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OPA

A seeded optical parametric amplifier in a box: a pump and a seed go in, the amplified signal, a new idler and the leftover pump come out.

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In the real world

An optical parametric amplifier (OPA) moves energy from a strong pump to a weak seed inside a crystal whose lattice has no centre of inversion, so that it has a second-order (χ⁽²⁾) nonlinearity. Each pump photon that disappears creates one photon that amplifies the seed — the signal — and one new photon at the difference frequency, the idler[1,2]. Energy is conserved photon by photon, which fixes the idler wavelength and how the converted pump power divides:

1λp=1λs+1λi,ΔPi=λsλi ΔPs,−ΔPp=λsλp ΔPs\frac{1}{\lambda_p} = \frac{1}{\lambda_s} + \frac{1}{\lambda_i}, \qquad \Delta P_i = \frac{\lambda_s}{\lambda_i}\,\Delta P_s, \qquad -\Delta P_p = \frac{\lambda_s}{\lambda_p}\,\Delta P_s
Energy conservation and the Manley–Rowe relations: one signal and one idler photon per pump photon, so the idler carries λs/λi watts for every watt the signal gains. The ideal, lossless parametric process leaves no quantum-defect heat in the crystal; parasitic absorption can still heat it.

Why the gain is exponential. The pump and the seed together drive a polarization at the idler frequency, so an idler builds up; the pump and that idler then drive one at the signal frequency, which adds to the seed. Each wave feeds the other, and while the pump is not depleted the signal grows exponentially with the crystal length. The growth rate Γ rises with the nonlinear coefficient and with the square root of the pump intensity[1,4]:

Γ2=8π2deff2 Ipε0c npnsni λsλi,G=1+Γ2g2sinh⁡2(gL),g=Γ2−(Δk/2)2\Gamma^2 = \frac{8\pi^2 d_\text{eff}^2\, I_p}{\varepsilon_0 c\, n_p n_s n_i\, \lambda_s \lambda_i}, \qquad G = 1 + \frac{\Gamma^2}{g^2}\sinh^2(gL), \quad g = \sqrt{\Gamma^2 - (\Delta k/2)^2}
Small-signal gain of a plane-wave OPA (Baumgartner & Byer eq. 46; Manzoni & Cerullo eqs. 2.9–2.13). Phase matched (Δk = 0) it is cosh²(ΓL) ≈ ¼e2ΓL: pulsed pumps reach 104–108 in a few millimetres.

Phase matching sets the gain band. The three waves only keep exchanging energy while their phases stay in step: the mismatch Δk = kp − ks − ki must be small over the crystal. Turning a birefringent crystal (BBO, LBO) or choosing the poling period of a quasi-phase-matched one (PPLN, PPKTP) selects which signal wavelength is matched: that is how an OPA is tuned, and the idler follows. The range of signal wavelengths that still sees gain — the gain bandwidth — is set by the crystal's dispersion and length, chiefly by the group-velocity mismatch between signal and idler; it narrows with a longer crystal and widens slowly with gain[4].

Gain only while the pump is there. A parametric amplifier stores no energy, unlike a laser amplifier: it amplifies only while a pump pulse overlaps the seed. The seed has to be timed to the pump, usually with a delay stage, and the amplified pulse carries almost nothing outside that window — one reason OPAs give pulses with high contrast[2]. Pulses of different group velocities separate as they cross the crystal, which limits useful crystal lengths for femtosecond pulses[3,4].

Saturation and back-conversion. Once the pump is depleted, the gain saturates at once; past an optimum length an ideal plane wave converts the signal and idler back into the pump[1]. Real beams and pulses are pumped unevenly across their profiles, so the conversion of a whole pulse stays well below the plane-wave limit: about 10 % of the pump photons in preamplifier stages and about 30 % in power stages are typical[4].

How a packaged OPA is built. A femtosecond OPA has three parts: a seed generator, most often a white-light continuum made by focusing a small part of the driving pulse into a sapphire or YAG plate; one or more gain stages pumped by the driving laser or its harmonics; and an optional compressor[4]. Gain is usually split over stages: a preamplifier with gain around 103–105 picks the phase-matched slice of the continuum, and a power amplifier with gain around 10–102, driven into saturation, takes most of the pump energy[4]. Ti:sapphire (800 nm) and Yb (≈1030–1040 nm) lasers and their harmonics are the usual pumps[4]; a single amplified Yb fiber laser can drive two picosecond OPAs for nonlinear microscopy[7].

Variants. A noncollinear geometry (NOPA), in which the signal's group velocity equals the projection of the idler's along the signal direction, amplifies bandwidths wide enough for sub-20-fs pulses[5,4]. Stretching the seed before amplification and compressing it afterwards — optical parametric chirped-pulse amplification (OPCPA) — lets a long, energetic pump pulse be converted efficiently[6,8]. With signal and idler identical in wavelength and polarization, the amplifier becomes phase-sensitive and can amplify without excess noise; without any seed, the crystal amplifies vacuum fluctuations into optical parametric generation[2].

OPA or laser amplifier? An OPA has no transition to tie it to a wavelength, so it tunes across the transparency of its crystal; its gain per unit length under pulsed pumping far exceeds a laser's; the ideal parametric process produces no quantum-defect heat, since the pump energy leaves as signal and idler, although parasitic absorption — of a mid-infrared idler, for instance — can still heat the crystal and disturb its phase matching at high average power[2,4]; and it has no stored energy, so it amplifies only during the pump pulse[2]. The price is the need for an intense, well-timed pump and, at high gain and power, effects such as gain guiding that limit how far the output can be scaled[9].

In OpticalSetup

Ports. Send the pump into the upper rear port (P) and the seed into the lower one (S), each within 20° of the body axis. Every beam leaves at the height it came in: the residual pump from the front port P, opposite the pump port, and the amplified signal from the front port S, opposite the seed port, with the idler from the port I between them. A setup can therefore be aligned straight through the box. Output idler and Output residual pump switch those ports off, which removes that light from the bench rather than handing it to another output. All outputs leave parallel to the body axis, and rotate and flip with it.

Settings, as a data sheet gives them:

  • Tuned signal λ — the centre of the gain band, the wavelength a real OPA's crystal angle or poling would phase-match. The Idler λ readout gives the idler this makes with the pump that actually arrives.
  • Gain bandwidth — the full width at half maximum of the excess gain G − 1, a Gaussian around the tuned wavelength (at high gain, practically the width of G itself).
  • Peak small-signal gain — in dB at the band centre and at the pump's peak intensity; the Peak gain readout gives it as a factor.
  • Pump depletion limit — the largest fraction of the pump that can be converted at any instant. 1 is the plane-wave limit; the conversion of a whole pulse stays below it.
  • Input apertures and output beam diameter — the size of the ports and of the output beams (0 draws a single line).
G0(λ)=1+(10GdB/10−1) e−4ln⁡2 (λ−λ0)2/Δλ2G_0(\lambda) = 1 + \left(10^{G_\text{dB}/10} - 1\right)\, e^{-4\ln 2\,(\lambda - \lambda_0)^2/\Delta\lambda^2}
The gain spectrum this element uses at the pump’s peak: a Gaussian excess gain of FWHM Δλ around the tuned wavelength λ₀. The element is phenomenological in three places: this authored gain band, the depletion limit (an energy cap per instant with the undepleted gain law, not the depleted coupled-wave solution) and the generated pulses (timed and sized from the pump–seed overlap).

What is computed. The same functions as the OPA calculator take it from there. The gain at each wavelength becomes an equivalent ΓL (G = cosh²ΓL). The gain is then evaluated instant by instant through the pump and seed pulses, with the pump's intensity at each instant — so the delay matters, a seed that misses the pump pulse is not amplified, and a continuous seed gains only while a pump pulse is there. The pump pays for every signal and idler photon, and no instant can give up more than the depletion limit. Several seeds at one pump share its energy where they meet it. Pump and seed are timed as they arrive at the ports: glass, fibers and compressors on the way stretch or compress them, and the durations used are those the beam probe reads there. A beam whose duration the tracer cannot state there — for instance light of unknown spectral phase sent through glass, or a beam whose rays took paths of different dispersion — is not amplified on a guess; the readout says why.

Seeds. The seed is amplified as a source emits it: a single line, a Gaussian laser line, a flat supercontinuum or a lamp's lines. A broad seed is cut into slices across its overlap with the gain band, each amplified with the gain at its own wavelength, so only the phase-matched part of a supercontinuum grows; a lamp's lines are amplified line by line and stay lines. Once amplified, the seed leaves inside the signal beam, the seed and the gain added to it as one beam, as in a real amplifier: its spectrum is the seed's with the amplified part added, so the rest of a supercontinuum is still there, and a spectrometer downstream shows both. A seed that is not amplified — outside the band, mistimed, refused — passes through on its own. One spectrum holds both parts only while a grid of at most 4097 points resolves the narrower one; a gain a tenth of a nanometre wide on a 600 nm continuum cannot be, and then the continuum passes through and the amplified band leaves beside it as a beam of its own. The idler carries the spectrum the gain made.

Stretched seeds (OPCPA). A chirped seed carries its colours at different times: with a group-delay dispersion φ″, the part at angular frequency ω arrives φ″(ω − ω₀) after the centre. Stretch the seed — set a chirp on the laser, or pass it through a pulse compressor with positive GDD, glass or a fiber — and each slice of its spectrum meets the pump at its own time, with the seed's transform-limited envelope. For a Gaussian spectrum the slices add up to the stretched pulse exactly (their spread and the transform limit add in quadrature); any other spectrum is mapped this way only once stretched past twenty transform limits, where the mapping holds whatever the shape. The pump's envelope therefore shapes the amplified spectrum: a pump shorter than the stretched seed amplifies only the colours it meets, a late pump the colours that arrive late, and saturation flattens the band[8,10].

The signal keeps the seed's chirp. Gain changes the amplitude of each colour, not its phase, so the amplified signal leaves with the seed's GDD and a compressor after the OPA recompresses it. Its duration, before and after the compressor, is the transform of the amplified spectrum — the seed's own profile times the gain each slice received — with that phase, as for a filtered pulse. This holds while the pump gates each colour slowly: gating the field with a gain window T (τp/√ΓL at the peak gain) adds a band of its own, 4 ln 2 / T in angular frequency, which slices cannot represent. The signal keeps the seed's phase while four conditions hold: that band is at most 0.35 of the amplified band; the amplified band spans at least four slices; the stage's gain is at least 1000, so the seed passing through is a negligible part of the output (below that, the output is seed and gain together and the gain has no duration of its own); and the amplified light is centred within half a seed FWHM of the seed's centre (a pump timed onto the seed's wing amplifies its tail, where the slices are least accurate). Checked against the field amplified coherently (undepleted, phase matched) over 266 such cases — stretch ×1 to ×100, 20 to 60 dB, gain windows of 3 to 60 transform limits, pump delays up to 1.5 stretched durations — the recompressed duration is within 6.1 %. Outside that domain the readout says so and the signal's spectral phase is unknown, as the idler's always is.

Watts. The gain moves power from the pump to the seed, so both sources need an average-power setting. The signal beam carries the seed's watts and the gain's together; it and the idler are counted against the pump laser, which supplies the gain (a detector's breakdown by source therefore lists the pump for the seed's share too). Detectors on the three outputs read watts that add up to what went in, and the idler receives exactly λs/λi of the signal's gain.

Readouts. The Amplifier readout gives the pump in and out and the fraction converted; for each seed, the signal power and the pulse-averaged gain (as a factor and in dB, usually below the peak setting, because the gain is averaged over the pulses), and the idler wavelength and power. It says when the depletion limit is binding or the pulses barely overlap. When nothing is amplified it says why: no pump, no seed, a seed outside the band or shorter than the pump, pulses that never meet, sources without a power setting, more than one pump, or a modulated or filtered beam. It also says when light comes back to an OPA it already went through.

Two stages. Because every beam leaves at the height it came in, a second OPA placed behind the first receives the residual pump in its pump port and the amplified signal in its seed port, as in the usual preamplifier followed by a power amplifier[4,7]. The second stage is planned from what the first one actually delivers: its pump is the first stage's leftover pump, and its seed is the first stage's signal beam — the seed and the gain added to it — with the spectrum and timing the first stage gave it. The first stage's idler leaves on the axis and is stopped by the second stage's rear face. Up to six stages are planned in turn; the readout says if a longer chain has not settled. Each stage sends one signal beam on, so a chain carries one seed beam from stage to stage; a stage with several seeds cuts each into fewer spectral slices, and says so if there are too many to slice at all. Light sent back into an OPA it already went through — directly, through another OPA or through a fiber — is stopped at the port rather than amplified again in a loop, and the readout says so. A beam probe on an output reads its whole power, as a power meter does. Below a gain of 1000 the seed is a sizeable part of the signal beam, and its pulse duration — the gain's estimate — carries a caveat that every reading downstream shows; the probe's duration card marks it “≈ … estimate”.

Try it. The scene above sends 1 W of 515 nm pump and 1 µW of 780 nm seed into the OPA, tuned to 780 nm with 40 dB of peak gain. The signal leaves at a few mW and a 1516 nm idler appears, while the pump loses the sum. Move the seed's pulse delay to watch the gain disappear; swap the seed for a supercontinuum and a spectrometer to see only the tuned slice grow; raise the gain until the depletion limit binds. For the same physics with every formula, graph and its precision, open the calculator.

Simplified vs. reality

The gain spectrum is a Gaussian stand-in for the crystal's phase matching: no crystal, angle, temperature or dispersion is modelled, and the gain band does not move with the pump. Plane waves at the pump's peak intensity: no beam profile, walk-off, gain guiding or diffraction, and no group-velocity mismatch or chirp inside the crystal. The depletion limit is an energy cap per instant, not the depleted coupled-wave solution: past the optimum a real amplifier converts energy back into the pump, which this element does not show (the calculator's exact curve does). There is no parametric noise — an unseeded OPA gives nothing — and no degenerate, phase-sensitive case. A modulated (gated) pump or seed, from an AOM or a chopper, is not amplified: the readout says so rather than guessing how the gain follows the modulation. Neither is a seed whose spectrum was reshaped upstream, such as a filtered continuum: seeds are amplified as sources emit them (a line, a Gaussian line, a flat continuum or a lamp's lines). The idler's spectral phase — the conjugate of the seed's — is not modelled, so its duration after dispersion is unavailable; the signal keeps the seed's phase only in the domain described above, and otherwise its pulse takes the pump–seed overlap with an unknown phase. Only the seed's quadratic phase (GDD) is carried; higher orders, the parametric phase of a mismatched stage and saturation-induced phase are not. The slices' timing uses a linear chirp: a stretcher's higher-order dispersion is not modelled. One pump per element. In a cascade, each stage sees the previous one's output as it arrives; a filter or dichroic between the stages reshapes the signal's spectrum, and the next stage then reports its seed unsupported, as for any filtered seed. Feedback loops, such as a multipass or ring amplifier that returns the signal to the same element, are not modelled.

Related components

OPOCrystalPulsed LaserSupercontinuum laserDichroic mirrorMechanical delay lineSpectrometerPower meter

References

  1. R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15, 432–444 (1979)
  2. RP Photonics Encyclopedia — Optical Parametric Amplifiers
  3. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74, 1–18 (2003)
  4. C. Manzoni and G. Cerullo, “Design criteria for ultrafast optical parametric amplifiers,” J. Opt. 18, 103501 (2016), open access
  5. T. Wilhelm, J. Piel and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22, 1494 (1997)
  6. A. Dubietis, G. Jonušauskas and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992)
  7. F. Vernuccio, A. Benachir, E. M. Fantuzzi, B. Morel, S. Bux, E. Martin et al., “Dual picosecond fast tunable optical parametric amplifier laser system for wide-field nonlinear optical microscopy,” APL Photonics 9, 096113 (2024)
  8. I. N. Ross, P. Matousek, G. H. C. New and K. Osvay, “Analysis and optimization of optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 19, 2945 (2002)
  9. G. Arisholm, R. Paschotta and T. Südmeyer, “Limits to the power scalability of high-gain optical parametric amplifiers,” J. Opt. Soc. Am. B 21, 578 (2004)
  10. B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras et al., “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014)

Further reading