# Segmented Composite Optical Parametric Amplification
## 4 Summary and Conclusions  
In summary, we used the similarity between the three wave mixing equations and the time-dependent Schrodinger equation to transfer concepts from quantum physics to nonlinear optics. Specifically, we have suggested to use segmented composite crystals for optical parametric amplification in analogy with the composite pulses in NMR and quantum optics. The approach used here is based on sign-alternating dual-compensating composite pulse sequences similar to those of Shaka and Pines [12,13]. These are particularly suited for optical parametric amplification because besides the standard quasi-phase-matching they require only additional sign flips of the nonlinear optical susceptibility at specific locations corresponding to the segment frontiers. We have demonstrated numerically that this technique is especially powerful for broadband OPA. The present approach does not require very long crystals and, for the given example of MgO:LiNbO\({}_{3}\), is compatible with pump intensities significantly below the damage threshold for ps or sub-ps illumination [35,36]. Note that the derivation of the optimum segment lengths was done in the general dimensionless case and is therefore independent of the material being selected for the implementation. Therefore, the technique presented here can be applied in principle to any nonlinear material permitting phase matching at the central wavelengths of the envisaged frequency conversion process. In combination with QPM, the technique can thus be applied to any material that can be structured by periodic poling (such as LiNbO\({}_{3}\), LiTaO\({}_{3}\), or KTiOPO4) or by orientation patterning during the growth process such as GaAs. However, QPM is not always necessary and the phase matching at the central wavelengths may be realized also by birefringence phase matching in the cases where this is possible. In such cases, it is sufficient to stack a small number of nonlinear crystals of the appropriate thicknesses with mutually reversed axes orientations, as discussed earlier in connection to SFG [30]. In contrast to periodically poling or orientation patterning that generally lead to a limited input aperture, the crystal stacking approach may therefore permit also to realize devices being addressable by very large area pump beams. Conceptualization, A.A.R. ; methodology and simulations, M.A.-M., A.A.R., and G.M. ; validation, V.C. ; manuscript preparation, M.A.-M., A.A.R., and G.M. ; reviewing and editing, all authors; coordination: G.M., V.C. All authors have read and agree to the published version of the manuscript. This research was funded by the EU Horizon-2020 ITN project LIMQUET (contract number 765075) and by the Bulgarian Science Fund Grant No. DN 18/14. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} OPA & Optical Parametric Amplifier \\ QPM & Quasi-phase-matching \\ NMR & Nuclear Magnetic Resonance \\ SFG & Sum Frequency Generation \\ DFG & Difference Frequency Generation \\ SHG & Second Harmonic Generation \\ \end{tabular}   
Appendix A Mapping between Two State Quantum System and SFG in Case of Undepleted Pump Approximation  
In this appendix, we show the relationship between three-wave mixing frequency conversion process and the quantum dynamics of a driven two-state quantum system. As mentioned above, the analogy is exact only for the case of SFG and in the undepleted pump approximation, where the three wave interaction can be reduced to an effective interaction of only two waves, which is the reason for illustrating this case here. Nevertheless, the related quantum-inspired approaches can be extended to the depleted regime and to other nonlinear interactions, as shown in the main text.