Visualizing the pump profile in the output fluence

This guide shows what happens when a collimated beam with a uniform energy distribution passes through a medium whose pump spot does not fill the full aperture. Because the gain is stronger where the pump is most intense, the output fluence map at the detector reproduces the transversal pump profile — even though the input beam was flat. The complete, runnable program is opossum_core/examples/amplifier_gaussian_pump_fluence.rs; run it with

cargo run -p opossum_core --example amplifier_gaussian_pump_fluence

The setup

The optical chain is minimal: a source, a single amplifier head, and a fluence detector.

oscillator ──[200 mm]── amplifier head ──[100 mm]── output fluence

The amplifier head is a plane-parallel glass slab (flat surfaces, 100 mm thick, n = 1.5). No special node type is needed — a Lens with infinite radii of curvature is the active medium. Marking it as an amplifier is what makes the GUI show it in the pump-scenario editor:

#![allow(unused)]
fn main() {
document.set_is_amplifier_node(head, true);
}

Pump scenario

A pump scenario assigns the gain model and the pump source to the head separately.

Gain model. MonochromaticSmallSignalGain integrates the local gain coefficient along each ray’s path through the medium: G = exp(∫ g₀·β ds). The peak coefficient g₀ = 0.2 cm⁻¹ is the gain per unit length where the pump is strongest (on axis). For a ray going straight through the 100 mm slab, the peak single-pass gain is

G = exp(g₀ · L) = exp(0.2 cm⁻¹ × 10 cm) = exp(2) ≈ 7.4

Pump source. The pump carries only the spatial shape — how the gain coefficient is distributed across the medium. Here it is a standard Gaussian (SuperGaussian of order 1) with a half-width σ = 5 mm, combined with a flat longitudinal profile. A flat longitudinal profile means the inversion is the same at the entrance face and at the exit face, so the only spatial variation is the Gaussian fall-off across the aperture.

#![allow(unused)]
fn main() {
scenario.set_gain_model(
    head,
    GainModel::MonochromaticSmallSignalGain(MonochromaticSmallSignalGain::new(
        reciprocal_centimeter!(0.2),
    )?),
);
scenario.set_pump_source(
    head,
    PumpSource::Analytic(AnalyticPump::new(
        TransversalProfile::SuperGaussian(SuperGaussianShape::new(
            millimeter!(0.0, 0.0),  // pump centered on the optical axis
            millimeter!(5.0, 5.0),  // 1/e² half-width 5 mm
            1.0,                    // order 1 = standard Gaussian
            degree!(0.0),
            false,
        )?),
        LongitudinalProfile::Flat,   // uniform inversion from entrance to exit
        (64, 64, 16),                // 64 × 64 transversal cells; 16 longitudinal
    )?),
);
}

For an explanation of the grid argument and a comparison with the Lambert-Beer longitudinal profile, see Shaped pump profiles.

Source and detector

The input source uses 10 000 rays distributed on a Fibonacci grid, which tiles a circular aperture of radius 10 mm without clustering. The energy distribution is a high-order Super-Gaussian (order 8 ≈ flat-top): every ray starts with roughly the same energy per unit area, so any fluence variation at the output is entirely due to position-dependent gain, not to the input beam shape.

The output detector is a FluenceDetector using the Voronoi estimator, which assigns each ray an area equal to its Voronoi cell and reports the energy per area. With a Fibonacci source grid the cells have nearly equal area, giving a low-noise estimate.

What to look for

Open the .opm file in the GUI, select the Gaussian pump scenario in the pump-scenarios panel, and run the analysis. The fluence map at the output detector should show:

• A bright circular spot in the centre where the Gaussian pump profile is strongest, and where the gain is highest.
• A smooth radial fall-off that mirrors the pump’s σ = 5 mm half-width. At a radius of 5 mm the fluence has dropped to 1/e of its axial value.
• Near-zero fluence beyond the pump spot (r ≫ σ): rays there barely see the pump and leave the medium essentially unamplified.

If you switch the gain model to Const with the same overall factor for a quick comparison, the fluence map becomes uniform across the aperture — the spatial information that MonochromaticSmallSignalGain preserves is lost.

When to use a flat longitudinal profile

LongitudinalProfile::Flat is the right choice when the pump is not significantly absorbed on its way through the medium — for example when the medium is short compared with the pump absorption length, or when the pump is a side-pump geometry whose longitudinal variation is captured in the transversal profile instead. For end-pumped media where the pump is partially absorbed along the optical axis, LongitudinalProfile::LambertBeer models the exponential fall-off of the pump intensity from entrance to exit. That case is covered in Shaped pump profiles.

For the full list of transversal and longitudinal profile options and their parameters, see Pump scenarios.