## 1 Introduction  
A recent breakthrough of ultrafast laser science has been the ability to produce laser pulses with duration close to the optical cycle (2.7 fs at 800 nm) with controlled waveform, _i.e._, controlled carrier-envelope phase (CEP). The availability of such pulses has provided new insight into attosecond electronic processes in matter [1]. CEP-controlled few-cycle pulses are routinely used at moderate intensities to probe attosecond electronic dynamics in atoms or molecules. More recently, few-cycle pulses with relativistic intensities (above 10\({}^{18}\) W/cm\({}^{2}\) at 800 nm) have been used to study collective electronic dynamics in laser-driven plasmas, such as few-fs electron bunch acceleration from gas jets [2,3] or high-harmonic generation from solid targets [4]. Unfortunately, all these pioneering experiments were performed without CEP control. Recent experiments at Laboratoire d'Optique Appliquee have demonstrated, for the first time, attosecond time-scale control over plasma electron dynamics using a CEP-controlled few-cycle laser system at 1 kHz (Salle Noire), as well as the ability to isolate single attosecond pulses from the harmonic emission via spatio-temporal gating of the laser-plasma interaction [5,6]. Moreover, few-cycle laser-driven energetic particle acceleration was also demonstrated using the same experimental set-up [7]. These pioneer experiments were performed with the Salle Noire laser, delivering 1.2 mJ, 5 fs pulses and a relative CEP drift of 250 mrad rms [8]. Reaching the relativistic regime with few-cycle pulses, especially on solid targets, requires both an increase in the pulse energy and temporal contrast. As a consequence, we are in the process of upgrading our laser system to produce CEP-controlled, 5 mJ, 5 fs pulses with a temporal contrast ratio better than 10\({}^{10}\). Nowadays, two major techniques are widely used to efficiently enhance the final pulse contrast: plasma mirrors at the end of the laser chain [9,10] and nonlinear temporal filters in a double-CPA scheme [11]. In the past few years, we have developed and qualified a nonlinear filtering device relying on cross-polarized wave (XPW) generation [12]. XPW generation is an achromatic and degenerated four wave mixing process relying on the anisotropy of the \(\chi^{3}\) tensor in isotropic crystals [13]. When an intense, linearly polarized input beam (fundamental) illuminates a nonlinear crystal placed between crossed polarizers, it gives rise to an orthogonally polarized wave (XPW). The cubic dependence between output and input intensities provides an improvement in temporal contrast that is limited only by the extinction ratio of the crossed polarizers. Nowadays, XPW-based contrast enhancement has become widespread in high peak-power laser systems [10,14,15,16,17]. The planned upgraded Salle Noire laser will first consist of a Ti:Sa double-CPA system, providing 1 kHz, 10 mJ, 25 fs pulses. The first CPA is a commercial CEP-stabilized laser system. The compressed pulses are then temporally filtered by an XPW setup and stretched to about 50 ps during propagation through a SF57 bulk and an AOPDF (Dazzler). Further amplification will occur in two multipass amplifiers. Pulse compression will be achieved in a specially designed, high-energy, grism compressor [18]. It has been shown that XPW process and compression in grisms both preserve CEP stability [19]. The double-CPA is therefore expected to produce high-contrast, multi-mJ, CEP-stabilized pulses. Further post-compression in a hollow-core fiber setup to the few-cycle regime will aim at providing around 5 mJ, 5 fs pulses for relativistic laser-plasma interaction [8,20]. In this paper, we present a detailed characterization of the CEP-controlled, high-contrast injector for the second CPA, consisting of a Ti:Sa CPA followed by a high-efficiency XPW contrast filter at the mJ level.