The Impact of Standing Waves in the LO path of a Heterodyne Receiver

Many observations of molecular lines in interstellar space or planetary atmospheres are affected by serious problems with standing wave patterns in the spectra. This becomes particularly nasty when studying broad extragalactic or pressure broadened atmospheric lines. When observing at THz frequencies these problems become more and more prominent due to the increased required bandwidth. Mostly, such patterns are attributed to reflections in the telescope optics, particularly from the sub-reflector in a Cassegrain telescope. But there are many other sources of standing waves in the quasi-optics of a heterodyne receiver. In this paper we describe the effect of reflections between mixer and local oscillator (LO) inside of a receiver. Some portion of the signal radiation becomes reflected by the mixer, and propagates partly to the LO with reduced amplitude due to the generally small reflectivity of the beam combiner. Nevertheless, although the power in one roundtrip becomes significantly reduced, there is still enough amplitude left, so that interference with the incoming signal radiation becomes visible. The situation is depicted in Fig.1. In the figure the local oscillator and mixer reflectivity is indicated by the power reflection coefficients rL and rM respectively. The beam splitter reflects and transmits the power with coefficients r and t. The field of the LO at the mixer is composed of the superposition of all partial beams which are reflected back and forth between the LO and the mixer. Consequently, after summing up all partial beams, the total LO power coupled to the mixer is: ) ( 0 L L L A P r P ν ⋅ ⋅ = with ( ) 1 2 2 )] / 2 ( sin 4 1 [ ) ( − ⋅ ⋅ ⋅ + − = ν π ν c s u u A PL0 is the power of the LO itself as is incident on the beam splitter, and νL is the LO frequency. A(ν) is the Airy-function as is well known for optical resonators. u = r·√rM·√rL is the roundtrip efficiency for the field amplitude within the cavity, s is the optical path length between mixer and LO, and c is the speed of light.