## 1 Introduction  
A method for controlling the spectral phase and amplitude of broadband coherent light from high-order harmonic generation (HHG) is presented. The method considers a feedback loop scheme [1] and takes advantage from the coherent emission in HHG. Controlling the phase and amplitude of a broad spectral region in HHG represents a formidable challenge of general implication to many areas of science [2]. In particular, the shaping of the phase and amplitude in a broadband is an essential ingredient for the reconstruction of the time profile of attosecond pulses. It is well known that the broadband emission from HHG is a source for coherent attosecond light pulses, which can span photon energies from the ultraviolet to the soft X-ray region [3]. Controlling the amplitude and phase of the harmonic radiation is crucial to produce pulses with a duration as short as the bandwidth of the generated radiation in principle allows and to isolate them by compressing the energy generally delivered as pulse trains from the HHG process. Isolated attosecond pulses have demonstrated a great potential in the investigation of ultrafast electronic processes, and they can be produced by spectral selection of the few harmonics in the cutoff region, which are most in phase [4; 5; 6]. Several other techniques have been investigated to generate isolated and twin-pulses [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19], which include spectral amplitude and phase control by means of polarization and intensity modulation of the driving pulses [7; 8; 9; 10; 11; 12], the use of dispersive elements for pulse compression [13], and different other techniques [14; 15; 16] that have been reviewed in [18; 19]. These important efforts are able or promising to produce isolated attosecond pulses by considering a particular spectral bandwidth of the harmonics spectrum. The feedback loop control presented here allows to directly control the HHG process such that the light is emitted with the desired shape from any chosen spectral bandwidth of the harmonics spectrum. As it will be shown, this technique is very robust in particular for the production of isolated attosecond pulses. In a recent work [20], it has been shown that the spectral phase of the emission from HHG can be directly manipulated in any suitable broad spectral region by considering the coherent addition of a filtered spectral width of the HHG spectrum, with optimal delay and attenuated intensity, to the strong IR input pulse. This procedure is controlled by a numerical algorithm and allows to optimally shape a broadband spectral phase, so that isolated attosecond pulses can be produced from different bandwidths of the spectrum and at different central photon energies. In the present work, this control technique is further examined by considering the spectral amplitude of the HHG spectrum as an alternative control target in the optimization procedure. As it will be shown, by flattening the shape of the spectral amplitude in a large bandwidth of the harmonics spectrum, isolated attosecond pulses are produced, which provides a significant example of HHG broadband amplitude control. The present results therefore extend the capabilities of the HHG control technique first described in [20]. As mentioned above, the feedback loop is based on using a filtered spectral width of the HHG spectrum to slightly reshape the HHG driving pulse, which is accomplished by a coherent combination of a weak XUV pulse with the strong IR driving field. Combining attosecond XUV pulses with the driving IR field has been studied for HHG [21; 22; 23; 24; 25; 26; 27], although the possibility to shape the amplitude and phase of a broad region of the spectrum by combining a weak XUV pulse with the intense IR driving pulse has not been considered before.