Synchronously pumped picosecond OPO
A frequency-doubled 1032 nm picosecond laser pumps a cavity whose round trip lasts one pump period, giving an 800 nm signal.
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An optical parametric oscillator feeds one of its two generated waves back through a χ⁽²⁾ crystal so that it keeps being amplified. With a mode-locked pump the crystal only has gain while a pump pulse is inside it, and between pulses there is none[1].
Synchronous pumping makes the cavity's round-trip time equal one pump period. A signal pulse leaves the crystal, travels once around the resonator and arrives back just as the next pump pulse does, so it is amplified on every pass. For a pump at repetition rate frep the round trip must take 1/frep: a one-way optical path of c / (2 frep), 1.87 m at 80 MHz. Strictly this is the group optical path, so a dispersive crystal inside the cavity makes the mirrors sit a little closer together than that distance.
Frequency-doubled mode-locked lasers can pump picosecond OPO sources for coherent Raman imaging, which needs two synchronised colours. Near-transform-limited pulses of a few picoseconds can provide bandwidths comparable to many molecular Raman bands, balancing spectral selectivity against peak intensity[2]. A singly resonant cavity reflects only the signal band: the pump enters through one of its mirrors, the idler and residual pump leave through another, and a fraction of the signal leaves through the output coupler on every round trip.
What this setup demonstrates
The scene is an illustrative layout with illustrative settings, representative of picosecond OPOs of this kind rather than any one instrument or publication. A 1032 nm, 2 ps, 80 MHz laser is frequency-doubled in an SHG crystal that converts half of it to 516 nm. A shortpass dichroic sends the residual 1032 nm fundamental up to a dump and passes the green pump on to the OPO; in coherent Raman sources that fundamental can instead serve as a third synchronised beam.
The green pump enters a Z-shaped cavity, M3 → F1 → M1 → crystal → M2 → M4, whose one-way path is exactly c / (2 × 80 MHz) = 1873.7 mm — a round trip of 12.5 ns, the pump period. Every fold is at a 12° angle of incidence, so the beam turns back on itself as it does on real cavity mirrors, and one flat fold, F1, keeps the long arm on the page. The crystals are thin surfaces, so the whole path is air and group and geometric lengths coincide. M1 and M2 are band reflectors that return the 650–950 nm signal band and transmit the pump and idler. The pump enters through M1; the idler and residual pump leave together through M2 and are separated by a dichroic outside the cavity. M4 is an output coupler reflecting 90 % of the signal.
The OPO crystal is set to a 516 nm pump and an 800 nm signal, placing the idler at 1453.5 nm. The signal is authored with a 10 cm⁻¹ FWHM (0.64 nm) and the pump's 2 ps duration, a time–bandwidth product of 0.60, longer than the 1.47 ps its bandwidth allows; its pulses are therefore set as positively chirped, a transform-limited pulse carrying the dispersion that stretches it to 2 ps, which a pulse compressor on the output could remove. That is an authored assumption, not a result of the cavity. The idler width, about 3.8 nm, is derived from pump and signal as uncorrelated Gaussians. Beam probes read the wavelength of the 1032 nm fundamental, the 516 nm pump, the signal circulating in the long arm and the residual pump, and spectrum probes show the separated idler and signal.
The OPO crystal removes a fixed, illustrative 35 % of the green pump, its authored pump depletion. By photon energy that is 22.6 % of the green as signal and 12.4 % as idler — 11.3 % and 6.2 % of the 1032 nm laser, which is what the detectors read against. The idler detector reads its 6.2 % in one pass. The tracer sums six output-coupler leaks of the signal before its path-depth limit, about 5.3 % of the laser; infinitely many would recover the generated 11.3 %. Neither is a steady-state prediction.
This is a phenomenological OPO, not a cavity simulation. Both crystals convert a fixed fraction on a single pass; there is no threshold, gain, build-up or saturation, and changing the cavity length does not detune anything — in a real synchronously pumped OPO it shifts the signal and can stop oscillation. The signal output is a finite sum of traced leakage paths. The SHG crystal scales the pump spectrum with the wavelength and keeps the pump's duration, which doubles the frequency width. In the undepleted, ideal Gaussian limit the second harmonic would be √2 wider in frequency and √2 shorter; the green here is about 14.7 cm⁻¹ instead of about 10.4 cm⁻¹, and that carries into the derived idler width.
Drawing concessions: M1 and M2 are drawn flat. Synchronously pumped cavities commonly focus into the crystal with curved mirrors, but the workbench's curved mirrors are not wavelength-selective. Many picosecond OPOs couple signal and idler out collinearly; here the idler leaves through M2. The pump is a single axial ray, so the scene shows chief-ray routing only, with no focus, waist, resonator mode or beam overlap. Crystal lengths, temperature tuning and intracavity dispersion are not modelled, and the output widths, durations, output coupling and conversion fractions are authored.