  An exact closed-form representation is derived of a vector elegant
Laguerre-Gaussian wave packet. Its space-time representation consists of three
mutually orthogonal field components - of a common azimuthal index and
different radial indices - uniquely distinguished by first three powers of the
paraxial parameter. The transverse components are of tm-radial and te-azimuthal
polarization and appear, under their normal incidence, to be eigenmodes of any
horizontally planar, homogeneous and isotropic structure, with eigenvalues
given by the reflection and transmission coefficients. In this context, the
interrelations between the cross-polarization symmetries of wave packets in
free space and at medium planar interfaces are discussed.
