  The locking of lasers to optical cavities is ubiquitously required in the
field of precision interferometry such as Advanced LIGO to yield optimal
sensitivity. Using higher-order Hermite-Gauss (HG) modes for the main
interferometer beam has been a topic of recent study, due to their potential
for reducing thermal noise of the test masses. It has been shown however that
higher-order HG modes are more susceptible to coupling losses into optical
cavities: the misalignment and mode mismatch induced power losses scale as
$2n+1$ and $n^{2}+n+1$ respectively with $n$ being the mode index. In this
paper we calculate analytically for the first time the alignment and mode
mismatch sensing signals for arbitrary higher-order HG modes with both the
traditional sensing schemes (using Gouy phase telescopes and quadrant
photodetectors) and the more recently proposed radio-frequency jitter-based
sensing schemes (using only single element photodiodes). We show that the
sensing signals and also the signal-to-shot noise ratios for higher-order HG
modes are larger than for the fundamental mode. In particular, the alignment
and mode mismatch sensing signals in the traditional sensing schemes scale
approximately as $\sqrt{n}$ and $n$ respectively, whereas in the jitter-based
sensing schemes they scale exactly as $2n+1$ and $n^{2}+n+1$, respectively,
which exactly matches the decrease in their respective tolerances. This
potentially mitigates the downside of higher-order HG modes for their suffering
from excessive misalignment and mode-mismatch induced power losses.
