Wider frequency domain for negative refraction index in a quantized composite right-left handed transmission line

The refraction index of the quantized lossy composite right-left handed transmission line (CRLH-TL) is deduced in the thermal coherence state. The results show that the negative refraction index (herein the left-handedness) can be implemented by the electric circuit dissipative factors(i.e., the resistances R and conductances G) in a higher frequency band (1.446 GHz ≤ ω ≤ 15 GHz), and flexibly adjusted by the left-handed circuit components (C_l, L_l) and the right-handed circuit components (C_r, L_r) at a lower frequency (ω=0.995 GHz). The flexible adjustment for left-handedness in a wider bandwidth will be significant for the microscale circuit design of the CRLH-TL and may make the theoretical preparation for its compact applications.