Objective Nonlinear frequency conversion, which leverages nonlinear optical effects to transform light from one frequency to another, is a crucial approach for obtaining light across various spectral bands. The efficiency of this conversion depends on satisfying phase- matching conditions, which are typically achieved through either birefringence in nonlinear crystals or quasi- phase matching in periodically poled crystals. These methods ensure coherent interaction among the interacting light waves. In the context of laser- driven inertial confinement fusion research, efforts are focused on minimizing laser- plasma instabilities by shortening laser wavelengths and reducing spatial and temporal coherence. High- power laser drivers usually employ cascaded frequency conversion schemes to convert narrowband neodymium glass lasers to third harmonics. However, this conventional approach is notably sensitive to fluctuations in pump wavelength, crystal temperature, and beam propagation angles. Consequently, there is a trade-off between achieving high conversion efficiency and maintaining a broad acceptance bandwidth. To reconcile both high efficiency and broad bandwidth, we propose a frequency conversion methodology inspired by adiabatic passage theory, similar to population control in two- level atomic systems. In our study, we implement a gradient deuteration technique to induce a refractive index gradient within the crystal. This approach fulfills the criteria for adiabatic passage and enables efficient broadband frequency conversion. Methods In this study, we use gradient-deuterated KDP crystals and a dual- frequency mixing technique to achieve triply frequency- converted light, combining both broadband and narrowband sources. First, we direct a low- coherence broadband fundamental wave with a central wavelength of 1058 nm and a bandwidth of 10 nm onto the KDP crystal at the phase- matching angle. The 18- mm- thick KDP crystal, which acts as the frequency- doubling crystal, produces broadband frequency- doubled light. Next, we introduce a narrowband fundamental wave at 1053 nm to interact with the broadband second harmonic light. Both beams are simultaneously directed into the gradient-deuterated crystal, facilitating the broadband-narrowband frequency mixing process and resulting in broadband triply frequency- converted light. We then adjust the crystal length and the deuterium concentration gradient to find the optimal conditions for adiabatic passage. We perform a detailed analysis to understand how factors such as crystal length, deuterium concentration gradient, pump intensity, and choice of nonlinear crystal material affect frequency conversion efficiency. Our approach aims to achieve a balance between broadband operation and high conversion efficiency by using the analogy of adiabatic passage in two- level atomic systems for better control over nonlinear frequency conversion processes. Results and Discussions In this study, broadband third harmonic light is generated through a frequency conversion process involving both second- harmonic generation and sum- frequency mixing. This process converts two lower- frequency photons into one photon with three times the original frequency. An 18- mm- long KDP crystal is used for second- harmonic generation, and a gradient-deuterated crystal is employed for sum- frequency mixing. The sum- frequency mixing process utilizes a wide-narrowband frequency mixing technique. The optimal conditions for adiabatic passage are achieved with an 80- mm- long gradient-deuterated crystal and a 10 degrees o deuterium concentration gradient, which results in nearly 80 degrees o conversion efficiency and produces third harmonic light with a bandwidth close to 2 nm. Adjustments to the crystal length and deuterium concentration gradient are then made to define the parameter range that meets adiabatic passage criteria, with practical considerations guiding the choice of crystal dimensions and concentration gradients. By varying the pump intensity of the narrowband fundamental beam, we assess how well the adiabatic passage method handles fluctuations in pump power, which demonstrates good robustness. A comparison between the KDP crystal and the gradient-deuterated crystal reveals that the frequency conversion efficiency using the adiabatic passage method with the gradient-deuterated crystal greatly exceeds that of standard phase- matching techniques. This highlights the potential of custom crystal designs and the adiabatic passage concept for enhancing nonlinear optical frequency conversion processes, especially for broadband and high- efficiency applications. Conclusions In this paper, we develop a model for broadband frequency tripling using the adiabatic passage method and analyze key parameters affecting the conversion process, such as the length of the nonlinear crystal, the concentration gradient of deuterium doping, and the intensity of the narrowband fundamental pump laser. Our findings demonstrate that using a crystal with a varying deuterium concentration gradient in the adiabatic passage can efficiently convert broadband second harmonic light into third harmonic light. Deviations from the optimal adiabatic conditions, caused by changes in crystal length and doping gradient, result in a significant reduction in conversion efficiency. When adiabatic conditions are met, variations in the deuterium concentration gradient affect the effective length of the adiabatic passage, which in turn influences both the conversion efficiency and the acceptance bandwidth. Specifically, the highest conversion efficiency is achieved with a crystal length of 101.5 mm and a concentration difference of 36.7 degrees o, nearly achieving complete conversion from second harmonic to third harmonic light. Our study explores the broadband frequency tripling process based on the adiabatic passage scheme, examining how adjustments to parameters like crystal length, deuterium doping gradient, and fundamental laser intensity affect the dynamics of the adiabatic passage during frequency conversion. The insights from this analysis provide valuable guidance for future experimental work in advanced nonlinear optical frequency conversion strategies.
