  Recently, there has been a drive towards the realization of topological
phases beyond conventional electronic materials, including phases defined in
more than three dimensions. We propose a versatile and experimentally realistic
approach of realizing a large variety of multi-component topological phases in
2D photonic crystals with quasi-periodically modulated defects. With a length
scale introduced by a background resonator lattice, the defects are found to
host various effective orbitals of $s$, $p$ and $d$-type symmetries, thus
providing a monolithic platform for realizing multi-component topological
states without requiring separate internal degrees of freedom in the physical
setup. Notably, by coupling the defect modulations diagonally, we report the
novel realization of an ``entangled'' 4D QH phase which cannot be factorized
into two copies of 2D QH phases, each described by the 1st Chern number. The
structure of this non-factorizability can be quantified by a classical
entanglement entropy inspired by quantum information theory. In another
embodiment, we present 4D p-orbital nodal lines in a nonsymmorphic photonic
lattice, hosting boundary states with an exotic manifold. Our simple and
versatile approach holds the promise of novel topological optoelectronic and
photonic applications such as one-way optical fibers.
