Ultra-wideband (UWB) electronically scanned arrays (ESA) with high efficiency, excellent polarization agility, and wide-scan matching remain essential for servicing multifunctional RF front-ends and other communications, sensing, and jamming or countermeasure systems. To this day, the most popular antenna array element in modern UWB-ESA systems is the Vivaldi, or flared notch, due to its superior wide-scan wide impedance bandwidth, well-known design guidelines, and practical embodiment versatility. Despite their popularity, these arrays tend to radiate unacceptably high cross-polarization levels, thus encouraging a great research opportunity. This dissertation presents the theory and design of a new class of UWB-ESAs, termed Sliced Notch Antenna (SNA) arrays, that remedy the high cross-polarization problems in Vivaldi arrays while maintaining their desirable impedance performance. The critical enabling insight of this work lays in revealing the nature of polarization purity or cross-polarization ratio (CPR) degradation in Vivaldi arrays to arise from a highly imbalanced ratio of longitudinal and transverse currents within the element. This work introduces a novel design strategy that intrinsically balances these currents over a UWB operating band, achieving decade-order (10:1) bandwidths and low cross-polarization. Moreover, the design approach is simple, intuitive, and can be implemented in a manner that does not inflate cost expenditures. In fact, the proposed topology can facilitate significantly reduced costs and manufacturing times in Vivaldi arrays by permitting electrically disconnected elements over a large portion of the original Vivaldi fin. Following the presentation of the theoretical and operational principles, a few infinite SNA array design implementations are proposed that achieve decade-order bandwidths and low cross-polarization (e.g. active VSWR A single-polarized 19×19 SNA array and its Vivaldi counterpart are designed, fabricated, assembled, and measured to comparatively demonstrate similar wideband impedance behavior over a 1.2-12 GHz (10:1) operating range that covers near the entirety of four popular RF bands (L, S, C, and X); center embedded element impedance measurements show good agreement with finite array simulations out to θ=60° scans. The SNA array embedded element pattern offers better than 15 dB cross-polarization level improvements over the Vivaldi array out to wide angles in the D-plane. Active finite array scan simulations suggest both arrays closely track the directivity in the principal planes (e.g. less than 0.5 dB co-polarized gain drop at broadside), while the SNA array offers up to 25 dB improvements in co-polarized gain for non-principal plane scans in and around the D-plane with approximately 15 dB improvement on average over the Vivaldi array in the mid-band and high-band.