Local oscillator (LO)

A local oscillator is a reference wave generated at the receiver and mixed with the incoming signal, so that the detector responds to the product of the two fields. In optical coherent detection it is a continuous-wave laser, tuned close to the signal's optical frequency and much stronger than the signal: about 10 mW (+10 dBm) in telecom receivers, against received signals of microwatts or less. The term comes from radio, where a local oscillator converts the received carrier to an intermediate frequency; the optical version does the same, with the photodiode acting as the mixer.

Beat term and gain

A photodiode responds to intensity, the square of the total field. With signal power $P_s$ and LO power $P_\text{LO}$ on the same polarization, the photocurrent is

$$\begin{aligned} i = \mathcal{R}\big[&P_s + P_\text{LO} \\ &+ 2\sqrt{P_s P_\text{LO}}\cos(\Delta\omega\,t + \Delta\phi)\big], \end{aligned}$$

where $\mathcal{R}$ is the responsivity, $\Delta\omega$ the frequency difference and $\Delta\phi$ the phase difference. The third term is the beat, and it is linear in the signal field: its amplitude follows the signal amplitude and its phase follows the signal phase, which is what allows QPSK and QAM constellations to be read. For $P_s = 1$ µW and $P_\text{LO} = 10$ mW, $2\sqrt{P_s P_\text{LO}} = 200$ µW, so the beat amplitude is 200 times the direct-detection term $\mathcal{R}P_s$, a factor of 46 dB in electrical power. The constant $\mathcal{R}P_\text{LO}$ is removed by balanced detection, which subtracts the two outputs of the optical hybrid, in which the beat terms appear with opposite signs, so the beat adds while the LO's DC level and most of its relative intensity noise cancel.

Shot-noise-limited detection

The gain matters because it lifts the signal above the receiver electronics. The LO's own shot noise grows as $\sqrt{P_\text{LO}}$, the same as the beat, so once the LO is strong enough for its shot noise to exceed the amplifier's thermal noise, the signal-to-noise ratio stops depending on LO power and reaches the shot-noise limit set by the signal photon number alone. With $\mathcal{R} = 0.8$ A/W, 10 mW of LO gives 8 mA of photocurrent and a shot-noise density of $\sqrt{2qI} = 5.1 \times 10^{-11}$ A/√Hz, compared with $1.8 \times 10^{-11}$ A/√Hz for the thermal noise of a 50 Ω load at 290 K: the LO shot noise is 9.0 dB higher in power. The heterodyne detection entry gives the resulting SNR formula and the 3 dB difference between heterodyne and homodyne reception.

Frequency offset and linewidth

The LO is an independent laser, usually a narrow-linewidth tunable laser of the same type as the transmitter; many coherent pluggable modules split one laser between the transmitter and the LO. Three arrangements are named by the offset between LO and signal: homodyne (equal frequency and locked phase), heterodyne (an intermediate frequency above the signal bandwidth), and intradyne, the standard in telecom, where the LO is set near the signal but not locked to it. The residual offset, which is set by how accurately each laser sits on its grid frequency and can reach a few gigahertz, is estimated and removed in the digital signal processor, together with the slow wander of both lasers; what the coherent DSP does describes those stages.

What the DSP cannot remove completely is fast phase noise. The relevant figure is the combined linewidth of transmitter and LO multiplied by the symbol duration. For 16QAM with feedforward carrier-phase recovery, the tolerable product is of order 10⁻⁴ for about 1 dB of penalty, which at 32 GBd is a combined linewidth of about 3 MHz. Commercial integrated tunable lasers specify linewidths of about 100 kHz, leaving margin for 16QAM and making 64QAM practical at today's higher symbol rates; low-cost DFB lasers with linewidths of several megahertz are adequate for QPSK at high symbol rates but not for dense constellations.

Outside telecom

The same principle appears wherever optical phase or frequency is measured. A laser Doppler vibrometer uses a frequency-shifted part of its own laser as LO, and an FMCW lidar beats the return against a copy of the outgoing chirp. In these self-referenced systems the LO and signal share one laser, so phase noise cancels for delays shorter than the coherence time.

Pitfalls

The beat requires matched polarization, so telecom receivers split both signal and LO into two polarizations and detect each separately. The LO's intensity noise appears directly in a single-ended receiver; poor balance in the photodiode pair lets it through. Excess LO power saturates the photodiodes or amplifier without further benefit.

Common questions

Why does a coherent receiver need a local oscillator?

A photodiode detects only power, which discards optical phase. Interfering the signal with a known reference converts phase differences into intensity changes the photodiode can record.

How much LO power is used?

About +10 dBm in telecom coherent receivers, divided among the hybrid outputs and photodiodes. The aim is for LO shot noise to dominate receiver thermal noise without saturating the photodiodes.

Does the LO have to be phase-locked to the signal?

Not in intradyne receivers: the DSP estimates the frequency offset and tracks the phase digitally. Optical phase locking is needed for true homodyne detection and is used mainly in laboratory and some sensing systems.

References: K. Kikuchi, "Fundamentals of coherent optical fiber communications," Journal of Lightwave Technology 34, 157 (2016); G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); M. Seimetz, "Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation," Optical Fiber Communication Conference, OTuM2 (2008).