Heterodyne detection

In heterodyne detection, a stable local oscillator laser is offset in frequency from the optical signal by an intermediate frequency $f_{IF}$, typically in the RF or microwave range (10 MHz – 50 GHz). The interference at the photodetector produces a photocurrent containing the signal information at $f_{IF}$:

$$i(t)\propto 2\sqrt{P_S{P}_{LO}}\cos (2\pi f_{IF}t+{\varphi }_S(t)-{\varphi }_{LO}(t))\mathrm{.}$$

Subsequent RF demodulation recovers signal amplitude $\sqrt{P_S}$ and phase ${\varphi }_S$.

Heterodyne vs homodyne vs intradyne.

Strengths of heterodyne over homodyne:

• No optical phase lock required: LO frequency offset is set by the LO laser tuning, eliminating the need for a precision optical phase-locked loop
• DC drift immunity: beat at non-zero frequency avoids 1/f noise and DC offsets in the photodiode and amplifiers
• Compatible with single-photodiode receivers: homodyne requires balanced 90° hybrid

Strengths of homodyne/intradyne over heterodyne:

• Direct I/Q recovery without RF demodulation: simpler signal processing chain
• Lower-frequency electronics: homodyne electronics need not exceed signal bandwidth, while heterodyne electronics must operate at 2× signal bandwidth (because the signal occupies $f_{IF}\pm B\mathrm{/}2$)

Sensitivity. With a local oscillator strong enough that its shot noise dominates the receiver, the signal-to-noise ratio of the IF photocurrent in a bandwidth $B$ is

$${\text{SNR}}_{het}=\frac{\eta P_S}{h\nu B}$$

with $\eta$ the detector quantum efficiency: the number of detected signal photons per resolution time, independent of the LO power and of the receiver's thermal noise once the LO is large enough. Homodyne detection gives twice this, $2\eta P_S\mathrm{/}h\nu B$, because the homodyne beat is a baseband current at full amplitude, while the heterodyne beat oscillates at the intermediate frequency and carries half the mean-square current against the same LO shot noise; in quantum terms, heterodyne detection recovers both quadratures and pays for it with the vacuum noise of the image band. That is the 3 dB by which heterodyne trails homodyne and intradyne at the quantum limit. In numbers, 1 nW of signal at 1550 nm in a 1 GHz bandwidth gives ${\text{SNR}}_{het}=7.8$ (8.9 dB) at $\eta =1$, which is why heterodyne receivers can work on picowatts of signal where direct detection needs nanowatts to microwatts. Modern coherent telecom receivers use intradyne detection for the extra 3 dB and for direct I/Q recovery; the LO shot-noise limit is reached in practice only after the LO's own RIN has been canceled by balanced detection.

Bandwidth and linewidth requirements. The IF must sit above the signal bandwidth so that the two sidebands do not fold onto DC: $f_{IF}\ge B\mathrm{/}2$ plus a guard, and the photodiode and IF chain must pass $f_{IF}+B\mathrm{/}2$, roughly twice the signal bandwidth. The beat note carries the sum of the two lasers' phase noise, so its width is the sum of the two linewidths (for Lorentzian lines), and the phase of the IF is usable only over times shorter than the combined coherence time; heterodyne measurement of a narrow laser therefore needs a reference laser of comparable or narrower linewidth, or the fiber-delay trick of the delayed self-heterodyne method.

Applications where heterodyne is preferred over intradyne.

Heterodyne in early optical communication. Heterodyne detection was the early approach (1980s – 1990s) before high-speed ADCs enabled intradyne and DSP-based coherent receivers. Modern long-haul telecom uses intradyne with DSP frequency tracking, but heterodyne remains the standard for measurement and metrology applications.

The term is borrowed from RF radio receivers, where heterodyning (mixing the received signal with a local oscillator) was introduced by Reginald Fessenden in the early 1900s and became the basis of Edwin Armstrong's superheterodyne receiver in 1918.

References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 10 (advanced lightwave systems, including coherent detection). L. G. Kazovsky, S. Benedetto, and A. E. Willner, Optical Fiber Communication Systems (Artech House, 1996), chapter 4. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007), chapter 11.