  Vector modes are well-defined field distributions with spatially varying
polarisation states, rendering them irreducible to the product of a single
spatial mode and a single polarisation state. Traditionally, the spatial degree
of freedom of vector modes is constructed using two orthogonal modes from the
same family. In this letter, we introduce a novel class of vector modes whose
spatial degree of freedom is encoded by combining modes from both the Hermite-
and Laguerre-Gaussian families. This particular superposition is not arbitrary,
and we provide a detailed explanation of the methodology employed to achieve
it. Notably, this new class of vector modes, which we term Hybrid
Hermite-Laguerre-Gaussian (HHLG) vector modes, gives rise to subsets of modes
exhibiting polarisation dependence on propagation due to the difference in mode
orders between the constituent Hermite- and Laguerre-Gaussian modes. To the
best of our knowledge, this is the first demonstration of vector modes composed
of two scalar modes originating from different families. We anticipate diverse
applications for HHLG vector modes in fields such as free-space communications,
information encryption, optical metrology, and beyond.
