Equations & boundaries
w² = w₀² + (M² λ L / πw₀)²
Collimated Gaussian-equivalent beam, waist at transmitter; no focusing optimization or aperture truncation.
w_eff² = w² + 4(L σθ)²
σθ is independent one-axis RMS Gaussian jitter. Bias and uncompensated transverse latency form an orthogonal residual offset. This is a long-time mean, not a tracking servo simulation.
capture = ∫receiver 2 exp(−2|r−d|²/w_eff²)/(πw_eff²) dA
Numerical circular-aperture integration, 1,000 midpoint samples of a one-dimensional Gaussian integral. Receiver is normal to beam; no obscuration.
P_DC = min(P_bus, P_laser η_opt 10^(−αL_km/10) capture η_PV η_DC)
Laser input is optical source output before transmitter losses. Wall-plug efficiency excludes auxiliaries.
Q = P_incident (absorptance − η_PV)
T = T_ambient + Q R_thermal
Lumped steady-state temperature only. Excludes DC-conditioning heat and dumped excess electricity. No local hotspots, temperature feedback, transients, cooling design, turbulence or scintillation. Measured PV efficiency must match illumination, temperature and load.
Validation plan
- Characterize the chosen receiver at low power: wavelength response, I–V curve, maximum-power point, reflected power and temperature.
- Validate the static link: measure optical power at each stage and usable electrical output into a calibrated load.
- Measure low-power moving-target tracking: residual pointing distribution, latency and power interruptions against speed.
- At a professionally controlled facility, increase power in stages and verify the receiver, cooling and protection systems.
- Accept the milestone only when ≥1 kW usable DC at ≥1 km is measured on the moving receiver for a predefined duration, speed and uptime.
Record beam profile, weather, calibration uncertainty, electrical load, receiver temperature and failures. The model provides no statistical confidence interval without measured input distributions.
Before procurement
Confirm receiver spectral compatibility, source beam quality, optical damage thresholds, tracking requirements, cooling capacity, test-site controls and independent power-meter calibration. High-power outdoor tests require a qualified laser-safety lead and site-specific controls.
Technical references
Edmund Optics: Gaussian beam propagation
2025 research: dedicated 1070 nm laser photovoltaic converters
The paper demonstrates device-specific conversion; its efficiency is not assumed transferable to satellite multijunction panels. Cost ranges and baseline settings are independent planning assumptions.