Transmission spectra in symmetrical Fibonacci superlattices composed of positive and negative refractive index materials

Using the transfer matrix method, we have calculated the transmission spectra of symmetrical Fibonacci superlattices composed of positive and negative refractive index materials. In the ideal case where negative refractive index can be approximated as a constant in the frequency range considered, self-similarity behavior and perfect transmission peaks are observed in the spectra. While in the more realistic case where both ε and μ   are negative, dispersive and modeled by the split-ring resonators (SRR) and cut-wires, both zero n¯=0 gap and Bragg reflection gaps are obtained. These transmission spectra are also compared with those of symmetrical Fibonacci superlattices with purely positive refractive index materials.