提出了用波导本征模展开的方法计算射频调制的短脉冲电子束在矩形波导中的自发辐射。模展开系数决定了辐射进入ＴＥ（０ｎ）模的功率。将短脉冲理想化为时间上的δ函数，可以发现当辐射频率正好等于用来调制电子束的射频的整数倍时，辐射模式表现为“纯”的波导本征模，此时辐射功率最强。用此方法估算了设计中的上海远红外波导自由电子激光器的辐射功率。 Proposed the method of waveguide eigenmode expansion to calculate the spontaneous emission of RF modulated short pulse electron beam in a rectangular waveguide. The modulo expansion coefficient determines the power radiated into the TE (0n) mode. By idealizing the short pulse as a delta function over time, it can be found that the radiation pattern behaves as a “pure” waveguide eigenmode when the radiation frequency is exactly equal to an integral multiple of the radio frequency used to modulate the electron beam, at which point the radiation power is strongest . Using this method, the radiation power of Shanghai Far Infrared Waveguide free-electron laser in the design was estimated.