Morse Critical Points of Dispersion Equations of Open Resonators

Peculiarities of a waveguide-coaxial resonator on the TEM-oscillations with a resonance short-circuit plunger

“…От описанного эффекта полностью избавиться не удается, так как идеаль-но выполнить волновод и МДЭ практически не-возможно. Исследование подобного явления, по-лучившего название междутиповых колебаний, подробно проведено в [11].…”

Oscillations in Slotted Resonators with Several Slots: Application of Approximate Semi-Inversion

“…The insert shows the enlarged fragment containing the (extreme right) point of intersection of the µ (1) 11 (a 1 ) and µ (1) 20 (a 1 ) curves, the DP (λ * , a * ) ≈ (0.762, 4.126).…”

“…The function λ − F ν,µ (λ) can be reduced in the vicinity of P * to a canonical quadratic form [5] which exhibits a characteristic saddle-type behavior in the (λ, ξ)-plane (close to (λ * , a * )) corresponding to a typical case of interaction. The roots λ * ν were determined in the vicinity of λ ν = µ (1) 11 (N = M = 1, i 0 = 1) and λ ν = µ (1) 20 (N = 2, M = 0, i 0 = 1) which merge at a DP P * = (λ * , a * ) determined from (132) at n 1 = m 1 = 1 and n 2 = 2, m 2 = 0 (i = 1):…”

“…On the other hand, structures with inhomogeneities of very small relative dimensions cannot be efficiently analyzed using purely numerical approach because the characteristic size of the mesh becomes comparable with the diameter of inclusion(s); in addition, a numerical method undergoes a computational collapse in the vicinity of various critical points (CPs), in particular, eigenfrequencies of the cavities formed by partial domains and certain degeneration points (DPs), where the most interesting phenomena are often observed [1,2] that lead to restructuring of fields, etc. Among such phenomena, we note a resonance increase in the amplitude of the diffracted fields reported in [3] and [4] for a family of open slotted resonators with noncomact boundaries.…”

“…The field distributions may become unstable with respect to parameters of the structure (geometric, permittivity, etc.) and the intertype interaction of oscillations [1] takes place when a geometric parameter is varied in the vicinity of a DP, where one or several resonant frequencies (eigenfrequencies) of the 'partial' resonators coupled by the aperture(s) coincide [5,9]. Such DPs can be determined independently for each partial resonator (partial cross-sectional domain) and there are usually a few of them in the chosen frequency range.…”