Trajectory-based analyses of ultrafast strong field phenomena

Semiclassical theories have proven to be a versatile tool in ultrafast strong field science. In this thesis, the power of classical trajectory Monte Carlo (CTMC) and quantum trajectory Monte Carlo (QTMC) simulations is celebrated by applying them in various strong field ionization settings. One question to be addressed concerns the way nonadiabaticity in the ionization process manifests itself. It will be shown how the assumption of a vanishing initial longitudinal momentum is the reason for the strong broadening of the initial time spread claimed in a popular nonadiabatic theory. Moreover, it will become clear how the broader time spread of this theory and the non-zero initial longitudinal momenta of another widely applied nonadiabatic theory approximately compensate each other during propagation for typically studied nonadiabatic parameters. However, parameters in the nonadiabatic but still experimentally relevant regime will be found where this approximation breaks down and the two different theories lead to distinguishably different momentum distributions at the detector after all, thus allowing to test which theory describes the situation at the tunnel exit more accurately. After having tunneled through the barrier formed by the laser and Coulomb poten-tial, the electron does not necessarily leave the atom for good but can be captured in a Rydberg state. A study of the intensity-dependence of the Rydberg yield will reveal, among other things, nonadiabatic effects that can be used as an independent test of nonadiabaticity in strong field ionization. Moreover, it will be shown that the duration of the laser pulse can be used to control both the yield and principal quantum number distribution of Rydberg atoms. The highly enhanced and spatially inhomogeneous fields close to a nanostructure are another setting in which atoms can be ionized. Here, the emergence of a prominent higher energy structure (HES) in the spectrum of photoelectrons will be reported. The narrow time-window in which the corresponding electrons are released suggests a promising method for creating a localized source of electron pulses of attosecond duration using tabletop laser technology. Having such potential applications in mind, analytical expressions are derived to describe the electrons’ motion in the inhomogeneous field, thus being able to control the spectral position and width of the HES. Moreover, a unifying theory will be developed in which the recently reported experimental finding of a low-energy peak (LEP) can be understood to arise due to the same mechanism as the theoretically predicted HES, despite those two effects having been found in different energy regimes so far. This unifying theory will show how the well-established experimental technique in which the LEP was reported, i.e. ionization directly from the nanotip rather than from atoms in its vicinity, should allow the realization of a prominent and narrow peak at higher energies as it was theoretically described in the framework of the HES. Despite being much weaker, the spatial inhomogeneity of the Coulomb potential can influence the photoelectron spectrum as well. It will be shown how the asymmetric Coulomb potential of a tilted diatomic molecule introduces an asymmetry in the photoelectron momentum distribution at the detector. The degree of asymmetry depends on whether the electron is born at the up- or downfield atom. This information is then used to quantify the ratio of ionization from the up- and downfield site from experimental photoelectron momentum distributions

Trajectory-based analyses of ultrafast strong field phenomena

Semiclassical theories have proven to be a versatile tool in ultrafast strong field science. In this thesis, the power of classical trajectory Monte Carlo (CTMC) and quantum trajectory Monte Carlo (QTMC) simulations is celebrated by applying them in various strong field ionization settings. One question to be addressed concerns the way nonadiabaticity in the ionization process manifests itself. It will be shown how the assumption of a vanishing initial longitudinal momentum is the reason for the strong broadening of the initial time spread claimed in a popular nonadiabatic theory. Moreover, it will become clear how the broader time spread of this theory and the non-zero initial longitudinal momenta of another widely applied nonadiabatic theory approximately compensate each other during propagation for typically studied nonadiabatic parameters. However, parameters in the nonadiabatic but still experimentally relevant regime will be found where this approximation breaks down and the two different theories lead to distinguishably different momentum distributions at the detector after all, thus allowing to test which theory describes the situation at the tunnel exit more accurately. After having tunneled through the barrier formed by the laser and Coulomb poten-tial, the electron does not necessarily leave the atom for good but can be captured in a Rydberg state. A study of the intensity-dependence of the Rydberg yield will reveal, among other things, nonadiabatic effects that can be used as an independent test of nonadiabaticity in strong field ionization. Moreover, it will be shown that the duration of the laser pulse can be used to control both the yield and principal quantum number distribution of Rydberg atoms. The highly enhanced and spatially inhomogeneous fields close to a nanostructure are another setting in which atoms can be ionized. Here, the emergence of a prominent higher energy structure (HES) in the spectrum of photoelectrons will be reported. The narrow time-window in which the corresponding electrons are released suggests a promising method for creating a localized source of electron pulses of attosecond duration using tabletop laser technology. Having such potential applications in mind, analytical expressions are derived to describe the electrons’ motion in the inhomogeneous field, thus being able to control the spectral position and width of the HES. Moreover, a unifying theory will be developed in which the recently reported experimental finding of a low-energy peak (LEP) can be understood to arise due to the same mechanism as the theoretically predicted HES, despite those two effects having been found in different energy regimes so far. This unifying theory will show how the well-established experimental technique in which the LEP was reported, i.e. ionization directly from the nanotip rather than from atoms in its vicinity, should allow the realization of a prominent and narrow peak at higher energies as it was theoretically described in the framework of the HES. Despite being much weaker, the spatial inhomogeneity of the Coulomb potential can influence the photoelectron spectrum as well. It will be shown how the asymmetric Coulomb potential of a tilted diatomic molecule introduces an asymmetry in the photoelectron momentum distribution at the detector. The degree of asymmetry depends on whether the electron is born at the up- or downfield atom. This information is then used to quantify the ratio of ionization from the up- and downfield site from experimental photoelectron momentum distributions

Using Self-Study as a Process for Teacher Inquiry into Classroom Diversity

Educators in our region of the country likely agree that although there is growing diversity in our public schools in terms of culture, race, ethnicity, gender-identification, primary language and other aspects of diversity, the diversity of practicing and developing teachers has remained relatively unchanged. According to a national report, 82% of all undergraduate degrees in education across the country were awarded to white students in 2009-10, three-quarters of whom were women (AACTE, 2013). In our region of the upper midwest, the statistics are closer to 96% white and 73% female (North Dakota State University, 2017). Although as a teacher workforce, there may be little visible diversity in our state and region, we have found varied and innovative ways in which new and practicing teachers work to be culturally responsive teachers. One of the ways good teachers work to build cultural competencies in our region is by building their capactity for empathy for their students. By taking the time to inquire further into the needs of one student, seeking out additional resources, and engaging in critical dialogue about the results of their inquiry, teachers build awareness, understanding, and empathy for students. In this paper, we will describe a self-study approach to teacher inquiry used in a professional development project to build cultural competencies for teaching. We will share two cases from the resulting efforts of the practicing teachers who, like many of us, work hard to address the needs of their students who struggle to find success in school, in a number of ways. We will also share our methods for conducting a self-study of teaching practice, and conclude with our recommendations for ways to use self-study as an equitable practice for educators at all levels

Preservice Teachers’ Beliefs about Struggling Readers and Themselves

This descriptive case study examines preservice teachers’ beliefs about themselves as teachers of reading as they develop identities for teaching through experiences in a Foundations of Literacy course and their tutoring relationships with elementary students during an accompanying practicum. As the preservice teachers learned about foundational literacy development and assessment, they came to understand some students as “struggling readers,” although their beliefs were not always grounded in assessment results. Practicum experiences both challenged and reinforced their existing beliefs about struggling readers, as well as their own sense of self-efficacy in responding to struggling readers’ needs. Findings suggest that the types of student information preservice teachers attend to shape both productive and inaccurate beliefs about teaching students who struggle

The Learner Profiles of Novice Literacy Coaches

Literacy coaches need support developing their professional capacities for coaching (Kern et al., 2018). This study explored the ways novice literacy coaches developed literacy coaching discourses during coursework in two reading specialist master’s degree programs. Through qualitative and discourse analysis of transcribed coaching videos and assignments, novice literacy coaching discourse was compared to professional literacy coaching discourse. Findings revealed candidates used coaching language and stances with varying degrees of success, but the discourse of novice and professional differed greatly. Five learner profiles of novice literacy coaching are presented: the interviewer, the role-player, the curious learner, the cheerleader, and the natural novice. Implications on literacy coach preparation and research are discussed, including the use of the learner profiles as a pedagogical tool for online course delivery

Wannier-Bloch approach to localization in high harmonics generation in solids

Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission in solids. We apply this model to investigate HHG in a ZnO crystal for two different orientations, corresponding to wider and narrower valence and conduction bands, respectively. Interestingly, for narrower bands, the HHG process shows significant localization, similar to harmonic generation in atoms. For all cases, the delocalized contributions to HHG emission are highest near the band-gap energy. Our results pave the way to controlling localized contributions to HHG in a solid crystal, with hard to overestimate implications for the emerging area of atto-nanoscience

Extraction of higher-order nonlinear electronic response to strong field excitation in solids using high harmonic generation

State-of-the-art experiments employ strong ultrafast optical fields to study the nonlinear response of electrons in solids on an attosecond time-scale. Notably, a recent experiment retrieved a 3rd order nonlinear susceptibility by comparing the nonlinear response induced by a strong laser field to a linear response induced by the otherwise identical weak field. In parallel, experiments have demonstrated high harmonic generation (HHG) in solids, a highly nonlinear process that until recently had only been observed in gases. The highly nonlinear nature of HHG has the potential to extract even higher order nonlinear susceptibility terms, and thereby characterize the entire response of the electronic system to strong field excitation. However, up till now, such characterization has been elusive due to a lack of direct correspondence between high harmonics and nonlinear susceptibilities. Here, we demonstrate a regime where such correspondence can be clearly made, extracting nonlinear susceptibilities (7th, 9th, and 11th) from sapphire of the same order as the measured high harmonics. The extracted high order susceptibilities show angular-resolved periodicities arising from variation in the band structure with crystal orientation. Nonlinear susceptibilities are key to ultrafast lightwave driven optoelectronics, allowing petahertz scaling manipulation of the signal. Our results open a door to multi-channel signal processing, controlled by laser polarization

Developing reflective practice in teacher candidates through program coherence

In this study, we explored the role of reflection at three stages of preparation across a teacher education program. Reflection has long been considered an essential aspect of professional practice for teaching; however, reflection is often vague and undefined. Through an examination of the opportunities we provided for our students to reflect, and systematic analysis of the levels of reflection our students engaged in, we found that the development of reflective practices could be understood and aligned across a professional preparation program. Furthermore, we considered our own pedagogical practices related to modality, prompting, scaffolding, assignment structure, and feedback in our analysis of a variety of student reflection artifacts, in order to understand the potential impact of our own pedagogical decisions across the program. Findings suggest that the program provided modeling and structures for reflection early on, encouraged the inclusion of multiple perspectives in relation to professional practice, and supported a synthesis of student learning of theory and practice as preservice teachers approached program completion. This article offers reflection as a tool for exploring issues of professional growth across a continuum of development

Developing reflective practice in teacher candidates through program coherence

In this study, we explored the role of reflection at three stages of preparation across a teacher education program. Reflection has long been considered an essential aspect of professional practice for teaching; however, reflection is often vague and undefined. Through an examination of the opportunities we provided for our students to reflect, and systematic analysis of the levels of reflection our students engaged in, we found that the development of reflective practices could be understood and aligned across a professional preparation program. Furthermore, we considered our own pedagogical practices related to modality, prompting, scaffolding, assignment structure, and feedback in our analysis of a variety of student reflection artifacts, in order to understand the potential impact of our own pedagogical decisions across the program. Findings suggest that the program provided modeling and structures for reflection early on, encouraged the inclusion of multiple perspectives in relation to professional practice, and supported a synthesis of student learning of theory and practice as preservice teachers approached program completion. This article offers reflection as a tool for exploring issues of professional growth across a continuum of development