How much of the electrical input of a cesium, rubidium, potassium or sodium arc comes out as light between 0.4 and 1.3 µm. We traced every spectrum in a 1978 Xerox paper from the full-resolution scan. Pulsed sodium reaches 94% in band, pulsed cesium 60%, dc potassium 62%. Xenon at dc reaches 17%.
W. F. Hug, C. M. Hains, C. J. Marlett, “Spectra of alkali metal vapor and noble gas flashlamps,” J. Opt. Soc. Am. 68(1), 62–67 (1978). doi:10.1364/JOSA.68.000062 · read the paper (PDF, LightCell sign-in)
Lamps: 8 mm bore, 8 cm gap, sapphire or Lucalox envelope near 850 °C, 0.15 atm Ne start gas, alkali pressure set by a reservoir heater (alkali). Water-cooled quartz, 4–7 mm bore (Xe, Kr). measured spectra from the paper. digitized our trace and integrals. model the cell simulator.
η = ∫ S(λ) dλ over the plotted band, where S is radiant output per µm per unit electrical input (W/µm/W at dc, J/µm/J pulsed). digitized ±3%. Hover a row to load it on the bench below.
| Lamp | Mode | Best condition | η in band | Band µm |
|---|
Put any of the 36 traced spectra, de Groot’s three sodium spectra (shape only, efficiency set by you), or a blackbody on a stack of up to three photovoltaic cells. Each cell has its own band edge, edge sharpness, quantum efficiency, temperature and radiative efficiency. Hover any curve in the spectra chart, a lamp in the list, a table row or a cell material to preview it; click to keep it. Curves in the band-gap sweep and the trapped-light chart load on click too. The model runs as a 10 KB WebAssembly module. model
| Cell | Eg eV | edge nm | absorbs | Jsc A/cm² | Voc V | FF | P W/cm² |
|---|
Uses cell 1’s edge width, EQE, temperature and radiative efficiency, and the coupling settings above.
A sodium arc can’t emit much through its strongest line. The D lines at 589 nm are so optically thick that the cooler gas near the wall reabsorbs them, which is why they show up as a dip. That energy isn’t lost. As power and pressure rise, it leaves through routes that can escape: the far wings of the D lines, the 819 nm (3d→3p) line, and Na₂ molecular bands near 551, 805 and 882 nm.
De Groot and van Vliet show this sequence in an experimental high-pressure sodium discharge built for strong self-reversal (Fig. 3.21, panels a → c at increasing input power and sodium pressure). The 1978 pulsed sodium lamp (Hug et al., 500 µs pulses) shares the red and near-IR part of that pattern: the D line reversed and the output peaking at 0.80–0.82 µm, where the 819 nm line and the 805 nm Na₂ band sit. It is also far brighter in the blue, from 0.41 to 0.55 µm, where de Groot’s steady discharge is nearly dark. That is a hotter plasma, with recombination light and lines from higher levels, which de Groot (§7.2) and Schöpp & Franke both report for pulsed operation. In both cases the plasma behaves like its own recycling cavity: collisions hand trapped energy around until it leaves at a wavelength that gets out. Hug’s 120–300 Å filters also blur the narrow dark D region into a shallower dip. measured spectra; shapes only, each curve scaled to its own maximum.
Data: degroot-fig321.json, traced from J. J. de Groot & J. A. J. M. van Vliet, The High-Pressure Sodium Lamp (Philips Technical Library, 1986), Fig. 3.21, p. 83. Arbitrary units; the 819 nm line runs off scale in panels a and b.
| Lamp | Fig. | Condition | η in band | Band µm |
|---|
| Lamp | Figures | η each | band | spread |
|---|
Data: lamps.json · lamps.csv. Every located marker and the traced curve on a 0.004 µm grid, with lamp metadata. Copied.
Calibration. From the full-resolution scan (3008 × 4320 per page). Each figure's axes are fitted to its own tick marks: about 130 px per 0.1 µm, residual under 1 px. That is ±0.001 µm and ±0.002 in spectral units.
Markers. Every plotted marker is located by normalized cross-correlation with templates learned from that figure's own markers. Each marker goes to its curve by shape (filled disk, open square, filled triangle, open diamond). Markers hidden under another curve's marker are shared. Three markers on the axis or fully covered were placed by hand from gridded close-ups.
Curves. The authors' drawn line is traced pixel by pixel between markers, following the ink, and integrated on a 0.002 µm grid. Where a curve runs hidden under another at its ends, it follows that curve. The cross-check table shows the result. The same dc 400 Torr lamp, traced independently from two or three figures, agrees within 0.3–4%. We quote ±3% on each integral.
What tracing cannot fix. The paper's sampling: interference filters every 330 Å from 0.41 to 0.71 µm and every ~500 Å above, each 120–300 Å wide. Self-reversed resonance lines between filters are only as resolved as the authors drew them. Every number is also a lower bound on total radiation. The data stop at 0.41 µm in the UV and at 1.1–1.28 µm in the IR. Pulsed Rb and K (Figs. 6 and 8) stop at 1.1 µm.
One cross-check from the paper. It says the 250 µs cesium spectra are about 25% above the 70 µs ones. Our integrals give 13–31% higher, depending on which current densities are paired.
Pulsed sodium at 94%. The dc 400 Torr reference curve is the same in Figs. 9 and 10 (36.1% vs 36.5%), so Fig. 10’s doubled axis was read correctly. Hug’s best dc sodium numbers (35–41% in 0.41–1.18 µm) also fit the measured energy balance of commercial sodium lamps: about 6% to the electrodes and roughly 70% of the discharge power radiated, 35% of input as visible light (de Groot & van Vliet §2.5). That makes a calibration error an unlikely source of the pulsed result. De Groot’s measurements show radiant efficiency rising with each lever the pulse pushes further: wall loading and input power (§4.2.1), sodium pressure (Fig. 4.14), buffer-gas pressure through extra line broadening (§5.3), and a flatter temperature profile, reaching unity when the plasma and wall temperatures meet (§4.2.2). Their steady lamps stop at about 0.4 W/mm² and 40 W/cm. Hug’s pulse runs near 5,000 W/cm with the arc filling the bore, beyond every measured trend. No independent measurement of pulsed sodium’s total radiant efficiency has been found yet; see the library for what exists.
Cavity recycling. Lamp and cells sit in a closed reflective cavity. Light leaving the lamp lands on the cells (their share of the cavity) or on the walls. Cells absorb the light above their edge and reflect the rest off the rear surface: about 95% for a gold back contact, about 98.5–99% for an air gap over gold, as in air-bridge thermophotovoltaic cells. Every return trip crosses the lamp, which absorbs a fraction per pass and re-emits a share of that power with its own spectrum. Light keeps bouncing until something absorbs it, so even a lamp that absorbs only a fifth of the light per pass eventually catches nearly everything that doesn't leak. The losses are the leaks: the cell rear, the walls, light the cells absorb but don't collect, and reabsorbed power the lamp loses to conduction instead of re-emitting. A round trip takes nanoseconds, so a 500 µs pulse is effectively steady state. Two simplifications: the lamp re-emits with its measured spectrum, and the envelope's own hot-sapphire glow, which falls below the edge and joins the bouncing light, is folded into the per-pass absorption.
The cell model. Detailed balance, one ideal diode per cell. Each cell absorbs everything above its edge through a logistic edge of the set width, times its EQE. The dark current comes from reciprocity with that absorptance, divided by the external radiative efficiency (ERE). Cells in a stack are wired independently (four-terminal), highest gap on top. The band edge does not shift with temperature; set it directly. Preset EQE and ERE values are illustrative. Check: a 5778 K blackbody at 0.1 W/cm² on a 1.34 eV ideal cell gives 31.2%, the Shockley–Queisser value.
More, with notes on what each contributes: LightCell library.