  A photonic spectrograph can be much smaller than a conventional spectrograph
with the same resolving power. Individual devices can be integrated with
optical fibres to improve the multiplex gain in astronomical spectroscopy.
Although experimental devices have been tested, the parameter space where
integrated photonic spectrographs give a significant advantage over traditional
methods has not been defined. This paper gives an overview of the theory with
verification by direct simulation using Fresnel propagation and quantifies the
benefit for representative spectroscopic capabilities. We thereby confirm the
advantage of photonic spectrographs, especially to the next generation of
Extremely Large Telescopes, and therefore conclude that these devices may be
important for the future development of astronomical instrumentation.
