Wiki / Nonlinear Optics / Crystal

Crystal

Converts a chosen fraction of incident light into harmonic, parametric, mixed, supercontinuum, or custom output, with an option to retain the residual pump.

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Third harmonic

1030 nm in, 343 nm out, separated from the residual fundamental by a dichroic. This is the app’s authored conversion proxy — one crystal emitting λ/3 at a set fraction — not a simulated cascade of a doubling and a sum-frequency crystal.

Supercontinuum in bulk YAG

A 1035 nm, 270 fs pump in YAG. The band on the spectrometer is estimated from the arriving pump and the medium: interpolated between reference spectra, an illustration rather than a prediction. Change the pump wavelength or the medium and the band follows; outside the reference data the crystal draws no continuum and asks for a manual range.

In the real world

A nonlinear optical crystal responds to intense light with a polarization that is no longer simply proportional to the optical field. In the perturbative regime the nonlinear contributions are usually small compared with the linear polarization, and the induced polarization can be expanded in powers of the field: the linear susceptibility χ⁽¹⁾ gives the linear refractive response, the second-order susceptibility χ⁽²⁾ mixes pairs of fields, and the third-order χ⁽³⁾ mixes three^[1]. Written this way the expansion is a scalar shorthand: the susceptibilities are tensors and depend on the frequencies of the interacting fields^[1]. Symmetry determines which terms are allowed, and intense laser fields make many nonlinear effects readily observable^[1]. The laser enabled landmark optical frequency-conversion experiments, including the 1961 demonstration by Franken and colleagues, who focused a pulsed ruby laser into crystalline quartz and detected its second harmonic^[2].

P = \varepsilon_0\left(\chi^{(1)}E + \chi^{(2)}E^{2} + \chi^{(3)}E^{3} + \dots\right)

Scalar shorthand for the induced polarization expanded in powers of the optical field E; the full response is tensorial and frequency dependent.

Nonlinear processes

For the bulk electric-dipole response, χ⁽²⁾ vanishes in any inversion-symmetric medium — an unbiased isotropic gas, liquid or glass, or a centrosymmetric crystal — so second-order processes need a material without inversion symmetry. The rule concerns the bulk: surfaces and interfaces break the symmetry, which is why SHG also serves as a diagnostic of surface properties^[3]. χ⁽³⁾ is symmetry-allowed in centrosymmetric media as well^[1]. The main processes are:

Second-harmonic generation (SHG): two photons at ω combine into one at 2ω^[1,3].
Sum- and difference-frequency generation (SFG, DFG): two input frequencies ω₁ and ω₂ produce ω₁ + ω₂ or |ω₁ − ω₂|^[1].
Parametric amplification and oscillation: one pump photon splits into a signal and an idler photon. In a single pass it can amplify a weaker input wave, as an optical parametric amplifier (OPA); in a resonator that feeds the signal or idler back it can sustain oscillation above threshold, as an optical parametric oscillator (OPO), described below^[1].
Third-harmonic generation (THG): light at ω produces 3ω, either directly through χ⁽³⁾ or sequentially through two second-order steps, SHG to 2ω followed by sum-frequency mixing of 2ω with the remaining ω^[1,3]. The sequential route can be implemented with separate SHG and SFG stages, and in well-designed systems it can be far more efficient than the direct one^[3].

The strength of a χ⁽²⁾ interaction is expressed by an effective coefficient d_eff, a combination of χ⁽²⁾ tensor components set by the crystal, the propagation direction and the polarizations; it is not a single material constant^[1].

Phase mismatch

Energy conservation is not enough. In collinear SHG the harmonic is driven by a polarization wave that travels with the fundamental, at wavevector 2k_ω, but it propagates freely with its own wavevector k_2ω, and dispersion generally makes the two differ. Harmonic light generated at different depths in the crystal then adds with different phases. Over one coherence length the driven and free waves slip by π; beyond it, newly generated contributions interfere destructively with the existing harmonic, and, without pump depletion, the harmonic intensity oscillates with crystal length instead of growing^[4]. For an undepleted plane-wave fundamental, negligible absorption and no harmonic at the input, the magnitude of the harmonic field after a crystal of length L is proportional to L·|d_eff|·|sinc(ΔkL/2)| for a fixed fundamental field, with sinc(x) = sin(x)/x and sinc(0) = 1, so the harmonic intensity is quadratic in the fundamental intensity and falls away once |Δk|L is no longer small^[4].

\Delta k = k_{2\omega} - 2k_{\omega}, \qquad \ell_c = \frac{\pi}{|\Delta k|} = \frac{\lambda}{4\,|n_{2\omega} - n_{\omega}|}

Phase mismatch and coherence length for SHG, with λ the fundamental vacuum wavelength and the refractive indices those of the chosen propagation direction and polarizations. At perfect phase matching ℓ_c is unbounded.

I_{2\omega} \propto d_{\text{eff}}^{2}\,L^{2}\,I_{\omega}^{2}\,\operatorname{sinc}^{2}\!\left(\frac{\Delta k\,L}{2}\right)

Undepleted plane-wave SHG, with sinc(x) = sin(x)/x and sinc(0) = 1: quadratic in the fundamental intensity and peaked at Δk = 0.

Phase matching

Phase matching makes Δk vanish. In birefringent phase matching the interacting waves travel with different polarizations, so that birefringence offsets the dispersion between fundamental and harmonic — in a uniaxial crystal, through the difference between ordinary and extraordinary refractive indices^[4]. Giordmaine, and Maker and colleagues, reported it in 1962^[5,6]. It is often tuned by the angle between the beam and the crystal's optic axis^[7]. For general propagation directions in a birefringent medium, an extraordinary wave's energy flow is not parallel to its wavevector, so the beams drift apart. This spatial walk-off can reduce beam overlap and limit the useful interaction length; suitable principal-axis geometries avoid it^[4,7].

In the sinc² law above the tolerable phase mismatch scales as 1/L: a longer crystal gives more phase-matched, undepleted conversion but tolerates a smaller Δk. Acceptance in wavelength, angle or temperature inherits that 1/L scaling where Δk varies linearly with the tuning parameter near the operating point^[8]. If the first derivative vanishes but the second does not, the leading mismatch is quadratic in the detuning and the acceptance scales as L^−1/2 instead.

Temperature changes the refractive indices and hence the phase mismatch. Where a suitable principal-axis configuration exists — in a uniaxial crystal, propagation at 90° to the optic axis — temperature can tune phase matching with reduced first-order angular sensitivity and no birefringent spatial walk-off. This is noncritical phase matching; temperature tuning alone does not imply it^[7].

Quasi-phase matching takes a different route. Instead of matching phase velocities, the sign of the nonlinear coefficient is periodically reversed, compensating the phase slip before new contributions start to cancel the harmonic; for the simplest first-order grating with a 50 % duty cycle, the reversal comes every coherence length. It was proposed by Armstrong, Bloembergen and colleagues in 1962 and became widely practical once patterned poling of ferroelectrics such as lithium niobate developed from the late 1980s. Because it does not require birefringent phase matching, all waves can share one polarization and access a large tensor component allowed by the material and geometry, propagation along a crystal axis can avoid birefringent spatial walk-off, and non-birefringent materials such as GaAs can be used. The price for a first-order grating is an effective coefficient of at most 2/π of d_eff^[4,9].

\Delta k_{\text{QPM}} = \Delta k - s\,\frac{2\pi}{\Lambda}, \quad s = \pm 1, \qquad |d_1| = \frac{2}{\pi}\,|d_{\text{eff}}|\,\sin(\pi D)

First-order quasi-phase matching with a grating of period Λ and duty cycle D (0 ≤ D ≤ 1), with s chosen to match the sign of Δk: matched when Δk_QPM = 0, so that Λ = 2π/|Δk| = 2ℓ_c, with the effective coefficient |d_1| largest at D = ½.

Temporal walk-off and practical design

Spatial walk-off separates beams in space. Ultrashort pulses can also separate in time, because their group velocities differ: over a length L the relative delay between pulses a and b is L·|1/v_g,a − 1/v_g,b|. Once this temporal walk-off is comparable to the pulse duration, the loss of temporal overlap limits the useful interaction length^[4,8].

Walk-off can also be put to use. In a long crystal where the fundamental and the second harmonic travel at very different group velocities, the phase-matching bandwidth for the harmonic becomes very narrow while a broad fundamental spectrum can still sum into it, so a broadband femtosecond fundamental is doubled into a narrowband picosecond second harmonic: spectral compression rather than the broadening a thin crystal gives. Marangoni and co-workers used a 25 mm periodically poled stoichiometric lithium tantalate crystal to turn tunable femtosecond pulses into 200 nJ second-harmonic pulses narrower than 8.5 cm⁻¹, tunable from 720 to 890 nm, at 20 % conversion efficiency^[10]. The same spectral-compression approach can produce narrowband green light to pump a picosecond optical parametric oscillator: Genchi and co-workers doubled a 1030 nm femtosecond laser in LBO to 515 nm with spectral compression, at about 40 % conversion, and used the picosecond green to pump a picosecond OPO for broadband stimulated Raman scattering microspectroscopy^[11].

A real conversion stage is therefore designed around more than one phase-matching condition: the wavelengths involved and the crystal's transparency and absorption there, the allowed polarizations with the crystal cut or poling period, the operating temperature, the crystal length and focusing, the pulse duration, and coating and optical-damage limits. d_eff, the acceptance bandwidths and the walk-off must be evaluated for the selected material, wavelengths and geometry.

Supercontinuum

Supercontinuum generation turns intense pulses into a broad continuum, often spanning hundreds of nanometres, rather than a new discrete line^[12]. Early demonstrations came in 1970, when Alfano and Shapiro broadened picosecond pulses in glasses and crystals^[13,14]. In glass and optical fibers the broadening arises mainly from third-order effects: depending on pump duration and dispersion it can involve self-phase modulation, modulation instability, soliton dynamics, dispersive waves, four-wave mixing and Raman scattering, and in photonic crystal fibers it can exceed an octave^[12].

A bulk crystal or glass does the same with a focused femtosecond beam: above the critical power for self-focusing the beam collapses into a filament, and self-phase modulation in it broadens the spectrum^[15]. Where the spectrum ends depends on the medium, the pump wavelength and the conditions. Multiphoton absorption and plasma clamp the filament's intensity, and the higher the order of that absorption, set by the bandgap over the photon energy, the higher the clamped intensity and the broader the spectrum, so wide-bandgap media reach furthest into the blue; the blue cut-off is also constrained by the material's dispersion. Once the beam breaks up into several filaments, more energy adds no further broadening; chirping the input or moving its focus tunes the blue cut-off, while a low numerical aperture and a longer medium extend the red side, which also grows with the pump wavelength^[15]. Pumped near 800 nm, sapphire typically spans about 410–1100 nm, YAG about 420–1600 nm, fused silica about 390–1000 nm and CaF₂ about 300–2000 nm; with 1.1–1.6 µm pumping YAG's blue cut-off holds near 530 nm while its infrared side keeps extending^[15]. The near-infrared half is useful in its own right: a 10 mm YAG plate pumped at 1035 nm has provided a 1050–1300 nm Stokes band for multiplex CARS microscopy^[16].

Optical parametric oscillators

In an optical parametric oscillator (OPO) the process runs the other way: inside a χ⁽²⁾ crystal each converted pump photon splits into two lower-energy photons, the signal and the idler. Naming varies: the signal often denotes the higher-frequency output^[17], or the desired one^[1]; this page instead calls the resonant wave the signal. Placing the crystal in a cavity that feeds one of them back lets the parametric gain overcome the cavity losses above threshold, making a tunable coherent source for spectral ranges that direct laser emission covers poorly or not at all^[17,18].

\frac{1}{\lambda_p} = \frac{1}{\lambda_s} + \frac{1}{\lambda_i}

Energy conservation: one converted pump photon becomes one signal and one idler photon.

\frac{P_s}{P_i} = \frac{\nu_s}{\nu_i} = \frac{\lambda_i}{\lambda_s}

Manley–Rowe: signal and idler are generated with equal photon fluxes, so the generated powers divide in proportion to photon energy.

Because the photon fluxes are equal, the longer-wavelength output is always generated with the smaller share of the power; what finally leaves a resonator also depends on its output coupling and losses. Pumped at 532 nm with an 800 nm signal, the idler lies at 1588 nm and receives about a third of the converted power. The penalty grows with the wavelength ratio: for a single conversion step that extracts only the 5 µm output, a 1 µm pump supplies at most 20 % of its converted power to that wave^[19].

Threshold. Like a laser, an OPO oscillates only once the round-trip parametric gain overcomes the cavity losses; at threshold the two balance^[18,19]. Unlike a laser, it relies on no stored population inversion: parametric gain requires the pump to be present. For a singly resonant OPO, where only the signal is fed back, the ideal plane-wave model predicts complete pump depletion at (π/2)² ≈ 2.5 times threshold^[20]; this is a theoretical limit, not a general operating point. Driven harder, signal and idler start converting back into pump light, so increasing pump power need not keep increasing the conversion efficiency^[19].

Linewidth. Energy conservation also holds for instantaneous frequency fluctuations, δν_p = δν_s + δν_i, so pump fluctuations must appear on the signal, the idler or both. The cavity constrains the resonant wave, and the non-resonant wave takes up what the pump and resonant wave leave. Pump frequency fluctuations that the resonant wave does not follow appear on the non-resonant one, so imposing them on the resonant wave with active feedback is a way to remove them from the other^[20]. This page and OpticalSetup call the resonant wave the signal; real OPOs resonate either. If pump and resonant wave fluctuate independently and both spectra are Gaussian, the non-resonant wave's frequency width is the quadrature sum of theirs; correlated fluctuations change that, which is why an idler can be narrower than its pump.

Common operating regimes:

Synchronously pumped fs and ps OPOs. In the usual arrangement with one pulse per round trip, the cavity round trip is matched to the repetition period of a mode-locked pump, so each signal pulse is amplified by the next pump pulse, and the output pulse trains stay locked to the pump's. One MgO:PPLN oscillator pumped by 80–100 fs pulses near 1 µm at 80 MHz produced 400–600 fs signal pulses and an idler tunable from 3132 to 4273 nm^[21]. Frequency-doubled mode-locked lasers can pump picosecond OPO sources for coherent Raman imaging; near-transform-limited pulses of a few picoseconds can provide bandwidths comparable to many molecular Raman bands, balancing spectral selectivity against peak intensity^[22].
Nanosecond OPOs pumped by Q-switched lasers are often used for high-energy pulses. Without spectral narrowing their linewidth is typically set mainly by the crystal's phase-matching bandwidth and the cavity, and is much broader than a single-frequency laser's^[19]. The oscillation needs time to build up from noise during each pump pulse, which raises the threshold^[19] and often makes the output pulses somewhat shorter than the pump's^[18].
Continuous-wave singly resonant OPOs pass the pump frequency fluctuations that the resonant wave does not follow on to the non-resonant wave^[20].

In OpticalSetup

Choose a conversion mode before expecting any output: with the default None the crystal does not interact with light at all. Every converting mode is a wavelength-and-power proxy that converts a fixed, authored fraction of the eligible incident light, whatever its intensity, and Transmit residual pump can keep the unconverted remainder on the same path; no residual branch is drawn at efficiencies of 99.9 % or more, and in non-OPO modes it is also omitted when the output centre wavelength equals the input centre wavelength.

The χ⁽²⁾ mode halves the wavelength of any incident light, and THG divides it by three: there is no phase-matching condition, so every input wavelength converts. THG maps a wavelength directly to a third of it; it does not simulate a cascaded SHG and SFG apparatus. The spectrum is scaled with the wavelength and the pulse keeps its train and duration, which makes the harmonic's frequency width n times the input's. Spectral compression in a long crystal with large group-velocity mismatch, described above, is not modelled: to draw a narrowband harmonic, use a narrowband fundamental or a Custom output line. This is not a calculated nonlinear pulse transformation: an undepleted, instantaneous n-th-order process acting on a transform-limited Gaussian pulse, without walk-off or phase-matching filtering, would give √n times the input frequency width, with a √n shorter pulse. The example doubles a 1064 nm pulsed laser to 532 nm and separates the harmonic from the remaining pump with a dichroic, with a beam probe on each branch.

Supercontinuum replaces the converted light with a flat band. By default its edges come from the pump that arrives and the chosen medium — YAG, sapphire, fused silica or CaF₂ — using spectra reported in a review of bulk supercontinuum generation at a few pump wavelengths per medium^[15]. At a pump the table includes, the band is the reference one — a single experiment, or a typical span or pump range the review summarises; between two, each edge is interpolated linearly, which is an illustration rather than a prediction, so a 1035 nm pump in YAG gives about 506–1776 nm. A pump outside the reference data this estimate includes, and continuous-wave input, draw no continuum; the literature reports other pumps too, and a manual range draws any band. The Continuum readout gives the band, says which kind of reference or interpolation it comes from, and notes when its red edge rests on a measurement limited by the detector. Set manually draws an authored band from any pump instead; scenes saved before the estimate existed open with their old 430–870 nm band as a manual range. Custom output is an authored output rather than a named physical process: it emits a single line at the entered wavelength, whatever the pump's bandwidth.

The same mode also mixes two beams, because one χ⁽²⁾ does both: a crystal that doubles a beam sums two of them as well. Each beam's second harmonic is drawn whatever else is present, and when a second wavelength reaches the crystal the pair also produces its sum frequency, 1/λ₃ = 1/λ₁ + 1/λ₂. Doubling takes its authored fraction of each beam first, and the mixing then takes its own fraction of what is left of both beams, which is what puts the mixed line in the same range as the two harmonics beside it: 30 % doubling with a 30 % mixing share turns two equal beams into harmonics at 0.30 each and a sum frequency at 0.42. No single-pass conversion fraction can be set above 60 % here. That is a cap this workbench imposes to keep authored fractions conservative, not a physical limit: published single-pass second-harmonic conversion reaches higher. OPO mode's pump depletion is a multi-pass result and has its own control and ceiling. The crystal pairs the incident light with every other wavelength present at least 1 nm away, each pair emitted once by its shorter beam, so three colours give three mixed lines. Also generate difference frequency adds 1/λ₁ − 1/λ₂ with λ₁ the shorter input, which is longer than that input but not necessarily longer than the other one — 400 nm with 1000 nm gives 667 nm, between the two; it is off by default, since that line usually falls outside the range a two-colour bench looks at. The Two-beam mixing readout names the pair, the output, and how far apart the two pulses arrive.

Only the mixing needs the two pulses together. Doubling needs one beam and happens whatever the timing, which is exactly what makes the mixed line a measurement: with two colours in one crystal the two second harmonics sit there unchanged, and the sum frequency appears between them only as the delay is brought to zero. That is how time zero is found on a bench. Each beam's arrival is its own optical path plus its emission offset, so moving a source, adding glass, or scanning a delay stage shifts it. For two Gaussian intensity envelopes of FWHM τ₁ and τ₂ arriving Δt apart, the signal is scaled by the overlap integral exp(−4 ln2 Δt²/(τ₁² + τ₂²)) and disappears below 2 % of its peak: scanning a delay through zero traces that curve, which is how time zero is found on a real bench. The mixed pulse is the product of the two envelopes, so its duration is (τ₁⁻² + τ₂⁻²)^(−1/2) — following the shorter input — and it peaks at the weighted mean of the two arrivals rather than at either one. A gate on either beam gates the signal, because both have to be there.

Only trains at the same repetition rate are modelled, together with a continuous beam, which is always present and needs no timing. Different rates are not drawn at all: they are not a physical impossibility — 80 MHz and 60 MHz coincide at 20 MHz, and slightly detuned trains sweep through the delay, which is what asynchronous optical sampling uses — but this model keeps no pulse-by-pulse bookkeeping for them, so it reports the timing as not modelled instead of inventing a result. Whenever a pair is present and no signal is drawn, the workbench says which of the two reasons applies.

OPO mode models a singly resonant oscillator phenomenologically. Set the pump wavelength the crystal is phase-matched for, its acceptance window, and the resonant signal wavelength; the idler is shown as a readout. Pump light converts when its centre lies inside the acceptance window, whatever its bandwidth. The signal stays where the cavity holds it and the idler follows the arriving pump by energy conservation. Signal and idler light generated by this OPO, and its descendants, is not converted again by the same OPO; a returning residual pump may convert again, and another crystal can convert the generated light. Its figure is Pump depletion, the fraction of the pump the oscillator removes, divided between signal and idler by the lossless Manley–Rowe split. It is a separate control from the single-pass modes' conversion efficiency because it is a different measurement: depletion builds up as the resonant signal is amplified over many round trips, and singly resonant OPOs are reported at 78 % depletion^[21]. It goes up to 95 %; scenes saved when the OPO shared the conversion efficiency carry that value over.

Linewidths are handled as FWHM in wavenumber. Signal as wide as the pump is a heuristic for synchronously pumped fs and ps OPOs; Signal width set suits ns and CW OPOs, where the cavity sets it; in both, the idler is derived as the uncorrelated Gaussian sum. Signal and idler widths set takes both from a measured or specified system. A zero width is a single line and a narrow width a Gaussian in wavelength; an output wider than 1 % of its frequency is represented by a finite sampled wavelength distribution drawn from its Gaussian in wavenumber, which leans toward long wavelengths. Dichroics, filters and spectrometers downstream act on these new spectra rather than on the pump's. At exactly twice the pump wavelength, signal and idler with equal widths form one degenerate beam; with different widths they stay two coincident beams, each with its own spectrum.

Pulses. Signal and idler are pulse trains of their own, synchronised to the pump: they keep its repetition rate, arrival timing and modulation gates, so with a pulsed pump and Transmit residual pump on, a detector reached by all three outputs sees a non-degenerate pump, signal and idler as three separate trains. There are three choices. By default they are Transform-limited: each duration follows from its own bandwidth. The two Duration set choices make each output last the pump's duration times Output duration (× pump duration) — 1 matches the pump, 2 is twice as long — and a duration shorter than the output's transform limit is raised to the limit. With spectral phase unknown nothing is claimed about the phase, so the model cannot predict compression and a compressor does not shorten the drawn pulse. Positively chirped (assumed Gaussian) is an explicit assumption that the output is a coherent Gaussian whose only spectral phase is a positive quadratic one: it is drawn as the transform-limited pulse carrying the group delay dispersion that stretches it to the set duration, so a compressor downstream can remove it. Duration and bandwidth alone do not establish that — excess bandwidth can be incoherent, as in a nanosecond OPO — which is why it is a choice rather than a default. An output with zero linewidth is a drawing convention for an idealised monochromatic pulse train, like a pulsed source set to 0 nm: it has no finite transform-limited duration, so it keeps its set one with its spectral phase unknown. Group delay dispersion is counted from the crystal exit. The inspector's Outputs readout lists each output's bandwidth, in nm and cm⁻¹, and its duration, marked transform limited, chirped or spectral phase unknown.

Simplified vs. reality

Mixing gates on arrival time only. No phase matching, polarization condition, focusing or spatial overlap is checked, so any two wavelengths mix if they coincide in time — a real crystal at one angle would not produce two second harmonics and their sum frequency with comparable efficiency, and each process would need its own polarizations. Doubling reserves its authored fraction of each beam first, and the mixing draws an authored share of what is left of both beams of a pair, each debited for what it gave; every pair a beam takes part in shares that one budget. The proportions are a drawing convention chosen to put the three lines in the same range — equal fractional contributions from both beams, not the photon-energy-weighted depletion a real stage would show — and not a power-dependent conversion prediction, and the two harmonics staying put while a mixed line rises is a weak-conversion convention. Every unordered pair of colours is formed, each emitted once by its shorter wavelength, so three colours give three mixed lines. Light this crystal generated is not mixed again by it. The mixed output's width is the two inputs' widths added in quadrature in wavenumber, which is the uncorrelated-Gaussian estimate rather than a calculated conversion spectrum, and the overlap factor is an ideal-Gaussian timing proxy rather than a cross-correlation of the real pulse shapes.

No mode calculates phase matching, d_eff, crystal length, acceptance bandwidths, spatial or temporal walk-off, or the dependence of conversion on intensity: SHG and THG convert every wavelength at the authored fraction, and no crystal material is selected. Supercontinuum is a flat band, not a model of filamentation, self-phase modulation or soliton dynamics. Its estimated edges come from reported experiments and review summaries with different focusing, energies, durations and crystal lengths, none of which the estimate reads, and bands between reported pumps are linear interpolations. Red edges reported at 2 µm and beyond were limited by the detector, so the band understates the red side there. Whether the pump exceeds the critical power, the damage threshold, disconnected bands such as CaF₂ shows at longer pumps, and the spectral shape inside the band are not modelled; the converted fraction is authored like the other modes. Harmonic spectra are scaled rather than calculated from the field, as described above.

OPO mode is a phenomenological model rather than a cavity simulation. Phase matching is not calculated from material data: the signal wavelength and acceptance window are authored, and crystal choice or temperature do not affect them. No threshold, resonant gain or self-consistent pump-depletion dynamics are calculated: the authored depletion removes the same fraction at any pump power, and that fraction is removed from a retained pump. Ray round trips and authored output-coupler losses are traced; resonant gain, synchronisation-dependent conversion, build-up time, group-velocity walk-off and spatial mode overlap are not calculated. Output durations are authored or set from the Gaussian transform limit; no general spectral-phase evolution is calculated. Pump spectra are reduced to a Gaussian of the same FWHM, taken from the spectrum where available and otherwise from the bandwidth, so structured spectral shapes are not carried into the outputs; and the idler width assumes uncorrelated Gaussian fluctuations unless both widths are set. A detector retains separate trains; its aggregate pulse summary suppresses duration and repetition-rate fields when train settings differ, and otherwise uses the shared settings with aggregate dispersion information. Use separate detectors for output-specific pulse readings.