Three wave mixing (TWM) processes in nonlinear crystals can be utilized to obtain laser frequencies that cannot be obtained directly from laser action. At the meantime, the secondary cascaded expands the frequency conversion range, allowing for nearer or farther laser frequencies through the quasi phase matching (QPM) technique [1,2]. However, the QPM technique fail to achieve both high efficiency and broadband frequency conversion at the same time [3,4]. In order to realize an efficient and broadband frequency conversion technique, nonlinear optical cascaded frequency conversion models based on adiabatic passage technique are proposed by analogy with stimulated Raman adiabatic passage (STIRAP) technique [5,6] and SCRAP technique [7,8] in atomic systems.

Compared to STIRAP technique, SCRAP technique has better stability and is not limited by the coupling order [[7], [8], [9]]. SCRAP technique utilizes a coupling modulation function κc(z) to connect two TWM processes to generate adiabatic crossings and form an adiabatic passage, thereby converting the signal wavelength energy to the idler wavelength energy [9]. Nevertheless, the system limited by the adiabatic conditions is more parametrically constrained and adiabatic evolution processes require long interaction length [10,11].

In order to accelerate the adiabatic process in a variety of quantum systems, the STA techniques including quantum transitionless driving [10,11], CD driving [12,13], and Lewis-Riesenfeld (LR) invariant based inverse engineering [14,15] have been developed. This method has been implemented in different fields, such as perform fast atomic transport in quantum systems [16] and multiparticle entangled state generation [17,18]. Analogous to atomic systems, the STA techniques have been applied to optical waveguide devices, including mode conversion [19,20], directional couplers [[21], [22], [23], [24]], and beam splitting [25,26]. With respect to frequency conversion, the STA techniques have also been used to improve sum-frequency generation (SFG) process [27,28] and cascaded frequency conversion processes [29].

In this paper, we propose a theoretical model of cascaded frequency conversion technique based on SCRSAP which is the application of the STA CD driving technique to SCRAP, and design the coupled modulation function to realize the STA technique by calculating the CD driving term under phase matching condition. Besides, we investigate the effect of system parameters on SCRSAP technique and compare it with SCRAP technique. Results of simulations show that SCRSAP technique improves robustness to delay parameters and pump laser intensity. Furthermore, the implementation of the STA technique enhances the resilience of the frequency conversion process against temperature fluctuations and variations in the signal wavelength.