### Energy Scalable Pulse Cleaning Techniques
#### 1.3.2 Nonlinear Fourier-Filter  
To exceed the shortcomings associated with the use of plasma mirrors, an alternative method, called nonlinear Fourier-filtering (NFF), has been proposed for temporal filtering of short UV pulses [34]. In this arrangement, the separation of the intense main pulse from the noise is based on a nonlinear interaction in the Fourier-plane and on the resulting directional modulation of the beam. The experimental realization (see the right half of Figure 3) uses a confocal telescope and a pair of conjugate filters, where the middle and outer parts of the beam are filtered out at the input and output of the system, respectively. The low intensity ASE is not (or negligibly) modulated and the output diaphragm blocks the remaining part of the beam. However, for the intense main pulse, the self-generated plasma introduces selective nonlinear phase-modulation of the different diffraction orders of the beam, which leads to modified directional properties, and as a result, significant throughput appears. In this way, the noise becomes spatially separable from the main pulse. An important feature of this arrangement is that the temporal filtering is accompanied by efficient spatial filtering.  
The first demonstration of this filtering technique in [34] showed 10\({}^{3}\) temporal contrast improvement and >40% energy throughput with a stable performance. Later investigations showed that the moderate value of contrast improvement was limited by the spatial contrast of \"conventional\" imaging of the input annular aperture containing (high) spatial frequency components that cannot be processed by the imaging system of NFF [42]. The most preferable solution was to introduce an imaging of low numerical aperture (NA) prior to Fourier-filtering (called pre-imaging) to exclude the higher spatial frequencies in the intermediate picture created by this pre-image system, as shown in the left half of Figure 3.  
Calculations show remarkable improvement; the spatial contrast of imaging was increased to the theoretical 10\({}^{10}\) level. A contrast improvement of >10\({}^{7}\) and >10\({}^{5}\) was experimentally demonstrated in the visible, and in the UV [42], providing significantly higher contrast improvement than the former techniques. Further advantages of this arrangement are that the amplification could be carried out simultaneously during the imaging (see Figure 3), and the pre-imaging part acts as a spatial filter at the same time, reducing the ASE coupling between the amplifiers.  
Figure 3: Schematic of the nonlinear Fourier-filter completed by a low NA pre-imaging and by possible positions of the amplifiers (based on [42]).  
The nonlinear Fourier-filter uses subsequent imaging systems and ionization of noble gases; therefore, it is expected to be energy scalable, and an excellent candidate for filtering short-pulses in a wide wavelength range. The special gain dynamics of excimer amplifiers--studied in detail later--necessitates the use of the filtering technique as close to the end of the amplifier chain as possible. Since the extension of this technique towards larger energies and larger cross-sections is technically challenging (and rather complicated), integration of this method had been realized in subsequent steps into a high-brightness _KrF_ laser system.