# What are the reasons for a high intermediate frequency in optical heterodyne detection?

In balanced homodyne or heterodyne detection, an optical signal (Sig) is interfered with a local oscillator (LO) on a symmetric beam splitter, e.g., a 3 dB fiber coupler, and the outcome is detected by a pair of photodiodes. The output photocurrents from these diodes can be subtracted (and amplified) to yield a difference current $I_{diff} \propto \sqrt{P_{LO}} \sqrt{P_{Sig}} \cos(\omega_{IF}t + \theta_{Sig}(t) - \theta_{LO}(t) )$, where $\omega_{IF} = \omega_{Sig} - \omega_{LO}$ is the intermediate frequency. In case of homodyne detection, $\omega_{IF} = 0$.

In this book chapter Coherent Optical Communications: Historical Perspectives and Future Directions, the author K. Kikuchi repeatedly states that heterodyne receivers require a rather high intermediate frequency, but without mentioning any specific reasons. For instance, section 2.2.2 starts with the statement Heterodyne detection refers to the case when $\omega_{IF} >> \omega_{b}/2$, where $\omega_{b}$ is the modulation bandwidth of the optical carrier determined by the symbol rate''.

As far as I can understand, the perils of choosing a low $\omega_{IF}$ are that typical optical communication diode lasers generally tend to be more noisy at low frequencies. They have high relative intensity noise (RIN) starting from very low frequencies until the $10$s of MHz frequencies. The phase noise, which is essentially the time derivative of $\theta_{SigNoise}(t) - \theta_{LO}(t)$, with $\theta_{Sig}(t) = \theta_{SigNoise}(t) + \theta_{SigMod}(t)$, may also have components in the few MHz to GHz regime. But is that all, or are there more reasons?

More specifically, if one were to choose very narrow linewidth lasers (which intrinsically have a low phase noise) that also have a low RIN, are there any other factors one needs to take care about?