窄线宽激光器的线宽表征方式通常采用延时自外差法测量技术。 该技术是通过延时光纤差拍产生一个与待测激光线宽相关的洛伦兹频谱, 因此该频谱只具有单一的线宽表现形式。 为了能够观察到激光器的线宽和频率噪声在其傅里叶频率分布下的完整特性, 报道了一种基于β算法计算窄线宽激光器线宽的方法。 该方法是结合频率噪声中的白噪声和1/f噪声分别诱导不同激光线型的理论, 从而确定激光线宽。 首先, 对β算法的基本原理进行了详细的分析说明。 通过基于维纳-辛钦定理, 分析了窄线宽激光器不同频率范围内的频率噪声和激光线宽的依赖关系。 阐明了在截止频率趋于0和无穷大的两个范围条件时, 激光频谱特性从高斯线型向洛伦兹线型演变。 同时推导出使两种线型转换的截止频率表达式, 并将其转换为频率噪声函数, 该函数定义为β分子线。 此时频率噪声分量中高斯线型的总和即为激光线宽计算公式; 其次, 对窄线宽激光器的频率噪声和激光线型进行数值仿真。 将通过OEwaves公司的OE4000互相关零差相位/频率噪声自动测试系统测得的频率噪声谱密度, 带入β算法理论公式中。 结果显示: 1/f噪声导致激光呈现高斯线型, 线宽随截止频率的增加而增大。 而白噪声将导致洛伦兹线型, 线宽不再随截止频率而改变。 此外, 在低频区域, 频率噪声电平远大于其傅里叶频率, 噪声调制系数较高, 该部分噪声可以决定线宽大小。 因此, 高斯线型区域对应的频率噪声的积分, 即为待测激光器的线宽; 在高频区域, 频率噪声电平与其傅里叶频率相差较小, 频率波动较快, 噪声对线宽影响可以忽略。 并且频率带宽在截止频率范围内, 计算的线宽误差较小。 最后, 实验上运用β算法对RIO公司的1 550 nm低噪声窄线宽激光器的频率噪声功率谱密度进行积分计算, 成功获得了其不同傅里叶频率分布下对应的激光线宽值。 其中β分子线将频率噪声中的白噪声和1/f噪声分隔两部分: 当频率噪声谱密度大于β分子线时, 激光即为高斯线型, 线宽随频率积分带宽的增加而减少; 而频率噪声谱密度小于β分子线时, 激光呈现洛伦兹线型, 线宽为定值不再改变。 同时为了对β算法进行实验验证, 搭建了延迟光纤为50 km、 移频频率为60 MHz的延时自外差法测量系统。 对注入电流为110 mA的RIO 1 550 nm低噪声窄线宽激光器的线宽进行实验测量, 测量结果表明激光线宽为1.8 kHz, 与上述β算法中2.8 kHz的频率带宽积分结果一致。 充分证明了此算法的准确性。 β算法可以对任意类型的窄线宽激光器进行线宽表征, 对窄线宽激光器的研究具有重要意义。

Traditional laser linewidth characterization is usually done by introducing a self-heterodyne technique. This technique is an optical fiber delay based on laser beat note, which generates a Lorentzian spectrum related to the linewidth of a laser. In order to obtain the complete characteristics of a laser linewidth and frequency noise spectrum in its frequency domain, a new method based on β algorithm is proposed. The basic principles of the β algorithm have been analyzed and explained at first. The relationship between frequency noise and laser linewidth in different frequency ranges are analyzed based on the Wiener-Khintchine theorem. When the cut-off frequency tends to be zero or infinity, the laser line shape evolves from Gaussian type to Lorentzian type. Meanwhile, the cut-off frequency of the conversion laser line shape has been deduced, which is represented by the frequency noise function, namely β separation line. Secondly, the frequency noise spectral density has been measured with OE4000 test system. The frequency noise and the line shape of diode lasers are numerically simulated. In the low frequency region, where the noise level is much larger than its frequency, it produces a slower frequency modulation than that in the high frequency region. The linewidth of the laser is an integration of the frequency noise in the Gaussian line shape region. The error in linewidth calculation is smaller over the entire cut-off frequency range. Finally, a set of measured frequency noise power spectral density of a RIO’s laser was used to calculate the linewidth using the β algorithm. When the frequency noise spectral density is greater than the β separation line, the laser appears as a Gaussian line shape and the linewidth decrease with frequency banwidth; on the contrary, the laser shows a Lorentzian line shape, and the linewidth is fixed. Meanwhile, a delayed self-heterodyne measurement system with delay fiber of 50 km and frequency shift of 60 MHz is constructed. The measured linewidth of a RIO’s laser working under 110 mA inject current is about 1.8 kHz, which is consistent with the calculated result of the β algorithm, of which the frequency bandwidth is ~2.8 kHz. In conclusion, β algorithm is able to characterize the linewidth of any type of narrow linewidth laser, which is of great significance to the research on narrow linewidth lasers.