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Physica Scripta

Cascaded frequency conversion via invariant engineering

Weixian Yu, Zhen Chen, Jiayu Zhang, Yongbo Xiao, Changshui Chen

Published Jun 13, 2025• 1 citation
Publisher

Abstract

Abstract Based on the Lewis-Riesenfeld (LR) invariant based inverse engineering for Shortcuts to adiabaticity (STA), we propose a cascaded frequency conversion technique. The technique maintains the same initial and final states as stimulated Raman adiabatic passage (STIRAP) but does not follow an adiabatic evolution during the intermediate processes. The results of numerical simulations show that the technique transfers the eigenstates from the initial state to the final state by designing an adiabatic evolutionary path, which is free to choose the length of the crystal within the crystal laser-induced damage threshold (LIDT), thus realizing a rapid adiabatic cascaded frequency conversion process with robustness under certain temperature variations and signal-laser wavelength variations.

DOI
10.1088/1402-4896/addfb2

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Abstract In recent years, a series of adiabatic passage techniques for atomic systems have been introduced into the field of nonlinear optics. We propose a theoretical model of the fourth-order three-process cascaded frequency conversion technique based on fractional stimulated Raman adiabatic passage (FSTIRAP). Building upon the STIRAP technique, the FSTIRAP technique splits the original third pump laser into two separate pump lasers, each subjected to Gaussian modulation. This achieves the simultaneous output of the first idler laser and the second idler laser with tunable output ratios at the end of the crystal, while ensuring the complete conversion of the signal laser. Numerical simulation results demonstrate that the FSTIRAP technique enables highly efficient frequency conversion, with the total conversion efficiency showing robustness across a wide range of pump laser intensities, coupling delay parameters, and crystal temperatures. Additionally, the output ratio of the first idler laser to the second idler laser can be controlled by independently tuning the delay parameter or the crystal temperature.
Shortcuts to adiabaticity (STA) are channels that can fast prepare a desired quantum state with high fidelity which obtains more and more research in the atomic domain. Based on stimulated Raman shortcut-to-adiabatic passage (STIRSAP), we propose a frequency conversion technique which works through a non-adiabatic route and produces the same energy distribution as in adiabatic evolution. Numerical simulation results show that the conversion is efficient and robust. Our results reveal a novel scenario for frequency conversion and relax the strict limitations on system parameters in adiabatic frequency conversion.
An analytical method is proposed in this paper to achieve complete energy conversion in sum frequency generation based on the Lewis-Riesenfeld invariants theory. In the proposed scheme, a quasi-adiabatic single control parameter model is established, and the value of single control parameter is selected to make the initial eigenstate perfectly converted to the final eigenstate as needed. Corresponding to the nonlinear frequency conversion process, a nonlinear crystal structure is designed by inverse engineering using the optimal control theory. It is robust against perturbations of the coupling coefficient and phase mismatch, including variations in the pump intensity and crystal polarization period, and achieves almost 100% conversion efficiency at any crystal length. Theoretical simulations show that frequency conversion can be achieved in the wavelength range of 2.6 µm-3.6 µm, and the spectral bandwidth of conversion efficiency exceeds 50% and approaches 400 nm when the crystal length L = 1 mm.
Abstract Cascaded frequency conversion is widely used to generate laser radiation at various wavelengths. Adiabatic schemes have been introduced into this field. In this paper, we propose a counter-diabatic driving scheme based on stimulated Raman shortcuts-to-adiabatic passage (STIRSAP), which does not rely on the mixing-angle approximation and remains effective even under phase mismatch conditions. Numerical simulations indicate that the proposed scheme maintains high conversion efficiency over a substantially broader parameter range than the conventional STIRSAP scheme.
Abstract The method of adiabatic frequency conversion, in analogy with a two‐level atomic system, has been put forward recently and verified experimentally to achieve robust frequency mixing processes such as sum and difference frequency generation. Here a comparative study of efficient frequency mixing using various techniques of shortcuts to adiabaticity such as counter‐diabatic driving and invariant‐based inverse engineering is presented. It is shown here that it is possible to perform sum frequency generation by properly designing the poling structure of a periodically poled crystal and the coupling between the input lights and the crystal. The required crystal length for frequency conversion significantly decreases beyond the adiabatic limit. This approach significantly improves the robustness of the process against the variation in temperature as well as the signal frequency. By introducing a single parameter control technique with constant coupling and combining with the inverse engineering, perturbation theory, and optimal control, it is shown that the phase mismatch can be further optimized with respect to the fluctuations of input wavelength and crystal temperature that results into a novel experimentally realizable mixing scheme.