Electromagnetic (EM) structures are crucial for high-speed communications and radar systems. Enhancing the performance of such components sometimes is a game changer for some applications that require unique features such as ultra-high sensitivity to perturbations, high output power, precise oscillation frequency, or high-power conversion efficiency. The performance of EM components is often limited by the regime of operation. This dissertation focuses on a new class of EM devices, whose architecture relies on dispersion engineering principles exploiting the so-called exceptional points of degeneracy (EPD) operational condition. The use of EPD regime allows to push the boundaries of the performance for some devices such as, for example, millimeter and terahertz frequencies high-power sources. EPD is a singularity point at which two or more spectral components of the EM field spatial distribution coalesce. In this dissertation, the degeneracy conditions in microwave, optical and electron beam devices are investigated where the remarkable physical properties of such devices, operating at the EPD regime, are studied. We have discovered an EPD that is induced in a system made of a linear electron beam interacting with an electromagnetic guided mode in a vacuum tube. This enables a degenerate synchronous regime in backward wave oscillators (BWOs) where power is extracted in distrusted fashion rather than at the end of the structure. The proposed concept is applied to BWOs operating at X-band and millimeter wave frequencies. We demonstrate using particle in cell simulations (PIC) that EPD-BWOs have much higher output power and power conversion efficiency compared to standard BWOs. Finally, we propose a method that finds the eigenmodes in the interactive system of a travelling-wave tube (TWT). The proposed solver is based on accurate PIC simulations of finite length hot structure. The determination of wavenumbers and eigenvectors of the hot modes supported in a TWTs is useful to study hot-mode degeneracy conditions in hot slow wave structure. Furthermore, the proposed method is applied to study electron beams in tunnels with complicated geometries, with the goal of estimating the reduced plasma frequency and understanding the degeneracy conditions.