Glossary entry

Linear optical sampling (LOS)

A measurement technique that samples a fast optical signal by interfering it with short pulses from a local oscillator in an optical hybrid, recording the signal's amplitude and phase at each pulse with slow detectors. It builds eye diagrams and constellations of signals too fast for electronic oscilloscopes.

Lab practice Fiber & telecomUpdated October 2026

Linear optical sampling (LOS) measures a fast optical signal by interfering it with a train of short pulses from a local oscillator (LO), usually a mode-locked laser, in a 90° optical hybrid. The balanced detectors after the hybrid only need to be fast enough to separate one LO pulse from the next, not to follow the signal: each pulse gives one pair of in-phase and quadrature values, which together are the signal's complex field at that instant. The time resolution is set by the duration of the LO pulses rather than by the bandwidth of the detectors and electronics. The method is a form of coherent detection with a pulsed LO in place of a continuous one.

Measurement principle

For a signal field $E_{S} (t)$ and LO pulses $E_{L O} (t - t_{n})$ arriving at times $t_{n}$ , the balanced outputs of the hybrid are proportional to

\begin{aligned} i_{I, n} & \propto Re ⁣ \int E_{S} (t) E_{L O}^{*} (t - t_{n}) d t, \\ i_{Q, n} & \propto Im ⁣ \int E_{S} (t) E_{L O}^{*} (t - t_{n}) d t . \end{aligned}

When the LO pulse is much shorter than the features of the signal, the integrals are proportional to the signal's complex envelope at the pulse center, $E_{S} (t_{n})$ , and the sequence of pairs $(i_{I, n}, i_{Q, n})$ is a sampled record of that envelope.

Bandwidth

Because each sample is the overlap integral above, the measurement acts on the signal as a filter whose transfer function is the spectrum of the LO pulse's field. For a transform-limited Gaussian pulse with an intensity full width at half maximum $τ_{p}$ , the 3 dB bandwidth of that filter is

f_{3 dB} = \frac{\ln 2}{π τ_{p}} \approx \frac{0.22}{τ_{p}},

about 1.1 THz for 200 fs pulses and 220 GHz for 1 ps pulses. The LO pulses are kept close to transform limited, since a chirped pulse samples the signal over its whole, longer duration.

Equivalent-time sampling

The LO repetition rate is far below the symbol rate of the signal, so consecutive samples fall on symbols far apart in the data stream. LOS is therefore an equivalent-time technique, like a sampling oscilloscope: an eye diagram or constellation is built up statistically from many samples, with the sampling instant stepped or swept across the symbol period, either by an optical delay line or by setting the LO repetition rate slightly away from a sub-multiple of the symbol rate. Random data can be measured this way. Reconstructing the waveform of a particular bit sequence needs a pattern that repeats, so that samples taken on many repetitions can be put in order.

Linear and nonlinear sampling

Optical sampling was first done with nonlinear gates, in which the sampling pulse and the signal interact in a nonlinear crystal or fiber, by sum-frequency generation or four-wave mixing, and the light generated is proportional to the signal intensity at the pulse time. Such gates are inefficient, so they need high peak powers, and they record only the intensity. Linear sampling replaces the gate with interference, which is linear in the signal field: it records the phase as well as the amplitude, which phase-modulated formats require, and it works at much lower signal powers.

Implementation

Component	Role
Mode-locked laser, such as an Er-fiber laser at 1550 nm	Source of the LO pulses
Optical delay line, or an offset in the LO repetition rate	Moves the sampling instant across the symbol
90° optical hybrid, polarization diverse for dual-polarization signals	Mixes signal and LO at four relative phases
Balanced photodetectors	Give the in-phase and quadrature values for each pulse
Digitizer running at the LO repetition rate	Records one pair of values per pulse
Software	Estimates the carrier phase, places samples by their timing and builds eyes, constellations or waveforms

As in any coherent receiver, the LO and the signal come from different lasers, so their relative phase drifts, and the carrier phase is estimated from the samples in software before a constellation is drawn.

Uses and alternatives

LOS is used to measure eye diagrams and constellations of signals whose symbol rates are beyond the bandwidth of electronic oscilloscopes, and to see the constellations of phase-modulated formats such as QPSK and QAM directly. An electronic sampling oscilloscope with an optical input detects only the intensity, and its bandwidth is limited by its photodetector and sampler. A coherent receiver with a continuous LO, the architecture of coherent transponders and of optical modulation analyzers, records the field continuously in real time, but it needs photodiodes and analog-to-digital converters with at least the bandwidth of the signal. LOS needs neither, at the cost of seeing only sparse samples: it characterizes a signal statistically but cannot follow the data symbol by symbol.

References: C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon and M. G. Raymer, "Linear optical sampling," IEEE Photonics Technology Letters (2003). C. Dorrer, "High-speed measurements for optical telecommunication systems," IEEE Journal of Selected Topics in Quantum Electronics (2006).