# Single-Shot Temporal Contrast Enhancement Measurement of a Plasma Mirror by a Chirped Pulse
## 2 Method for Spatiotemporally Overlapped Chirped Pulse  
The plasma mirror is a layer of dense plasma induced by the interaction between an intense laser pulse and target. Generally, the target of the PM is an antireflection (AR) coated glass plate for obtaining the maximum temporal contrast enhancement. When the intense laser pulses shoot onto the target, the low-intensity pedestal and prepulses are transmitted due to the AR coating. When the high-intensity main pulse arrives, the AR-coated target is rapidly ionized and generates dense plasma by tunneling and electronic avalanche ionization. Once the plasma reaches above the critical density and forms the PM, it changes rapidly from initial high transmission to high reflection, resulting in a temporal reflectivity difference between the high-intensity main pulse and low-intensity prepulses. Thus, the temporal contrast enhancement is determined by the contrast between plasma reflectivity and cold reflectivity. Considering the characteristics of the PMs above, the SOCP is suitable for obtaining the time-resolved reflectivity difference of PMs. Due to the continuous queuing of wavelengths, the spectral profile of SOCP is strongly modulated by PMs and the spectrum contains the temporal reflectivity information of PMs. The concept of SOCP is shown in Figure 1a. A high-power ultrashort pulse, defined as the igniting pulse, is focused on the AR-coated target of the PM. A SOCP is shot on the AR-coated target as probe pulse. For ensuring the igniting pulse is overlapped within the duration of the chirped pulse in the time domain, a delay line is set to adjust the relative delay between igniting pulse and SOCP. Figure 1b shows the temporal diagram of SOCP and igniting pulse. The red part represents the igniting pulse and the color part represents the various wavelength components queued continuously in the time domain of SOCP. The duration of a SOCP is much longer than that of the igniting pulse. According to the delay of different wavelength components relative to the igniting pulse, the whole process can be divided into three phases, as shown in Figure 1c-e. In phase 1 (Figure 1c), the main pulse of the igniting pulse has not yet arrived at the AR-coated target and a PM has not been generated. The AR-coated target shows extremely low reflectivity, resulting in the wavelength components arrived already from the SOCP after they pass through the target. During phase 2 (Figure 1d), the strong intensity main pulse arrives and rapidly produces a layer of dense plasma. When plasma reaches the critical density, the PM is completely formed and works as a mirror with ultrahigh reflectivity. The wavelength component corresponding to the chirped pulse temporally overlapped with the PM cannot pass through critical density, and is therefore reflected by the PM. In phase 3 (Figure 1e), the PM vanishes, and the surface of the AR-coated target has been damaged. The target shows low reflectivity again, and the rest of the wavelength components of the chirped pulse pass through or are scattered. The rapid change in reflectivity of the PM leads to the different reflectivity of the igniting laser at different phases. Only the wavelength components that temporally overlapped the duration of the PM can be highly reflected and collected into a spectrometer. Thus, the temporal reflectivity information of the PM is included in the recorded spectrum \(S_{1}(\lambda)\) of the reflected SOCP. Subtracting the background spectrum \(S_{b}(\lambda)\) from the recorded spectrum \(S_{1}(\lambda)\) and divided by the original spectrum \(S_{0}(\lambda)\), the spectral reflection efficiency profile of the SOCP is obtained. According to the chirp rate \(C\), the spectral profile can be converted into temporal profile \(R(t)\), representing the temporal reflectivity profile of the PM. The temporal profile \(R(t)\) can be written as Equation (1).