Terahertz (THz) air coherent detection is a broadband coherent detection technique, which has been used widely in the THz science and technology. In this paper, a frequency-dependent response function of THz air coherent detection is defined based on the nonlinear polarization of gas molecules induced by the ultrashort laser pulses and the THz pulses. Calculations show that the response function of this technique has a half of Gaussian-like profile, which has a high sensitivity in the low frequency range and low sensitivity in the high frequency range of THz waves. Two fitted functions are given based on the calculated results, which can provide a good reference bandwidth when using the air coherent detection with a given probe laser pulse. The distortions of THz pulses induced by the air coherent detection in the detection process are discussed as well. This study will help to understand the response bandwidth and the limitation of detection bandwidth of the air coherent detection technique.
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