定义：
由厄米-高斯方程描述的传播模式或谐振腔模式。

当光在自由空间或者各向同性光学介质中传播时，其强度截面会发生变化。而对于某些特定的电场分布，则不会这样：振幅截面形状是保持不变的，尽管有时光学相位和总光功率会发生变化。 
每一种光频率、光轴、焦点位置以及高斯光束在焦点处的光束半径的组合，组成了厄米高斯模式（TEMnm模）。若聚焦的情况下（傍轴近似），波动方程具有近似解。电场分布等于高斯方程与厄米多项式的乘积还有相位项： 

 

其中Hn(x) 为厄米多项式，指数n为大于等于0的整数。n和m决定了再x和y方向的形状。而w和R则在z方向上发生改变。 

Definition: propagation modes or resonator modes which are described with Hermite–Gaussian functions

More general terms: modes

When light propagates in free space or in a homogeneous optical medium, its intensity profile will generally change during propagation. For certain electric field amplitude distributions, however, which are called modes, this is not the case: the shape of the amplitude profile remains constant, even though there may be a re-scaling of the profile, an overall change in optical phase, and possibly also a change in the total optical power.

For each combination of an optical frequency, a beam axis, a focus position, and some beam radius of a Gaussian beam in the focus, there is a whole family of Hermite–Gaussian modes (TEM_nm modes, Gauss–Hermite modes). These are approximate solutions of the wave equation, valid for weak focusing (→ paraxial approximation). Their electric field distributions are essentially given by the product of a Gaussian function and a Hermite polynomial, apart from the phase term:

where H_n(x) is the Hermite polynomial with the non-negative integer index n. The indices n and m determine the shape of the profile in the x and y direction, respectively. The quantities w and R evolve in the z direction as described in the article on Gaussian beams.

The intensity distribution of such a mode (Figure 1) has n nodes in the horizontal direction and m nodes in the vertical direction. For n = m = 0, a Gaussian beam is obtained. This mode is called the fundamental mode or axial mode, and it has the highest beam quality with an M² factor of 1. Other Hermite–Gaussian modes with indices n and m have an M² factor of (1 + 2 n) in the x direction, and (1 + 2 m) in the y direction.

Figure 1: Intensity profiles of the lowest-order Hermite–Gaussian modes, starting with TEM₀₀ (lower left-hand side) and going up to TEM₃₃ (upper right-hand side).

A further generalization of the equation above would allow for different mode sizes and focus positions (astigmatism) for the x and y directions. The direction of the electric field, not specified in the equation above, determines the polarization.

The electric field distributions of the Hermite–Gaussian modes are a system of functions which are mutually orthogonal. Arbitrary field distributions can be decomposed into Hermite–Gaussian functions, where the amplitude content of each one is determine by an overlap integral.

Hermite–Gaussian modes can often be used to represent the modes of an optical resonator, if the optical elements in the resonator only do simple changes to the phase and intensity profiles (e.g., approximately preserving parabolic phase profiles) and the paraxial approximation is satisfied. As these conditions are very often fulfilled in laser resonators, laser resonator modes are often of Hermite–Gaussian kind. If such a laser operates on a single mode, a characteristic intensity profile of the output beam as in Figure 1 can be observed.

Another frequently used mode family is that of Laguerre–Gaussian modes, which fit better to situations with a rotational symmetry, because they are based on polar coordinates. Note, however, that lasers often contain components placed at a slight angle against the beam, which breaks rotational symmetry. Therefore, Hermite–Gaussian modes are often better suited for laser beams.