定义：
常用的一种近似，假设传播方向与光束轴之间的夹角很小。

采用傍轴近似可以简化许多光学中的计算，即假设光（例如，一些激光光束）的传播方向与光束轴之间的夹角很小。 

几何光学中的傍轴近似 
几何光学（射线光学）采用几何射线来描述光的传播。这时傍轴近似表示射线与光学系统的一些参考轴之间的夹角 θ 非常小，远小于1rad。在该近似下，可以假设tan θ ≈ sin θ ≈ θ。一些光学系统的光束偏移量（与参考轴之间的距离）和光束角的变化可由简单的ABCD矩阵来描述，偏移量和角度在光学元件或系统前后都是线性关系。 

波动光学中的傍轴近似 
将光看做波动现象时，能量的传播方向可认为与波前方向垂直（存在空间游走时除外）。如果傍轴近似成立，即传播方向接近于参考轴，二阶微分方程（由麦克斯韦方程得到）变成简单的一阶方程。根据得到的方程，得到高斯光束满足的方程，能够简单的理解光束传播机制以及一些基本限制因素，例如，最小光束参数乘积。当发散角保持小于1rad时，傍轴近似始终是满足的。并且束腰处的光束半径需要远大于波长。 
波导，尤其是光纤中的模式传播计算也是基于傍轴近似。因此分析的准确性要求波导中所有光束的有效模式面积足够大，并且发散角足够小。 
激光物理和光纤光学中许多现象都满足傍轴近似，但是在紧束缚情况下是不满足的。在这种情况下，偏振问题也需要仔细考虑，尤其是传播方向上的偏振分量。因此，光束传播需要采用更加复杂的方法。例如，可以采用光束传播方法（二维复电场振幅数列的传播），无需采用傍轴近似。 

Definition: a frequently used approximation, essentially assuming small angular deviations of the propagation directions from some beam axis

Many calculations in optics can be greatly simplified by making the paraxial approximation, i.e. by assuming that the propagation direction of light (e.g. in some laser beam) deviates only slightly from some beam axis.

Paraxial Approximation in Geometrical Optics

Geometrical optics (ray optics) describes light propagation in the form of geometric rays. Here, the paraxial approximation means that the angle θ between such rays and some reference axis of the optical system always remains small, i.e. ≪ 1 rad. Within that approximation, it can be assumed that tan θ ≈ sin θ ≈ θ. The evolution of beam offset (distance from the reference axis) and beam angle in some optical system can then be described with simple ABCD matrices, because there are linear relations between offset and angle of beams before and after some optical component or system. The paraxial approximation is extensively used in Gaussian optics.

Paraxial Approximation in Wave Optics

When describing light as a wave phenomenon, the local propagation direction of the energy can be identified with a direction normal to the wavefronts (except in situations with spatial walk-off). If the paraxial approximation holds, i.e. these propagation directions are all close to some reference axis, a second-order differential equation (as obtained from Maxwell's equations) can be replaced with a simple first-order equation. Based on this equation, the formalism of Gaussian beams can be derived, which gives a much simplified understanding of beam propagation and of fundamental limitations such as the minimum beam parameter product. Essentially, the paraxial approximation remains valid as long as divergence angles remain well below 1 rad. This also implies that the beam radius at a beam waist must be much larger than the wavelength.

The propagation modes of waveguides, particularly of optical fibers, are also often investigated based on the paraxial approximation. The validity of the analysis is then restricted to cases with a sufficiently large effective mode area and sufficiently small divergence of any beams exiting such a waveguide.

The paraxial approximation is very well fulfilled in a wide range of phenomena of laser physics and fiber optics, but it is clearly violated in cases with very strong focusing, where commonly used equations such as θ = λ / (π w₀) for the divergence angle break down. In that regime, polarization issues also demand special care. In particular, polarization components in the propagation direction can occur. For such reasons, the simulation of beam propagation then requires significantly more sophisticated methods. For example, beam propagation methods (propagating a two-dimensional array of complex field amplitudes) can be used which do not need that approximation.