A solar-pumped laser collects sunlight with a heliostat and a secondary concentrator

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Beams, resonators and guided-wave photonics

What an Instrument Can See, Ch Radiance, etendue and a throughput budget that is spent

Problem

A solar-pumped laser collects sunlight with a heliostat and a secondary concentrator, then relays it to a laser rod through a large-core optical fibre. The Sun's angular radius as seen from Earth is θs=0.267∘\theta_s = 0.267^\circ. ((a)) Estimate the maximum concentration ratio Cmax⁡=n2/sin⁡2θsC_{\max} = n^2/\sin^2\theta_s achievable by a passive concentrator working in air (n=1n=1). ((b)) The final stage of the concentrator is a solid fused-silica secondary of refractive index n=1.46n = 1.46 with its absorbing face immersed in the glass. Estimate Cmax⁡C_{\max} for this immersed stage, and state the factor by which immersion has raised the bound over the air value. ((c)) The relay fibre has a core diameter of 1.5 mm and a numerical aperture NA=0.48\mathrm{NA} = 0.48, matched to the concentrator's exit cone, and carries light near λ=550 nm\lambda = 550\,\mathrm{nm}. Estimate the number of independent spatial modes (beams) per polarisation that this fibre supports, using N≈Ξ/λ2N \approx \Xi/\lambda^2.

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