We propose a new approach leading to giant gain enhancement. It is based on unconventional slow wave resonance associated to a degenerate band edge (DBE) in the dispersion diagram for a special class of photonic crystals supporting two modes at each frequency. We show that the gain enhancement in a Fabry-Pérot cavity (FPC) when operating at the DBE is several orders of magnitude stronger when compared to a cavity of the same length made of a standard photonic crystal with a regular band edge (RBE). The giant gain condition is explained by a significant increase in the photon lifetime and in the local density of states. We have demonstrated the existence of DBE operated special cavities that provide for superior gain conditions for solid-state lasers, quantum cascade lasers, traveling wave tubes, and distributed solid state amplifiers. We also report the possibility to achieve low-threshold lasing in FPC with DBE compared to RBEbased lasers.

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An oscillator scheme based on the degenerate band edge (DBE) in a periodic, double-ladder resonant circuit made of lumped elements is proposed for the first time. The circuit exhibits a DBE in the dispersion diagram of its phase-frequency eigenstates and possesses unique resonance features associated with a high loaded Q-factor resonance, compared to a singleladder circuit. This oscillator is shown to have an oscillation threshold that is half that of a single LC ladder circuit having the same total quality factor, and thus is more robust than an LC oscillator in the presence of losses. Moreover, the double-ladder oscillators have a unique mode selection scheme that leads to stable single-frequency oscillations even when the load is varied. It is also shown that the output amplitude of the double-ladder oscillator is much less sensitive to the output loading compared to single-ladder oscillators. The authors show the analysis and design of such oscillators that potentially lead to enhancing the efficiency of RF components and sources.

Engineering of the eigenmode dispersion of slowwave structures (SWSs) to achieve desired modal characteristics, is an effective approach to enhance the performance of high power traveling wave tube (TWT) amplifiers or oscillators. We investigate here for the first time a new synchronization regime in TWTs based on SWSs operating near a third order degeneracy condition in their dispersion. This special three-eigenmode synchronization is associated with a stationary inflection point (SIP) that is manifested by the coalescence of three Floquet-Bloch eigenmodes in the SWS. We demonstrate the special features of "cold" (without electron beam) periodic SWSs with SIP modeled as coupled transmission lines (CTLs) and investigate resonances of SWSs of finite length. We also show that by tuning parameters of a periodic SWS one can achieve an SIP with nearly ideal flat dispersion relationship with zero group velocity or a slightly slanted one with a very small (positive or negative) group velocity leading to different operating schemes. When the SIP structure is synchronized with the electron beam potential benefits for amplification include (i) gain enhancement, (ii) gain-bandwidth product improvement, and (iii) higher power efficiency, when compared to conventional Pierce-like TWTs. The proposed theory paves the way for a new approach for potential improvements in gain, power efficiency and gain-bandwidth product in high power microwave amplifiers.I.

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