  The effect of strong confinement on the positional and orientational ordering
is examined in a system of hard rectangular rods with length L and diameter D
(L>D) using the Parsons-Lee modification of the second virial density
functional theory. The rods are nonmesogenic (L/D<3)and confined between two
parallel hard walls, where the width of the pore (H) is chosen in such a way
that both planar (particle's long axis parallel to the walls) and homeotropic
(particle's long axis perpendicular to the walls) orderings are possible and a
maximum of two layers are allowed to form in the pore. In the extreme
confinement limit of ,where only one layer structures appear, we observe a
structural transition from a planar to a homeotropic fluid layer with
increasing density, which becomes sharper as L->H. In wider pores (2D<H<3D)
planar order with two layers, homeotropic order, and even combined bilayer
structures (one layer is homeotropic, while the other is planar) can be
stabilized at high densities. Moreover, first order phase transitions can be
seen between different structures. One of them emerges between a monolayer and
a bilayer with planar orders at relatively low packing fractions.
