提出了在一定的条件下，周期函数经过线性正则变换，结果仍然是周期函数，即利用线性正则变换可以产生泰伯效应，并从理论上给出了证明，得出了产生泰伯效应的条件。推导了特殊形式的线性正则变换（菲涅耳衍射、分数傅里叶变换和Gyrator变换）产生泰伯效应的条件，通过数值模拟验证了Gyrator变换的自成像条件，证明了该理论的正确性，从而将泰伯效应推广到了线性正则变换域。

The virtual source for generation of rotational symmetric Lorentz-Gaussian (RLG) wave whose propagating dynamics present the rotational symmetry is identified. Closed-form expressions, including integral and differential representations, are derived for this kind of Lorentz-Gaussian (LG) wave, thereby yielding paraxial approximation of the RLG beam in the appropriate regime. From the spectral representation of this wave, the first three order corrections of nonparaxial approximations are determined for a corresponding paraxial RLG beam. Moreover, the relationship between the RLG beam and the Hermite-Gaussian beam is revealed.