  With the recent discovery of Gravitational waves, marking the start of the
new field of GW astronomy, the push for building more sensitive
laser-interferometric gravitational wave detectors (GWD) has never been
stronger. Balanced homodyne detection (BHD) allows for a quantum noise limited
readout of arbitrary light field quadratures, and has therefore been suggested
as a vital building block for upgrades to Advanced LIGO and third generation
observatories. In terms of the practical implementation of BHD, we develop a
full framework for analyzing the static optical high order modes (HOMs)
occurring in the BHD paths related to the misalignment or mode matching at the
input and output ports of the laser interferometer. We find the effects of HOMs
on the quantum noise limited sensitivity is independent of the actual
interferometer configuration, e.g. Michelson and Sagnac interferometers are
effected in the same way. We show that output misalignment only effects the
high frequency part of the quantum noise limited sensitivity. However, at low
frequencies, HOMs reduce the interferometer response and the radiation pressure
noise by the same amount and hence the quantum noise limited sensitivity is not
negatively effected. We show that the input misalignment to the interferometer
produces the same effect as output misalignment and additionally decreases the
power inside the interferometer. We also analyze dynamic HOM effects, such as
beam jitter created by the suspended mirrors of the BHD. Our analyses can be
directly applied to any BHD implementation in a future GWD. Moreover, we apply
our analytical techniques to the example of the speed meter proof of concept
experiment under construction in Glasgow. We find that for our experimental
parameters, the performance of our seismic isolation system in the BHD paths is
compatible with the design sensitivity of the experiment.
