Influence of magnetic field and temperature on negative refractive index in a degenerate three-level atomic system

This work investigates the manipulation of the negative refractive index in a degenerate three-level \( \Lambda \)-type atomic system in the presence of an external magnetic field and Doppler broadening. The results show that the bandwidth of the negative refractive index can be significantly broadened by increasing the coupling laser intensity; for example, when \( \Omega_c \) increases from \( 30\gamma \) to \( 60\gamma \), the bandwidth expands from \( [0.5\gamma, 1.5\gamma] \) to \( [1.2\gamma, 4\gamma] \). The spectral position can be flexibly tuned by adjusting the magnetic field, shifting toward lower (higher) frequencies for \( B = -1\gamma_c \) (\( B = 2\gamma_c \)). Temperature has a pronounced effect on both the range and amplitude; increasing the temperature from \( 200\,\mathrm{K} \) to \( 400\,\mathrm{K} \) narrows the range from \( [-1.6\gamma_c, -0.2\gamma_c] \) to \( [-1.1\gamma_c, -0.5\gamma_c] \). These findings may facilitate experimental realization and potential practical applications of EIT-based negative-index materials.