Investigation in hollow Gaussian beam from vectorial structure

The description of hollow Gaussian beam is directly started from the Maxwell's equations. Based on the vector angular spectrum representation of Maxwell's equations, hollow Gaussian beam is decomposed into the TE and TM terms. The analytical expressions of TE and TM terms are presented by means of mathematical techniques in the near field. By means of the method of stationary phase, the concise expressions of TE and TM terms in the far field have been also derived. The TE and TM terms are shown to be orthogonal to each other in the far field. According to the analytical representations of TE and TM terms, the light intensity distributions of the TE term, the TM term and the whole beam are depicted in the near and the far fields, respectively. The result obtained here is also compared with already known solutions. This research reveals the vectorial composition of hollow Gaussian beam, which is beneficial to enhance the applications of hollow Gaussian beam.