  A fundamental building block for on-chip quantum photonics is a single-photon
source with high repetition rates, which can enable many applications such as
high-speed quantum communication and quantum information processing. Ideally,
such single photon sources would then require a large on-chip photon extraction
decay rate, namely the rate of excited photons coupled into nanofibers or
waveguides, over a broad spectral range. However, this goal has remained
elusive till date. Here we propose a feasible scheme to enhance the on-chip
photon extraction decay rate of quantum emitters, through the tilting of the
optical axis of hyperbolic metamaterials with respect to the end-facet of
nanofibers. Importantly, the revealed scheme is applicable to arbitrarily
orientated quantum emitters over a broad spectral range, e.g., up to ~80 nm for
visible light. The underlying physics relies on the emerging unique feature of
hyperbolic metamaterials if their optical axis is judiciously tilted. That is,
their supported high-k (i.e., wavevector) hyperbolic eigenmodes, which are
intrinsically confined inside them if their optical axis is un-tilted, can now
become momentum-matched with the guided modes of nanofibers, and more
importantly, they can safely couple into nanofibers almost without reflection.
