  Detections of gravitational waves (GW) in the frequency band 35 Hz to 500 Hz
have led to the birth of GW astronomy. Expected signals above 500 Hz, such as
the quasinormal modes of lower mass black holes and neutron star mergers
signatures are currently not detectable due to increasing quantum shot noise at
high frequencies. Squeezed vacuum injection has been shown to allow broadband
sensitivity improvement, but this technique does not change the slope of the
noise at high frequency. It has been shown that white light signal recycling
using negative dispersion optomechanical filter cavities with strong optical
dilution for thermal noise suppression can in principle allow broadband high
frequency sensitivity improvement. Here we present detailed modelling of
AlGaAs/GaAs optomechanical filters to identify the available parameter space in
which such filters can achieve the low thermal noise required to allow useful
sensitivity improvement at high frequency. Material losses, the resolved
sideband condition and internal acoustic modes dictate the need for resonators
substantially smaller than previously suggested. We identify suitable resonator
dimensions and show that a 30 $\mu$m scale cat-flap resonator combined with
optical squeezing allows 8 fold improvement of strain sensitivity at 2 kHz
compared with Advanced LIGO. This corresponds to a detection volume increase of
a factor of 500 for sources in this frequency range.
