定义：
脉冲的脉宽和谱宽的乘积。
脉冲的时间带宽积指的是其时域脉宽和光谱宽度的乘积。在超快激光物理中脉宽和谱宽通常指的都是半高全宽（FWHM）。带宽极限脉冲具有最小的时间带宽积。高斯型脉冲的最小的时间带宽积约为0.44，双曲正割型脉冲的最小的时间带宽积约为0.315。因此对于一个给定的谱宽，其脉冲有着一个最小值下限。这个限制是由傅立叶变换的性质决定的。
时间带宽积通常用于表征脉冲脉宽距离其变换极限脉宽的距离。这是“脉冲质量”的一个很重要的方面；带宽极限脉冲具有其所能得到的最小的时间带宽积，而啁啾脉冲则具有较大的时间带宽积。许多锁模激光器可以产生近乎带宽极限的脉冲，尤其是当它们是基于孤子锁模的时候。
Acronym: TBP
Definition: product of temporal and spectral width of a pulse
Alternative term: duration–bandwidth product
Units: (dimensionless number)
The time–bandwidth product of a light pulse is the product of its temporal duration and spectral width (in frequency space). In ultrafast laser physics, it is common to specify the full width at half-maximum (FWHM) in both time and frequency domain. The minimum possible time–bandwidth product is obtained for bandwidth-limited pulses. For example, it is ≈ 0.315 for bandwidth-limited sech2-shaped pulses and ≈ 0.44 for Gaussian-shaped pulses. This means that for a given spectral width, there is a lower limit for the pulse duration. This limitation is essentially a property of the Fourier transform. It is also related to the time–energy uncertainty principle in quantum mechanics.
The time–bandwidth product (also sometimes called duration–bandwidth product) is often used for indicating how close a pulse is to the transform limit, i.e., how close the pulse duration is to the limit which is set by its spectral width. This is an aspect of “pulse quality”; bandwidth-limited pulses have the minimum possible time–bandwidth product, whereas chirped pulses have larger values. Many mode-locked lasers can generate nearly bandwidth-limited pulses, particularly when they are based on soliton mode locking. A high pulse quality then often means a time–bandwidth product well below 0.5.
Note that some pulses have a pedestal which is much broader than its FWHM; that is essentially ignored when specifying just the TBP, although a pedestal can also be an important aspect of (degraded) pulse quality.
