  Exceptional points (EPs) are singularities in non-Hermitian systems, where
the system transmission spectrum varies significantly at the phase transition
point. Here, we propose a practical scheme to study the changes of the
optomechanically induced transparency (OMIT) spectrum on the exceptional
surface (ES), which is formed by designing the structure of the waveguide in a
non-Hermitian cavity optomechanical system. By comparing the transmission
spectra of the system at different normal points, EPs on the same or different
ESs, and exceptional derived points, we find that the peak-valley conversion of
the system transmission spectra is obtained at the phase transition point and
the arbitrary manipulation of the system transmission spectrum can be realized
by moving the system on the same or different ESs. Furthermore, the phenomena
of conversion and enhancement of the fast-slow light in the system transmission
spectra have also been discovered in our researches. Different from the
isolated EP, our proposal can discuss the system properties at different EPs,
can find a richer transmission spectrum, and can provide more convenient
options for experimental implementation, which paves the way for studying the
nature of non-Hermitian systems in a higher dimension.
