Quantum effects in thermal Fock state for mesoscopic left-handed transmission lines
A quantization scheme for an ideal loss-less mesoscopic left-handed transmission lines (LH TL) unit cell equivalent circuit is proposed and the fluctuations of the current and the voltage of the LH TL equivalent circuit in thermal Fock space are studied by thermal field dynamics (TFD) theory. In thermal Fock state the negative refractive index (NRI) of the LH TL unit cell equivalent circuit is discussed. The results indicate that the quantum fluctuations show the linear dependent of NRI at some temperature, while the frequency and the thermal photons are destructive dependent of NRI within the microwave frequency band. When the unit cell equivalent circuit operates at the rising temperature, the NRI is decreasing. The results demonstrates the ideal loss-less mesoscopic LH TL equivalent circuit operating at a lower frequency, temperature and with little thermal photons is more conducive to NRI, which coincides with the macroscopic real LH TL.