the impedance matched condition. Atomic frequency comb (AFC) protocol proposed for such an inhomogeneously broadened system was used to store coherent light for a certain time. 56% overall efficiency was achieved, and the main limiting factor for reaching even higher efficiency was the inefficient coupling between incoming light and the cavity mode. Other possible loss mechanisms were analyzed as well.Long-time, on-demand, quantum memory experiments were conducted with the help of two efficient radio-frequency rephasing pulses. Storage time was extended from microseconds to milliseconds after compensating (most of) the residual earth magnetic field in the lab. The opportunities and challenges of combing the cavity assistant quantum memory and the long time, on demand quantum memory were analyzed and possible solutions were proposed. Another part of the thesis project involves slow light-based applications in rare-earth-ion-doped crystals. The strong slow light effect at the presence a spectral hole is due to the fact that the light interacts with the absorbing ions outside the spectral hole off-resonantly, and most of the light energy is stored inside the ions as a polarization. For example, with a group velocity of 300 km/s, 99.9% of the pulse energy is stored in the ions when the pulse propagates inside the crystal. The slower the light propagates, the more energy is stored inside the medium. Based on this, a frequency shifter that is capable of shifting the light frequency of ± 4 MHz was demonstrated, and frequency shift up to GHz was proposed. Group velocity control by a factor of 20 and pulse compression in time by a factor of 2 were also demonstrated. The frequency shift and group velocity of the light are solely controlled by the external electric field, which makes them ideal for weak light situation. The unique property of such a frequency shifter and group velocity controller is that they could be made to accept light from an arbitrary incoming angle and polarization, for example, scattered light.
We investigate the intensity and efficiency of a compressed echo, which is important in arbitrary waveform generation (AWG). A new model of compressed echo is proposed based on the optical Bloch equations, which exposes much more detailed parameters than the conventional model, such as the time delay of the chirp lasers, the nature of the rare-earth-ion-doped crystal, etc. According to the novel model of compressed echo, we find that reducing the time delay of the chirp lasers and scanning the lasers around the center frequency of the inhomogeneously broadened spectrum, while utilizing a crystal with larger coherence time and excitation lifetime can improve the compressed echo's intensity and efficiency. The theoretical analysis is validated by numerical simulations.
Solids containing rare earth (RE) ions have attracted spectroscopists' attention since the beginning of this century.In the last 30 years, their extremely narrow spectral features in combination with the use of non linear spectroscopy have served to sensitively measure ion-solid interactions and to progressively observe narrower homogeneous linewidths.The potential for using RE ion doped crystals as optical storage materials and processors has lately been a driving force in their investigations, Here, the ratio of inhomogeneous to homogeneous linewidth is regarded as an adequate measure of storage density and can become as big as 10 7 at cryogenic temperatures.Therefore, the analysis of line broadening is of fundamental as well as applied interest.This work is concerned with the investigation of interactions of RE ions with their environment.By means of a laser with a kilohertz resolution and non-linear spectroscopy, spectral dynamics as a function of intrinsic, external electric field, or light-pulse induced perturbations are analyzed on different time scales.In the first part, the theoretical background for the spectroscopy of RE ion doped crystals is outlined.The energy levels are presented and it is shown that due to their electronic properties RE ions have spectrally narrow electronic transitions, sometimes in the sub-kHz regime.The investigations of these narrow spectral features on the seconds to minutes time scale require very stable tunable laser sources.At present, such devices are not commercially available.In the second part, the performance of ahorne built laser system is characterized using persistent spectral holes, The results show that frequency selective materials can be used as powerful tools for the high resolution Vlll Abstract spectral analysis of laser sources.Complementary to that, they give a measure for the long term evolution of the spectral holes for the particular hole burning substance.In the third part, the effect of an external electric field on RE ion doped crystals is investigated.It is shown that for these systems the electric field induced frequency shifts are fully reversible.A general theory of Stark splittings of RE doped crystals is introduced and two methods are presented which allow for the determination of the magnitude and orientation of the electric dipole moment differences with sub-degree accuracy.Finally in the last part, spectral line broadening mechanisms of RE ion doped crystals are discussed and investigated by means of two-pulse photon echoes.Through variation of the experimental parameters, a discrimination between the different contributions is partly achieved and characteristic properties for different dephasing mechanisms are presented.In combination with the measurements from the third part, quantitative predictions of the electric dipole-dipole induced broadening are carried out, which are compared to the experimental results,
We describe a general numerical method for calculating short-pulse laser propagation in rare-earth-doped materials, which are very important as gain materials for solid-state lasers, fiber lasers and optical amplifiers. The split-step, finite difference method simultaneously calculates changes in the laser pulse as it propagates through the material and calculates the dynamic populations of the rare-earth energy levels at any position within the material and for times during and after the laser pulse has passed through the material. Many traditional theoretical and numerical analyses of laser pulse propagation involve approximations and assumptions that limit their applicability to a narrow range of problems. Our numerical method, however, is more comprehensive and includes the processes of single- and multi-photon absorption, excited state absorption (ESA), energy transfer, upconversion, stimulated emission, cross relaxation, radiative relaxation and non-radiative relaxation. In the models, the rare-earth dopants can have an arbitrary number of energy levels. We are able to calculate the electron population density of every electronic level as a function of, for example, pulse energy, dopant concentration and sample thickness. We compare our theoretical results to published experimental results for rare-earth ions such as Er3+, Yb3+, Tm3+ and Ho3+.
We theoretically and experimentally demonstrate the quantum coherent control of the resonance-mediated two-photon absorption in rare-earth ions by the phase-shaped femtosecond laser pulse. Our theoretical results show that the resonance-mediated two-photon absorption can be effectively controlled, but the control efficiency depends on the laser repetition rate in real experiment due to the long lifetime and the short decoherence time of the excited state, and the larger laser repetition rate yields the lower control efficiency. These theoretical results are experimentally confirmed in glass sample doped with Er3+ by utilizing the femtosecond lasers with low repetition rate of 1 kHz and high repetition rate of 80 MHz.