定义：
在一些过程中（如非线性相互作用），由于相位匹配程度的精确与否导致这些过程只在一定宽度的光谱范围内有效

参量的非线性相互作用只有当相位匹配条件满足时才会实现高效率的能量交换。这意味着，该相互作用的光波在传播方向上保持着一个恒定的相位关系。但是由于色散的存在，相位匹配只能在一个有限的带宽内实现，这是由于相互作用的光波的群速度失配导致的。例如，对于角频率泵浦光，信号光和闲散光角频率分别为ωp，ωs和ωi 的光学参量振荡器，其相位失配为： 

如果信号光的频率是变化的，而泵浦光的频率是恒定的，那么相位失配为： 

其中，第二项是因为闲散光频率会自动调整到修改后的信号频率。这两个微分项对应着两个光波的群速度的倒数。相位匹配带宽通常定义为相位失配（在器件整个长度下的累积量）为2.7831弧度时的带宽。（这对应的转换效率为一半）。对于长度为L的晶体，这意味着该相位匹配带宽是 

改进的相位匹配带宽会根据不同情况有不同的定义，例如，对于信号光波长固定而泵浦光波长变化的情况，上式中则应为泵浦光和闲散光之间的群速度失配。 
相位匹配带宽的时域等效为时域走离，由群速度失配导致。 
有时，在一些文献中会出现接收角带宽和角相位匹配带宽之类的术语。它们指的是临界相位匹配情况下的传播角度范围。这种角带宽与空间走离相关。
 

Definition: the width of an optical frequency range in which some process (e.g. a nonlinear interaction) can be efficient due to more or less precise phase matching

A parametric nonlinear interaction can lead to an efficient exchange of energy only when phase matching is achieved. Essentially this means that a constant phase relationship between the interacting waves is maintained along the propagation direction. Due to chromatic dispersion, phase matching can be achieved only in a limited bandwidth, which is related to the group velocity mismatch of the interacting waves. For example, consider an optical parametric oscillator with angular frequencies ω_p, ω_s and ω_i for pump, signal and idler, respectively. The phase mismatch is given by a difference of wavenumbers:

If the signal frequency is varied while the pump frequency is constant, the phase mismatch varies according to

where the second term arises from the fact that the idler frequency automatically adjusts itself to the modified signal frequency. The two derivatives can be related to the inverse group velocities of the two waves, as indicated in the equation. The phase-matching bandwidth is usually defined as the bandwidth in which the phase mismatch (as is accumulated over the whole length of the device) varies by 2.7831 rad. (This corresponds to the half-width of the conversion efficiency curve.) For a crystal with length L, this means that the phase-matching bandwidth is

Modified phase-matching bandwidth parameters can be defined for different conditions, e.g. for the variation of the pump wavelength for a fixed signal wavelength, where the group velocity mismatch between pump and idler occurs in the equation.

The time-domain equivalent of a limited phase-matching bandwidth is a temporal walk-off, as is already apparent from the fact that the group velocity mismatch is involved.

Angular Phase-matching Bandwidth

Sometimes, the terms angular acceptance bandwidth and angular phase-matching bandwidth occur in the literature. They basically mean the range of propagation angles for which critical phase matching can be achieved. The angular bandwidth is related to spatial walk-off.