  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
(1.446GHz\(\leq\omega\leq \) 15GHz), 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 (\(\omega\)=0.995GHz) . 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.
