## 2 Design of Single-Grating Monochromators for Ultrashort Pulses
In fact, the performances of blazed gratings in the CDM are critically dependent on the actual groove profile. In particular, the unavoidable smoothing of the sharp edges of the actual profile gives a decrease of efficiency with respect to the theoretical values that is more evident for extreme blaze angles, where the realization of an ideal saw-tooth profile is practically unfeasible. Configurations with pulse-front tilt in the range of hundreds of femtoseconds in the CDM require the use of gratings with extremely small blaze angles that are feasible although close to the limit of the present capabilities of manufacturers (\(\approx\)0.7\({}^{\circ}\)). Furthermore, since the realization of an ideal saw-tooth profile at such extreme blaze angles is practically impossible, the actual efficiency of a blazed grating will be lower than the theoretical predictions. An alternative to saw-tooth profiles is the adoption of laminar or sinusoidal profiles that exhibit lower efficiency. On the contrary, the grating efficiency in the OPM is less sensitive to the errors in the saw-tooth profile. Furthermore, the blaze angles required for the gratings used in the OPM are less extreme than the CDM, therefore, the deviation between the ideal and the actual saw-tooth profile is lower. This also contributes to the increase of efficiency with respect to the CDM. All these factors confirm the advantage of the OPM in terms of monochromator efficiency. The comparison is even more favorable to OPM for pulse-front tilts in the range of tens of femtoseconds. In this case, the groove density required for CDM is extremely low and the corresponding blaze angle (\(\approx\)0.1\({}^{\circ}\) in the present example) is practically unfeasible. Laminar profiles have to be adopted, and the resulting efficiency is extremely low. On the contrary, the blazed gratings used in the OPM have parameters within the manufacturing capabilities even for few-femtosecond time responses, as is clear from the data presented in Table 1.  
The calculations can be generalized as resumed in Figure 5, where the two geometries are compared for pulse-front tilts in the 5-200 fs interval. For tilts above 100 fs, the CDM requires groove densities of few-to-several hundreds of grooves per millimeter and blaze angles that are feasible with present technologies, while the OPM requires higher groove densities and azimuth angles, therefore introducing a large distortion and rotation of the image after the diffraction [22]. On the contrary, for tilts below 100 fs, the CDM requires gratings with very low groove density and blaze angles that are  
Figure 3: Pulse-front tilt of the monochromator with the parameters listed in Table 1 (**a**) 100-fs pulse-front tilt at 35 nm; (**b**) 10-fs pulse-front tilt at 35 nm. presently unfeasible, while the OPM requires gratings with standard characteristics even at 5-fs response. As a general claim, the CDM should be preferred for monochromators when a relatively large pulse-front tilt can be tolerated, _i.e._, 100-200 fs, while the OPM has to be adopted for pulse-front tilts in the 5-50 fs range, providing both high efficiency and ultrafast temporal response. The spatial beam profile at focus becomes broader along the dispersion direction, due to the diffraction; therefore, rays at different wavelengths make different optical paths. In addition to the pulse front-tilt, the variation of the group delay within the bandwidth of a single harmonic given by the  
Figure 4: Efficiency curve of the gratings with the parameters listed in Table 1: (**a**) CDM; (**b**) OPM. Figure 5: Grating parameters as a function of the pulse-front tilt for 1-mm half-width beam section: (**a**) groove density at 30 nm (**left**) and 10 nm (**right**); (**b**) blaze angle. grating may alter the pulse duration at the output. It can be shown by ray-tracing simulations that this effect is totally negligible when dealing with pulses in the range from few to several tens of femtoseconds, as is the case of single-grating monochromators discussed here.