Optical receiver
= Optical receiver
An \b[optical receiver] converts an incoming optical signal into an electrical signal that can be measured or processed. A typical direct-detection receiver combines a <photodetector> with readout electronics; optical filtering, electrical amplification and bandwidth limitation determine which input variations survive. An optical receiver can characterize a modulated beam as well as receive a communications signal.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[p. 1, optical receiver frequency-response measurement]{ref}
In a simple linear <photodiode> model, the signal current is $i(t)=\rho P(t)$, where $\rho$ is the <spectral responsivity> at the operating wavelength and $P$ the incident <radiant power>. A low-frequency <transimpedance amplifier> gives $v(t)=-R_f i(t)$ for its ideal inverting readout. For an original example, $\rho=0.8\,\mathrm{A\,W^{-1}}$, mean power $20\,\mu\mathrm{W}$, modulation amplitude $4\,\mu\mathrm{W}$ and $R_f=10\,\mathrm{k\Omega}$ give mean photocurrent $16\,\mu\mathrm{A}$ and modulation amplitude $3.2\,\mu\mathrm{A}$. The corresponding output has mean $-0.16\,\mathrm{V}$ and modulation amplitude $0.032\,\mathrm{V}$, before offsets and frequency-response effects.
A motivating experiment measures the response to optical beating. Hale and colleagues combined two single-frequency lasers near $1319\,\mathrm{nm}$, with attenuators, polarization control and a beam splitter, into a single-mode fibre. Tuning their frequency difference supplied a tunable optical intensity modulation whose electrical response could be measured.<Frequency response metrology for high-speed optical receivers by Paul D. Hale and others>[p. 1, Heterodyne measurements and Figure 1]{ref}
For perfectly overlapping fields of equal polarization, the ideal incident power is
$$
P(t)=P_1+P_2+2\sqrt{P_1P_2}\cos(2\pi\Delta\nu t).
$$
A frequency difference of $100\,\mathrm{MHz}$ therefore produces a $10\,\mathrm{ns}$ intensity period; it is not the optical carrier period. Sweeping this difference probes modulation response. <Measurement calibration> must account for optical overlap, receiver gain, electrical losses and impedance mismatch. Spectral sensitivity at an optical wavelength and electrical modulation bandwidth are different specifications; a large direct-current output alone establishes neither low <noise> nor a fast receiver.