Wide Bandpass Filter

Wide band-pass filter from a long-pass edge filter on one face and a short-pass on the other: 50 % points, width and peak transmittance.

Model: Exact

n_H (high index)n_L (low index)n_substratePeriods per stack (N)Cut-on edge (nm), front face long-passCut-off edge (nm), back face short-pass

Pass band (50 % points)

509.2 – 684.5 nm

Width 175.4 nm

Peak T in the pass band

94.35 %

Mean 86.0 % between the 50 % points

Front face: (H/2 L H/2)⁸ at λ₀ = 423.9 nm, reflects 367.9–500.0 nm

Back face: (L/2 H L/2)⁸ at λ₀ = 806.6 nm, reflects 700.0–951.4 nm

Each face is an edge filter with λ₀ = λ_edge(1 ∓ Δg). The faces of the thick substrate add in intensity: T = T₁T₂/(1 − R₁R₂). Outside the two reflection zones (and near λ₀/3) the filter transmits again; a real filter adds blocking stacks there.

Model and references

Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers

Long-pass and short-pass edge filters on the two faces, transfer matrix, lossless constant indices, normal incidence; faces added incoherently. No blockers outside the two reflection zones.

Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (incoherent reflection), ch. 7 (edge filters) and ch. 8 (band-pass filters). CRC Press. doi:10.1201/9781420073034
Epstein L. I. (1952). The design of optical filters. J. Opt. Soc. Am. 42, 806. doi:10.1364/JOSA.42.000806

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