Bragg interactions in the double periodic left-handed line

Left handed transmission line (LHT) has been built with periodic loadings of capacitance and inductance or split ring resonator and fine wire. If their periodic loadings are periodically modulated again, double periodic structures of left handed line (DLH) can be realized which is easy to fabricate for practical design. This paper analyzes Bragg interaction phenomena in DLH by using perturbation technique of multiple scales [2]. At first, coupled mode equation around first Bragg region in DLH medium was analyzed by using first stage of multiple scale. A few tenth megahertz of stop band at first Bragg region was found together with leaky wave mode at a edge of lower dispersion curve. Next coupled mode equation around second Bragg reflection region was derived under second order of multiple scales, where product term of periodic indexes of permeability and permittivity was dominant. A narrow leaky wave stop band with self coupling effect was found which approaches to the edge of the lower dispersion curve on first Bragg region. With relation between first and second Bragg reflections it was found that when sign of modulation index of permeability is different from permittivity one, first stop band of Bragg reflection will be reduced with enhancement of second Bragg reflection. As an application of DLH, small UHF leaky wave antenna was designed using few picosecond capacitances and few nano henry inductances arranged with 50% periodic form, 20mm pitch and length of 12 cm, scattering parameters and radiation pattern were measured at 330 MHz.