Waves in gradient transmission lines: Physical fundamentals, mathematical basis and the first experiments

Gradient transmission lines (TL), characterized by heterogeneous continuously distributed capacitance and/or inductance are shown to possess the unusual non-local heterogeneity-induced dispersion in the microwave spectral range. This strong artificial dispersion, both positive and negative, is determined by the shapes and sizes of distributions of capacitance and inductance along the TL. To optimize the regimes of microwaves propagation in these structures the series of new exact analytical solutions of telegraph equation for gradient TL are obtained beyond of the scope of any assumptions concerning smallness or slowness of variations of fields or impedances along the line. These solutions visualize the formation of flexible non - Fresnel reflectance/transmittance spectra of TL, formed due to interference of forward and backward waves, occurring on the discontinuities of gradient and curvature of spatial distributions of impedance inside the line. The heterogeneity - induced dispersion is shown to provide the weakly attenuated tunneling regime for effective energy transfer in the microwave spectral range by evanescent and antievanescent modes in the gradient TL.