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arXiv:2206.12207 · Optics Express

Complete and robust energy conversion by sum frequency generation based on invariant engineering

Congfu Zhang, Zhaolu Wang, Hongjun Liu

Published Jan 11, 2023• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/oe.477959

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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 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.
We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems.
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.
Sum-frequency generation in nonlinear optics is a key technology enabling optical frequency conversion. However, how to most effectively enhance the frequency conversion efficiency in nonlinear crystals remains a fundamental problem; shorter crystal length and lower pump intensity while maintaining high-efficiency frequency conversion are critical for enhancing device integration potential and improving device performance in practical sum-frequency generation (SFG) device design. This study employed the Pontryagin maximum principle to investigate the SFG process. A cost functional was formulated that complies with the minimum constraint during SFG, enabling the derivation of optimal control parameters. A central finding revealed an inverse proportionality between the coupling coefficient and the crystal length: for a given crystal length, the pump intensity in the SFG is minimized, and vice versa. The optimal evolution trajectory follows a geodesic path on the Bloch sphere surface, representing the minimal-length evolutionary path from the signal field to the sum-frequency field. This geodesic behavior also indicates that the loss and absorption of the optical field in the crystal medium vanish during SFG. Furthermore, the crystal modulation period for the SFG is determined using the optimal phase-matching function. These results offer valuable insights for the design of compact optical chips and nonlinear optical devices.
Based on the QPM technology and the counter diabatic compensation approach in quantum physics, we propose an optimal scheme that the signal field completely converts into the sum frequency field under the condition of the superadiabaticity. With the geometric rotation plane designed, we subtly reveals the physical mechanism of the systems before and after adding a counter diabatic term. The property of the energy conversion which is analogous to the elastic collision is explained for the addition counter diabatic compensation. With the help of Bloch vectors in atoms physics, we can clearly show the physics process of the complete energy conversion and the physical mechanism for the shortcuts of the superadiabaticity from a new perspective. This new scheme can optimize adiabatic process, shorten the coupling region and nonlinear crystal length, reduce the influence of the dispersion effect, and also implement the robust efficient energy conversion under the condition of relatively weak pump intensity. Not only does this scheme provide a good theoretical basis for the design of nonlinear optical devices, but also its physical thoughts can be widely used in many other fields.
Abstract The creation of efficient broadband frequency conversion devices while maintaining robustness to manufacturing and setup errors is crucial for accurate multiphoton spectroscopy, broadband imaging and the design of robust optical sources. Traditionally, nonlinear optical conversion processes are either efficient but narrowband or broadband but with low photon conversion yield. Several methods have been introduced in recent years to obtain both with great success, among them we can find adiabatic frequency conversion and Shaka–Pines composite segmented design. Here, we expand the composite design and introduce the detuning modulated composite segmented (DMCS) scheme in nonlinear optics, which offers a broadband, efficient and robust method for frequency conversion. We also present the constant-length DMCS scheme, which offers multiple efficient and robust wavelength regimes for broadband upconversion. We apply these schemes to a system of quasi-phase-matching crystal for the sum frequency generation process, and demonstrate the high robustness and bandwidth of the composite schemes. We show that these schemes are robust to temperature and crystal length variations and can have a superior conversion bandwidth under length and power constraints compared to other conversion schemes, such as periodically poled and adiabatic chirped crystals. We believe that the new family of DMCS schemes will have many uses in applications of frequency conversion, due to their robustness, low energy demand and compact size.