Abstract

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

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References

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  1. I. W. Jackson, An Elementary Treatise on Optics (G. Y. Van Debogert, Schenectady, N.Y., 1852).
  2. F. J. Duarte, “Prism-Grating System for Laser Wavelength Measurements,” J. Phys. E. 16, 599 (1983).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, R. L. Byer, “High-Speed, High-Resolution Fiber-Diameter-Measurement System,” Appl. Opt.24, in press (1985), to be published.
    [CrossRef] [PubMed]
  4. M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
    [CrossRef]
  5. S. A. Myers, “An Improved Line Narrowing Technique for a Dye Laser Excited by a Nitrogen,” Opt. Commun. 4, 187 (1971).
    [CrossRef]
  6. E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
    [CrossRef]
  7. D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
    [CrossRef]
  8. L. G. Nair, “On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 23, 273 (1977).
    [CrossRef]
  9. R. Wyatt, “Comment on On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 9 (1978).
    [CrossRef]
  10. R. Wyatt, “Narrow Linewidth, Short Pulse Operation of a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 429 (1978).
    [CrossRef]
  11. G. K. Klauminzer, “New High-Performance Short-Cavity Dye Laser Design,” IEEE J. Quantum Electron. QE-13, 92D (1977);U.S. Patent4,127,828 (28Nov.1978).
  12. J. Krasiński, A. Sieradzau, “A Note on the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 28, 14 (1979).
    [CrossRef]
  13. F. J. Duarte, J. A. Piper, “A Double-Prism Beam Expander for Pulsed Dye Lasers,” Opt. Commun. 35, 100 (1980).
    [CrossRef]
  14. A. F. Bernhardt, P. Rasmussen, “Design Criteria and Operating Characteristics of a Single-Mode Pulsed Dye Laser,” Appl. Phys. B 26, 141 (1981).
    [CrossRef]
  15. B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
    [CrossRef]
  16. D. A. Greenhalgh, P. H. Sarkies, “Novel Geometry for Simple Accurate Tuning of Lasers,” Appl. Opt. 21, 3234 (1982).
    [CrossRef] [PubMed]
  17. F. J. Duarte, J. A. Piper, “Comparison of Prism-Expander and Grazing-Incidence Grating Cavities for Copper Laser Pumped Dye Lasers,” Appl. Opt. 21, 2782 (1982).
    [CrossRef] [PubMed]
  18. F. J. Duarte, J. A. Piper, “Narrow Linewidth, High prf Copper Laser-Pumped Dye-Laser Oscillators,” Appl. Opt. 23, 1391 (1984).
    [CrossRef] [PubMed]
  19. F. J. Duarte, J. A. Piper, “Multi-Pass Dispersion Theory of Prismatic Pulsed Dye Lasers,” Opt. Acta 31, 331 (1984).
    [CrossRef]
  20. F. J. Duarte, J. A. Piper, “Dispersion Theory of Multiple-Prism Beam Expanders for Pulsed Dye Lasers,” Opt. Commun. 43, 303 (1982).
    [CrossRef]
  21. H. J. Kong, S. S. Lee, “Dual Wavelength and Continuously Variable Polarization Dye Laser,” IEEE J. Quantum Electron. QE-17, 439 (1981).
    [CrossRef]
  22. T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
    [CrossRef]
  23. F. J. Duarte, “Variable-Linewidth High-Power TEA CO2 Laser,” journal to be published.
  24. C. S. Zhou, “Design of a Pulsed Single-Mode Dye Laser,” Appl. Opt. 23, 2879 (1984).
    [CrossRef] [PubMed]
  25. Quantaray, Molectron.
  26. Lambda Physik.
  27. J. R. M. Barr, “Achromatic Prism Beam Expanders,” Opt. Commun. 51, 41 (1984).
    [CrossRef]
  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]

1984 (5)

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

F. J. Duarte, J. A. Piper, “Narrow Linewidth, High prf Copper Laser-Pumped Dye-Laser Oscillators,” Appl. Opt. 23, 1391 (1984).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “Multi-Pass Dispersion Theory of Prismatic Pulsed Dye Lasers,” Opt. Acta 31, 331 (1984).
[CrossRef]

C. S. Zhou, “Design of a Pulsed Single-Mode Dye Laser,” Appl. Opt. 23, 2879 (1984).
[CrossRef] [PubMed]

J. R. M. Barr, “Achromatic Prism Beam Expanders,” Opt. Commun. 51, 41 (1984).
[CrossRef]

1983 (2)

F. J. Duarte, “Thermal Effects in Double-Prism Dye-Laser Cavities,” IEEE J. Quantum Electron. QE-19, 1345 (1983).
[CrossRef]

F. J. Duarte, “Prism-Grating System for Laser Wavelength Measurements,” J. Phys. E. 16, 599 (1983).
[CrossRef]

1982 (3)

1981 (3)

H. J. Kong, S. S. Lee, “Dual Wavelength and Continuously Variable Polarization Dye Laser,” IEEE J. Quantum Electron. QE-17, 439 (1981).
[CrossRef]

A. F. Bernhardt, P. Rasmussen, “Design Criteria and Operating Characteristics of a Single-Mode Pulsed Dye Laser,” Appl. Phys. B 26, 141 (1981).
[CrossRef]

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

1980 (1)

F. J. Duarte, J. A. Piper, “A Double-Prism Beam Expander for Pulsed Dye Lasers,” Opt. Commun. 35, 100 (1980).
[CrossRef]

1979 (1)

J. Krasiński, A. Sieradzau, “A Note on the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 28, 14 (1979).
[CrossRef]

1978 (3)

T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
[CrossRef]

R. Wyatt, “Comment on On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 9 (1978).
[CrossRef]

R. Wyatt, “Narrow Linewidth, Short Pulse Operation of a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 429 (1978).
[CrossRef]

1977 (2)

G. K. Klauminzer, “New High-Performance Short-Cavity Dye Laser Design,” IEEE J. Quantum Electron. QE-13, 92D (1977);U.S. Patent4,127,828 (28Nov.1978).

L. G. Nair, “On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 23, 273 (1977).
[CrossRef]

1975 (1)

D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

1972 (1)

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

1971 (1)

S. A. Myers, “An Improved Line Narrowing Technique for a Dye Laser Excited by a Nitrogen,” Opt. Commun. 4, 187 (1971).
[CrossRef]

Barr, J. R. M.

J. R. M. Barr, “Achromatic Prism Beam Expanders,” Opt. Commun. 51, 41 (1984).
[CrossRef]

Bernhardt, A. F.

A. F. Bernhardt, P. Rasmussen, “Design Criteria and Operating Characteristics of a Single-Mode Pulsed Dye Laser,” Appl. Phys. B 26, 141 (1981).
[CrossRef]

Bor, Zs.

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

Byer, R. L.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

M. M. Fejer, G. A. Magel, R. L. Byer, “High-Speed, High-Resolution Fiber-Diameter-Measurement System,” Appl. Opt.24, in press (1985), to be published.
[CrossRef] [PubMed]

Duarte, F. J.

F. J. Duarte, J. A. Piper, “Narrow Linewidth, High prf Copper Laser-Pumped Dye-Laser Oscillators,” Appl. Opt. 23, 1391 (1984).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “Multi-Pass Dispersion Theory of Prismatic Pulsed Dye Lasers,” Opt. Acta 31, 331 (1984).
[CrossRef]

F. J. Duarte, “Prism-Grating System for Laser Wavelength Measurements,” J. Phys. E. 16, 599 (1983).
[CrossRef]

F. J. Duarte, “Thermal Effects in Double-Prism Dye-Laser Cavities,” IEEE J. Quantum Electron. QE-19, 1345 (1983).
[CrossRef]

F. J. Duarte, J. A. Piper, “Dispersion Theory of Multiple-Prism Beam Expanders for Pulsed Dye Lasers,” Opt. Commun. 43, 303 (1982).
[CrossRef]

F. J. Duarte, J. A. Piper, “Comparison of Prism-Expander and Grazing-Incidence Grating Cavities for Copper Laser Pumped Dye Lasers,” Appl. Opt. 21, 2782 (1982).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “A Double-Prism Beam Expander for Pulsed Dye Lasers,” Opt. Commun. 35, 100 (1980).
[CrossRef]

F. J. Duarte, “Variable-Linewidth High-Power TEA CO2 Laser,” journal to be published.

Dunning, F. B.

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

Fejer, M. M.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

M. M. Fejer, G. A. Magel, R. L. Byer, “High-Speed, High-Resolution Fiber-Diameter-Measurement System,” Appl. Opt.24, in press (1985), to be published.
[CrossRef] [PubMed]

Greenhalgh, D. A.

Hanna, D. C.

D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Jackson, I. W.

I. W. Jackson, An Elementary Treatise on Optics (G. Y. Van Debogert, Schenectady, N.Y., 1852).

Kärkkäinen, P. A.

D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Kasuya, T.

T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
[CrossRef]

Klauminzer, G. K.

G. K. Klauminzer, “New High-Performance Short-Cavity Dye Laser Design,” IEEE J. Quantum Electron. QE-13, 92D (1977);U.S. Patent4,127,828 (28Nov.1978).

Kong, H. J.

H. J. Kong, S. S. Lee, “Dual Wavelength and Continuously Variable Polarization Dye Laser,” IEEE J. Quantum Electron. QE-17, 439 (1981).
[CrossRef]

Krasinski, J.

J. Krasiński, A. Sieradzau, “A Note on the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 28, 14 (1979).
[CrossRef]

Lee, S. S.

H. J. Kong, S. S. Lee, “Dual Wavelength and Continuously Variable Polarization Dye Laser,” IEEE J. Quantum Electron. QE-17, 439 (1981).
[CrossRef]

Magel, G. A.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

M. M. Fejer, G. A. Magel, R. L. Byer, “High-Speed, High-Resolution Fiber-Diameter-Measurement System,” Appl. Opt.24, in press (1985), to be published.
[CrossRef] [PubMed]

Myers, S. A.

S. A. Myers, “An Improved Line Narrowing Technique for a Dye Laser Excited by a Nitrogen,” Opt. Commun. 4, 187 (1971).
[CrossRef]

Nair, L. G.

L. G. Nair, “On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 23, 273 (1977).
[CrossRef]

Nightingale, J. L.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Piper, J. A.

F. J. Duarte, J. A. Piper, “Multi-Pass Dispersion Theory of Prismatic Pulsed Dye Lasers,” Opt. Acta 31, 331 (1984).
[CrossRef]

F. J. Duarte, J. A. Piper, “Narrow Linewidth, High prf Copper Laser-Pumped Dye-Laser Oscillators,” Appl. Opt. 23, 1391 (1984).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “Comparison of Prism-Expander and Grazing-Incidence Grating Cavities for Copper Laser Pumped Dye Lasers,” Appl. Opt. 21, 2782 (1982).
[CrossRef] [PubMed]

F. J. Duarte, J. A. Piper, “Dispersion Theory of Multiple-Prism Beam Expanders for Pulsed Dye Lasers,” Opt. Commun. 43, 303 (1982).
[CrossRef]

F. J. Duarte, J. A. Piper, “A Double-Prism Beam Expander for Pulsed Dye Lasers,” Opt. Commun. 35, 100 (1980).
[CrossRef]

Rácz, B.

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

Rasmussen, P.

A. F. Bernhardt, P. Rasmussen, “Design Criteria and Operating Characteristics of a Single-Mode Pulsed Dye Laser,” Appl. Phys. B 26, 141 (1981).
[CrossRef]

Rundel, R. D.

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

Sarkies, P. H.

Shimoda, K.

T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
[CrossRef]

Sieradzau, A.

J. Krasiński, A. Sieradzau, “A Note on the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 28, 14 (1979).
[CrossRef]

Stebbings, R. F.

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

Stokes, E. D.

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

Suzuki, T.

T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
[CrossRef]

Szabo, G.

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

Szatmári, S.

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

Walters, G. K.

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

Wyatt, R.

R. Wyatt, “Comment on On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 9 (1978).
[CrossRef]

R. Wyatt, “Narrow Linewidth, Short Pulse Operation of a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 429 (1978).
[CrossRef]

D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Zhou, C. S.

Appl. Opt. (4)

Appl. Phys. (1)

T. Kasuya, T. Suzuki, K. Shimoda, “A Prism Anamorphic System for Gaussian Beam Expander,” Appl. Phys. 17, 131 (1978).
[CrossRef]

Appl. Phys. B (1)

A. F. Bernhardt, P. Rasmussen, “Design Criteria and Operating Characteristics of a Single-Mode Pulsed Dye Laser,” Appl. Phys. B 26, 141 (1981).
[CrossRef]

IEEE J. Quantum Electron. (3)

H. J. Kong, S. S. Lee, “Dual Wavelength and Continuously Variable Polarization Dye Laser,” IEEE J. Quantum Electron. QE-17, 439 (1981).
[CrossRef]

G. K. Klauminzer, “New High-Performance Short-Cavity Dye Laser Design,” IEEE J. Quantum Electron. QE-13, 92D (1977);U.S. Patent4,127,828 (28Nov.1978).

F. J. Duarte, “Thermal Effects in Double-Prism Dye-Laser Cavities,” IEEE J. Quantum Electron. QE-19, 1345 (1983).
[CrossRef]

J. Phys. E. (1)

F. J. Duarte, “Prism-Grating System for Laser Wavelength Measurements,” J. Phys. E. 16, 599 (1983).
[CrossRef]

Opt. Acta (1)

F. J. Duarte, J. A. Piper, “Multi-Pass Dispersion Theory of Prismatic Pulsed Dye Lasers,” Opt. Acta 31, 331 (1984).
[CrossRef]

Opt. Commun. (10)

F. J. Duarte, J. A. Piper, “Dispersion Theory of Multiple-Prism Beam Expanders for Pulsed Dye Lasers,” Opt. Commun. 43, 303 (1982).
[CrossRef]

J. Krasiński, A. Sieradzau, “A Note on the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 28, 14 (1979).
[CrossRef]

F. J. Duarte, J. A. Piper, “A Double-Prism Beam Expander for Pulsed Dye Lasers,” Opt. Commun. 35, 100 (1980).
[CrossRef]

S. A. Myers, “An Improved Line Narrowing Technique for a Dye Laser Excited by a Nitrogen,” Opt. Commun. 4, 187 (1971).
[CrossRef]

E. D. Stokes, F. B. Dunning, R. F. Stebbings, G. K. Walters, R. D. Rundel, “A High Efficiency Dye Laser Tunable from the UV to the IR,” Opt. Commun. 5, 267 (1972).
[CrossRef]

L. G. Nair, “On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen Laser Pumped Dye Laser,” Opt. Commun. 23, 273 (1977).
[CrossRef]

R. Wyatt, “Comment on On the Dispersion of a Prism Used as a Beam Expander in a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 9 (1978).
[CrossRef]

R. Wyatt, “Narrow Linewidth, Short Pulse Operation of a Nitrogen-Laser-Pumped Dye Laser,” Opt. Commun. 26, 429 (1978).
[CrossRef]

B. Rácz, Zs. Bor, S. Szatmári, G. Szabo, “Comparative Study of Beam Expanders Used in Nitrogen Laser Pumped Dye Lasers,” Opt. Commun. 36, 399 (1981).
[CrossRef]

J. R. M. Barr, “Achromatic Prism Beam Expanders,” Opt. Commun. 51, 41 (1984).
[CrossRef]

Opt. Quantum Electron. (1)

D. C. Hanna, P. A. Kärkkäinen, R. Wyatt, “A Simple Beam Expander for Frequency Narrowing of Dye Lasers,” Opt. Quantum Electron. 7, 115 (1975).
[CrossRef]

Rev. Sci. Instrum. (1)

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser Heated Miniature Pedestal Growth Apparatus for Single Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Other (9)

I. W. Jackson, An Elementary Treatise on Optics (G. Y. Van Debogert, Schenectady, N.Y., 1852).

M. M. Fejer, G. A. Magel, R. L. Byer, “High-Speed, High-Resolution Fiber-Diameter-Measurement System,” Appl. Opt.24, in press (1985), to be published.
[CrossRef] [PubMed]

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.

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.

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.

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.

Quantaray, Molectron.

Lambda Physik.

F. J. Duarte, “Variable-Linewidth High-Power TEA CO2 Laser,” journal to be published.

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Figures (10)

Fig. 1
Fig. 1

Standard down–up–up–down (compensating pair of compensating pairs) achromatic four-prism beam expander. This device consists of two pairs of nearly achromatic two-prism beam expanders, with the second pair inverted with respect to the first. It achieves nearly collinear input and output beams but does not optimize transmission.

Fig. 2
Fig. 2

Three-prism up–up–down beam expander. This configuration is optimal for achromatic three-prism beam expanders.

Fig. 3
Fig. 3

Four-prism up–up–up–down beam expander. This configuration is optimal for achromatic four-prism beam expanders of a single material with total magnification ≳10 and probably also for lower magnifications.

Fig. 4
Fig. 4

N-prism up–up … up–down beam expander. This configuration is optimal for achromatic single-material prism beam expanders of moderate to large magnification, specifically, for magnifications greater than about [2 − 1/(2N−1 − 1)]N. In addition, if each prism magnification is 2, such a device achieves a total magnification of 2N, a dispersion of 1/2N−1 that of a single prism, and a transmission of 98% per prism.

Fig. 5
Fig. 5

Prism geometry.

Fig. 6
Fig. 6

Optimal prism configurations vs magnification for single-material three-, four-, five-, and six-prism achromatic beam expanders. Exact solutions derived herein are shown as dark dots, which are extended to indicate the estimated range of magnifications for which each configuration is optimal. The up–up … up–down configuration appears optimal for large magnifications for all PBEs.

Fig. 7
Fig. 7

Estimated optimal transmission vs magnification for several configurations for an N-prism single-material achromatic beam expander. Each configuration is optimal at some characteristic magnification and also in a neighborhood about that point but becomes nonoptimal near another configuration's characteristic magnification. (The horizontal axis can be interpreted as total magnification or magnification per prism). The dashed line illustrates the optimal transmission for a nonachromatic single-material PBE (see Sec. II), which attains maximal (100%) transmission for Brewster angle incidence, when the total magnification is nN. Note that at the characteristic magnifications, m1, … , m5, optimal nonachromatic transmission and optimal achromatic transmission (using the appropriate configuration) are equal.

Fig. 8
Fig. 8

Four-prism (up–up–up–down) achromatic PBE/Littrow-grating dye laser. The up–up–up–down configuration should be more efficient than the down–up–up–down configuration for relatively large magnifications, such as ∼40.

Fig. 9
Fig. 9

Three-prism (up–up–down) achromatic PBE/Littrow-gratingdye laser. For a magnification of ∼40, a transmission of ∼50% canbe achieved.

Fig. 10
Fig. 10

Three-prism (up–up–down) achromatic PBE/grazing-incidence-grating dye laser. Such a hybrid design is more efficient than the PBE/Littrow-grating design or the grazing-incidence design.15 Use of a three-prism achromatic design (vs the nonachromatic two-prism design of Ref. 15) should allow thermally stable single-mode operation and should further improve efficiency. (In Figs. 810, the pump beam is shown entering from above for diagrammatic simplicity only.)

Tables (1)

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Table I Exact Optimal Achromatic PBE Solutions

Equations (22)

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M i = cos ϕ i cos θ i cos ν i cos μ i ,
M = i = 1 N M i .
T i = 4 n i cos ϕ i / cos θ i ( n i + cos ϕ i / cos θ i ) 2 ,
T = i = 1 N T i .
α i opt = ϕ i opt , i = 1 , , N ,
M i = cos ϕ i cos θ j .
T i = 4 n i M i ( n i + M i ) 2 ,
T = 4 n 1 M 1 ( n 1 + M 1 ) 2 4 n 2 M 2 ( n 2 + M 2 ) 2 4 n N M N ( n N + M N ) 2 .
L ( M i ) = ( n 1 + M 1 ) ( n 2 + M 2 ) ( n N + M N ) ,
M 1 M 2 M N = M .
M i opt = n i ( n 1 n 2 n N ) 1 / N M 1 / N , i = 1 , , N ,
θ i opt = arcsin [ ( M i opt ) 2 1 ( M i opt ) 2 1 / n i 2 ] ,
α i opt = arcsin [ ( M i opt ) 2 1 n i 2 ( M i opt ) 2 1 ] .
γ i n i = sin α i cos ϕ i cos ν i .
γ ( N ) = i = 1 N i γ i
γ ( N ) x = i = 1 N i γ i x .
γ ( N ) x = i = 1 N i γ i x j = i + 1 N M j .
γ ( 2 ) x = 1 M 2 1 γ 1 x 2 γ 2 x ,
γ ( 3 ) x = 1 M 2 M 3 1 γ 1 x + 1 M 3 2 γ 2 x + 3 γ 3 x ,
γ ( 4 ) x = 1 M 2 M 3 M 4 1 γ 1 x + 1 M 3 M 4 2 γ 2 x + 1 M 4 3 γ 3 x + 4 γ 4 x .
γ ( N ) n N + N 1 2 + N 2 4 + N 3 8 + + 1 2 N 1 .
i = 1 N i m i 1 = 0 ,

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