This award is made in response to Dear Colleague Letter 24-130, as part of the ECosystem for Leading Innovation in Plasma Science and Engineering (ECLIPSE) interdisciplinary program. Extreme ultraviolet (EUV) light is crucial for creating faster and smaller electronic devices, such as the microchips in smartphones and computers. By producing more focused and more powerful EUV beams with shorter wavelengths, this project can help make computer chips smaller and more efficient, enabling faster computing and improved digital technologies for everyday use. Additionally, better EUV imaging can lead to new breakthroughs in medicine, materials science, energy and environmental monitoring, benefiting society broadly by advancing technology and improving quality of life. In this project, advanced methods of generating extreme ultraviolet light are explored by using high-intensity laser beams interacting with dense plasma to produce extremely bright and tunable EUV radiation. This approach, known as relativistic high-order harmonic generation, surpasses current limitations of traditional EUV sources by significantly increasing conversion efficiency, reducing contamination from debris, and enhancing the beam's coherence and focusability. The work includes detailed studies on EUV generation efficiency, beam quality, and polarization control, aiming to revolutionize semiconductor manufacturing and high-resolution imaging techniques essential for boosting US competitiveness in the sem