= Optical heterodyne detection
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= Heterodyne detection
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\b[Optical heterodyne detection] combines a signal field with a reference field at a different <frequency>, producing an electrical beat within a receiver's bandwidth. The reference is a <local oscillator>. A <photodetector> responds to the squared sum of the fields; averaging over optical carrier cycles removes the fast sum-frequency term but can retain the difference-frequency interference.
For constant powers $P_s,P_{\rm LO}$ incident on a linear detector of <responsivity> $R$, a useful model is
$$
i(t)=R\left[P_s+P_{\rm LO}
+2|\gamma|\sqrt{P_sP_{\rm LO}}
\cos\!\left(2\pi(\nu_s-\nu_{\rm LO})t+\phi\right)\right].
$$
The <mode-overlap factor in optical heterodyne detection> satisfies $|\gamma|\leq1$ and includes spatial and polarization matching. The beat frequency is $|\nu_s-\nu_{\rm LO}|$, while its phase carries a relative optical <wave phase>. Orthogonal polarizations can give $\gamma=0$ and no beat despite nonzero power from both sources.
For an original chosen $P_s=1\,\mathrm{nW}$, $P_{\rm LO}=1\,\mathrm{mW}$, $R=0.50\,\mathrm{A/W}$ and $|\gamma|=1$, the beat's peak current is $1.0\,\mathrm{\mu A}$. The signal alone produces only $0.50\,\mathrm{nA}$ of current, but the mixed DC level is about $0.50\,\mathrm{mA}$. A chosen frequency difference of $10\,\mathrm{MHz}$ is measurable electronically even though each carrier has an optical frequency. Increasing the reference also increases its noise and can overload the receiver; beat amplitude is not an unlimited sensitivity gain.
NIST's physical receiver-characterization experiment combined an external-cavity semiconductor laser and a Nd:YAG laser near $1319\,\mathrm{nm}$. Variable attenuators, a beam splitter, a polarizer and single-mode fibre controlled the powers and matched the modes before the receiver. Sweeping the optical frequency difference generated a tunable test modulation.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[PDF p. 1, Heterodyne measurements; pp. 1–2, electrical mismatch/loss corrections]{ref}
The receiver must pass the beat frequency and preserve the intended overlap. A single real beat frequency supplies the magnitude of the frequency difference; identifying which optical frequency is higher needs additional information. At zero difference, the corresponding fixed-phase measurement is <optical homodyne detection>.
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