Naruse H, Tateda M
Access Network Service Systems Laboratories, NTT, 1-7-1, Hanabatake, Tsukuba, Ibaraki 305-0805 Japan.
Appl Opt. 2000 Dec 1;39(34):6376-84. doi: 10.1364/ao.39.006376.
We theoretically analyze the relationship between the electric field envelope shape of an optical pulse launched into an optical fiber and the power spectrum of the spontaneous Brillouin backscattered light it produces. The electric field envelope is characterized by the pulse width, leading-trailing time, and steepness. The peak power of the launched, pulsed-light power spectrum is proportional to the square of the pulse width regardless of the pulse leading-trailing time and steepness, and the power spectrum broadens in inverse proportion to the pulse width. The peak power of the spontaneous Brillouin backscattered light produced by the launched, pulsed light is proportional to the pulse width when it is above approximately 100 ns and is proportional to the square of the pulse width when it is below approximately 1 ns. The power spectrum of the spontaneous Brillouin backscattered light also broadens rapidly corresponding to the pulse width, when the pulse width falls below approximately 30 ns. As the pulse leading-trailing time is shortened or the pulse leading-trailing part becomes steep, the Brillouin backscattered-light power spectrum broadens greatly, even if the launched pulse width remains constant. Our analysis showed that an optical pulse with a triangular-shaped electric field envelope forms the Brillouin backscattered-light power spectrum with the narrowest profile and consequently gives the minimum error in measuring the peak-power frequency, when the pulse width is below approximately 50 ns. The measurement error with the triangular-shaped pulsed light is 1/square root(2) times smaller than that for a rectangular-shaped pulsed light, when the pulse width falls below several nanoseconds. By contrast, the rectangular-shaped envelope gives the minimum error when the pulse width exceeds approximately 50 ns.
我们从理论上分析了输入光纤的光脉冲电场包络形状与其产生的自发布里渊后向散射光功率谱之间的关系。电场包络由脉冲宽度、前沿-后沿时间和陡度来表征。无论脉冲的前沿-后沿时间和陡度如何，输入的脉冲光功率谱的峰值功率与脉冲宽度的平方成正比，且功率谱与脉冲宽度成反比展宽。当输入的脉冲光产生的自发布里渊后向散射光的脉冲宽度大于约100 ns时，其峰值功率与脉冲宽度成正比；当脉冲宽度小于约1 ns时，其峰值功率与脉冲宽度的平方成正比。当脉冲宽度降至约30 ns以下时，自发布里渊后向散射光的功率谱也会随着脉冲宽度迅速展宽。随着脉冲前沿-后沿时间缩短或脉冲前沿-后沿部分变陡，即使输入脉冲宽度保持不变，布里渊后向散射光功率谱也会大幅展宽。我们的分析表明，当脉冲宽度小于约50 ns时，具有三角形电场包络的光脉冲形成的布里渊后向散射光功率谱轮廓最窄，因此在测量峰值功率频率时误差最小。当脉冲宽度降至几纳秒以下时，三角形脉冲光的测量误差比矩形脉冲光小1/√2倍。相比之下，当脉冲宽度超过约50 ns时，矩形包络的误差最小。
