In the Supplement 1 of Ref. [1], we have made an error in the calculation of the second harmonic generation (SHG) efficiency. The phase mismatch $\delta$ was by mistake multiplied by a factor of $\pi$, leading to an efficiency of $\propto \mathrm {sinc}^2 (\pi \delta )$, instead of $\propto \mathrm {sinc}^2 (\delta )$, which is the correct equation. As a consequence, the phase matching bandwidths shown in Fig. S1 b, c in the original publication are too narrow. The corrected calculation (Fig. 1) is in much better agreement with the spectral bandwidths achieved in the experiment (Fig. 2 in Ref. [1]). The initially assumed discrepancy between experiment and theory was explained by the spectral broadening due to self-phase modulation (SPM), which was observed in the experiment but not included in the simulations. Although SPM was clearly observed in the experiment, the corrected calculation results suggest, that SPM is not necessary to achieve the broad spectral bandwidths demonstrated in the experiment. All other statements in Ref. [1] remain unaffected by this correction.

 

Fig. 1. Ray tracing simulations of phase-matching. (a) Ray tracing geometry and OAPM orientations. (b) Calculated propagation angle inside the BBO crystal as a function of wavelength for both OAPM orientations and phase-matching angle for type I SHG (top). The refraction at the air/BBO interface was taken into account in these simulations. The bottom panel shows the corresponding normalized SHG efficiencies. (c) Calculated SHG efficiency for both OAPM orientations as a function of prism compressor length $L_1$.

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