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2 Material and methods
J. Eur. Opt. Society-Rapid Publ. 21, 18( 2025) Recent studies demonstrate that a MPC post-compression setup working in the EFCR is an excellent candidate to generate clean short pulses. This scenario has been discussed theoretically in gas-filled MPCs [ 10, 11 ] and in an all-bulk setup [ 13 ], and demonstrated experimentally in gas-filled MPCs [ 12 ]. All these works demonstrate that the spectral phase obtained after the spectral broadening process is smooth but not as simple as one would desire, showing high order terms( mostly even contributions). Therefore, we need to find a compressor setup with enough degrees of freedom to be able to compensate this spectral phase without using chirped mirrors. A compressor consisting of a pair of grisms could be a good solution to start with.
To reach these spectrally broadened non-compressed pulses, we simulate the propagation of the pulses in the MPC in the EFCR. In this case we have focused on an all-bulk MPC system, which we believe is the most complex and extreme situation. We will take advantage of previous simulation results recently obtained in all-bulk MPC setups in the EFCR [ 13 ]. These simulations are done using a standard split-step Fourier method including both the linear effects – diffraction and dispersion – and the main nonlinear effects: SPM, self-steepening and Raman effects. A complete description of the numerical strategy can be seen in [ 11 ]. Our first attempt will be with the output pulse obtained when introducing a pulse centered at 800 nm, with 220 lJ and 150 fs pulse duration( half width at 1 / e 2 of the intensity distribution) into an MPC with two identical concave mirrors separated 40 cm. We assume that the beam is perfectly coupled to the fundamental mode of the cavity with a waist of 500 lm. The cavity is vacuum-sealed, and we add two thin fused silica plates 500 lm thick placed at the cavity mirrors as nonlinear media. After the pulse travels through the cell during 40 round trips the output on-axis intensity distribution doubles the temporal duration of the input one, but with a much broader spectrum, being compatible with a very clean Transformed Limited Pulse( TLP) of 20.7 fs full width at half maximum( FWHM) and with temporal sidelobes below 0.3 % of the TLP peak intensity. The spectral phase of the output spectrum on-axis is quite smooth with a big quadratic component but, as described in [ 13 ], also with other relevant even components.
To achieve the phase compensation of this output pulse( case I) we will design a compressor based on a pair of grisms. In our case, we have simulated a grism compressor following the phase response described in [ 18 ]. Although a system based on a pair of grisms compensates fairly well the phase of the output pulse, we will demonstrate that we can improve the setup by introducing a piece of dispersive material, as shown in Figure 1. We have, therefore, developed a multivariable optimization of the compression process taking into account eight tuning parameters: the angle of the prism apex( a D), the angle of incidence( h in), the entrance position in the grism( L in), the grisms separation( L GRISM), the tip-to-tip distance of the prisms( L tip), the diffraction grating density( C Grating), the material used
Figure 1. Compressor scheme based on a pair of grisms and a piece of glass.
for the extra piece of glass, with a particular refractive index( n g), and its thickness z. For both the prisms and the piece of glass, we have used SF10 as the material, for which we use the Sellmeier coefficient to simulate the complete dispersion curve [ 19 ]. The optimization is done by looking for a compressed pulse with the highest peak intensity, as close as possible to the TLP peak intensity, while doing the scan over all the compressor parameters enumerated above.
3 Results and discussion
Figure 2a shows the compressed pulses obtained with the grism-only approach( red line) and with the grism with a 46.5-mm thick SF10 plate added in the setup( green line), both compared with the TLP( blue line). As can be observed, the grism-only compressor is enough to successfully shorten the pulse to almost the same temporal duration as the TLP, with an intensity peak that reaches 83 % of the TLP peak intensity, but showing side lobs as intense as 4.73 % of the pulse peak intensity. The configuration of the compressor that yields this compressed pulse is detailed in the first row of Table 1. As can be observed it does not include any extra piece of glass( z).
If we introduce an additional piece of glass( SF10 in this case) before the retro-reflecting mirror( RM), it is possible to perform a better compression of the pulse, reaching 95.87 % of the peak intensity of the TLP and showing side lobs with a maximum intensity value of 0.59 % of the pulse peak intensity. The configuration of this new compressor proposal is detailed in the second row of Table 1. Adding the piece of glass in the setup notably improves the performance of the compressor since we introduce an additional degree of freedom to optimize the compression process.
To check if this combined compressor setup is also valid to achieve clean few-cycle pulses we can use the output pulse coming out of the third compression stage proposed in [ 13 ]. In that case the on-axis output spectrum obtained corresponds to a 3.88 fs FWHM TLP, with sidelobes reaching 0.03 % of the TLP peak intensity. Figure 2b shows the compressed pulses obtained with the grism-only approach( redline) andwiththegrismwitha3.55-mmthickSF10 plate added in the setup, both compared with the TLP