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Applied Optics

Applied Optics


  • Vol. 24, Iss. 8 — Apr. 15, 1985
  • pp: 1130–1138

Achromatic N-prism beam expanders: optimal configurations

Rick Trebino  »View Author Affiliations

Applied Optics, Vol. 24, Issue 8, pp. 1130-1138 (1985)

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In this paper, we calculate optimal prism configurations for achromatic N-prism beam expanders of a single material; we argue that for moderate to high magnifications, that is, M ≳ [2 − l/(2N−1− 1)]N, the up-up … up–down configuration is generally optimal, in the sense that it maximizes the transmission for given magnification. We also derive exact expressions for the incidence and apex angles that optimize a nonachromatic N-prism beam expander of arbitrary materials. The use of simple three-prism (up–up–down) and four-prism (up–up–up–down) single-material achromatic beam expanders is suggested for applications requiring compactness, achromaticity, and temperature stability.

© 1985 Optical Society of America

Original Manuscript: October 18, 1984
Published: April 15, 1985

Rick Trebino, "Achromatic N-prism beam expanders: optimal configurations," Appl. Opt. 24, 1130-1138 (1985)

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  28. We note here that intracavity laser applications, for example, generally require high temperature stability but could actually benefit from some dispersion, which could act to further decrease the laser linewidth somewhat. Thus a device with ∂γ(N)/∂T ≈ 0 at all relevant wavelengths but with large ∂γ(N)/∂λ, constructed necessarily of more than one material could be quite useful. Whether the appropriate materials exist to fabricate such a device is unknown to this author.
  29. The arrangement of this example may actually be of practical interest. Using a finite number of identical glass (n = 1.5) prisms, each with a magnification of 2, yields a device with magnification 2N, dispersion equal to 1/2N−1 of that of a single prism (perhaps small enough for many applications), and a reflection loss of only 2% per prism.
  30. A far from optimal three-prism achromatic expander can be constructed easily and cheaply from already coated off-the-shelf 45–45–90 BK-7 prisms, yielding a magnification of 20.1 and a transmission of 65%. The required incidence angles are 80°, 77°, and 53°, respectively. The use of smaller apex angles will more closely approach optimality and hence will yield higher transmission. The above nonoptimal case is probably of practical value, however.
  31. The question of thermal stability due to PBE dispersion is greatly complicated by the issue of the thermal stability of the mechanical mounts used for the optics in the cavity which can cause as much as ∼0.5 cm−1/°C drift in the dye-laser wavelength.32 The use of thermally stable or compensated construction for such mounts is critical even in multimode devices. Taking such care, we have observed mechanical mount-induced thermal drifts of <0.1 cm−1/°C near room temperature. Commercial designs, in general, do even better.
  32. F. J. Duarte, “Thermal Effects in Double-Prism Dye-Laser Cavities,” IEEE J. Quantum Electron. QE-19, 1345 (1983). [CrossRef]

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