外腔共振和频系统中阻抗匹配的理论研究

Theoretical investigation of impedance matching in the process of sum-frequency generation in an external resonator

外腔共振是提高和频效率的有效方法.实现外腔共振高效和频需要基频光高效地耦合到外部谐振腔中,因此系统要达到阻抗匹配.本文分别建立了双波长和单波长外腔共振和频系统的理论模型,分析了腔增强因子与耦合腔镜反射率、入射基频光功率等参数的依赖关系,通过数值模拟获得最优化的共振光耦合腔镜反射率,使系统达到阻抗匹配,提高和频效率.研究表明,无论双波长还是单波长外腔共振和频系统,共振基频光的最佳耦合腔镜反射率只会随着另一束共振或者不共振的基频光入射功率的增加而减小,而其本身的入射功率变化则影响较小;进一步分析表明,若共振基频光的耦合腔镜反射率超过阻抗匹配值,和频光功率将会迅速减小,而小于阻抗匹配值时,和频光功率减少速度相对较慢,因此实验过程中要尽量避免过耦合的情况出现.本文的理论分析过程将对外腔和频实验有一定的指导意义.

The sum-frequency conversion efficiency is directly proportional to the product of two fundamental laser powers. Therefore, sum-frequency conversion efficiency is rather low when the fundamental beams pass through a nonlinear crystal only once. External resonant technique as an effective means of improving the powers of the fundamental light has been widely applied to the field of nonlinear frequency conversion. This technique can greatly improve the sum-frequency conversion efficiency and is particularly suitable for the situation in which the input power of the fundamental frequency lasers bas been limited. The implementation of high efficient sum-frequency generation in an external resonator requires that the fundamental frequency laser should be efficiently coupled to the external cavity. Therefore, the system needs to achieve impedance matching. In the part of theoretical analysis, first, we derive the enhancement factor when traveling- wave cavity is resonant, and then, establish the theoretical models of doubly resonant and singly resonant sum-frequency generation in an external resonator respectively. The variation of enhancement factors as functions of reflectivity of the input couplers and power of the input fundamental light for doubly resonant and singly resonant sum-frequency systems is derived from Boyd-Kleinman theory in detail based on the theoretical models described in the text. The expressions of enhancement factors reflect the nonlinear correlation characteristics of two fundamental light beams in the process of sum-frequency generation. In the part of numerical simulation, firstly, we draw contour plots of output power as functions of reflectivity of the input couplers at two input frequencies in the doubly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input couplers under the condition of different powers of input fundamental light. Secondly, we draw the contour plots of output power as functions of the reflectivity of the input coupler at the resonant frequency, and the input power of non-resonant frequency light in the singly resonant sum-frequency system by theoretical simulation, and achieve an optimum reflectivity of the input coupler at the resonant frequency. These optimum values enable the system to achieve impedance matching; consequently, the sum-frequency conversion efficiency is improved. Finally, this paper analyzes the infuence of input power on the impedance matching, and shows that the optimal coupling mirror reflectivity of the resonant fundamental frequency will decrease with the increase of incident power of the other resonant or non-resonant fundamental frequency laser, otherwise, the resonant incident power of its own has less influence on the optimal coupling mirror reflectivity, whether the system undergoes doubly resonant or singly resonant sum-frequency. In addition, if the coupling mirror reflectivity exceeds the optimum value, the power of sum-frequency light will decrease rapidly, while if it is less than the optimum value, the power of sum-frequency light decreases relatively slowly. Therefore an input coupler that may yield over-coupling should be avoided. These results will have a certain guiding significance to related experiments.