High intensity lasers have a wide range of uses in basic science, industry, and national defense applications. To achieve the highest intensities, a laser must be focused to the smallest spot size possible. To achieve a small focus, the structure of the electromagnetic fields within a laser focus must be measured and optimized. In this project, the researchers place electrons within a very high intensity laser focus, and then study the light these electrons emit (nonlinear Thomson scattering) to understand the field structure within the focus. The patterns in the spatial structure and polarization of this nonlinear Thomson scattering contain information about the structure of the fields in a laser focus that is hard to measure in other ways. The researchers will study light emission patterns while varying focal properties of the laser and the distribution of electrons within the focus, with a goal of learning how to measure, understand, and improve the laser focus. These are very challenging measurements to make, and most previous work has been restricted to theoretical and computational predictions. The research project will involve and train approximately a dozen undergraduate students and three graduate students in the challenging blend of high-intensity laser methods used to drive the electrons and the single-photon detection methods used to measure the scattered light. The researchers will incorporate results from this project into a free online optics textbook that is widely used at the university level.<br/><br/>This project studies nonlinear Thomson scattering from very diffuse (near-vacuum density) free electrons in a laser focus and enables the study of this fundamental relativistic phenomenon without the confounding influence of plasma dynamics. These measurements will be carried out for several lower-order harmonics in a reference frame that allows the angular structure of the photoemission to be measured. The researchers will: (1) characterize for the first time the polarization-resolved angular emission patterns of individual harmonic orders over virtually the entire emission sphere, (2) investigate the signature of the ponderomotive ejection of electrons from the focus in the angular photoemission patterns and how this is influenced by focal parameters and pulse duration, and (3) study how coherence between electrons emitted from the same atom modifies nonlinear Thomson scattering, both the angular pattern and the strength. Each of these effects has the potential to contributes measurable amounts to the overall nonlinear Thomson scattering signal. Simulations of relativistic electron trajectories within a tight laser focus show that electron trajectories are sensitive to the details of the field vectors. An overarching goal is to be able to better correlate the vector fields of the laser focus with observed nonlinear Thomson scattering.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.