Abstract

We investigate the absorption distribution in a cylindrical gain medium that is pumped by a source of distributed laser diodes by means of a pump cavity developed from the edge-ray principle of nonimaging optics. The performance of this pumping arrangement is studied by using a nonsequential, numerical, three-dimensional ray-tracing scheme. A figure of merit is defined for the pump cavities that takes into account the coupling efficiency and uniformity of the absorption distribution. It is found that the nonimaging pump cavity maintains a high coupling efficiency with extended two-dimensional diode arrays and obtains a fairly uniform absorption distribution. The nonimaging cavity is compared with two other designs: a close-coupled side-pumped cavity and an imaging design in the form of a elliptical cavity. The nonimaging cavity has a better figure of merit per diode than these two designs. It also permits the use of an extended, sparse, two-dimensional diode array, which reduces thermal loading of the source and eliminates all cavity optics other than the main reflector

© 1993 Optical Society of America

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  1. L. C. Conant, C. W. Reno, “Laser diode pumped Nd:YAG laser,” Appl. Opt. 13, 2457–2458 (1974).
    [CrossRef] [PubMed]
  2. T. M. Baer, D. F. Head, M. Sakamoto, “High efficiency diode-bar pumped solid state laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical, Digest Series (Optical Society of America, Washington, D.C., 1989), p. 416.
  3. T. M. Baer, D. F. Head, P. Gooding. “High peak power Q-switched Nd:YLF laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.
  4. T. Y. Fan, “Diode-pumped solid state lasers,” Line. Lab. J. 3, 413–425 (1990).
  5. T. Y. Fan, “Efficient coupling of multiple diode laser arrays to an optical fiber by geometric multiplexing,” Appl. Opt. 30, 620 (1991).
    [CrossRef]
  6. As of February 1992, the maximum reported output powers for the tightly folded resonator was 10 W when fiber coupling was used: M. S. Keirstead, T. M. Baer, “10 W, TEM00 output from a diode-pumped, solid-state laser,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 490. In a geometric multiplex end-pump design, a 15-W multimode and a 6-W TEM00 have been obtained: S. C. Todwell, J. F. Seamans, C. E. Hamilton, C. H. Muller, D. D. Lowenthal, “Efficient, 15-W output power, diode-end pumped Nd:YAG laser,” Opt. Lett. 16, 584–586 (1991).
    [CrossRef]
  7. L. R. Marshall, A. Kaz, R. L. Burnham, “Highly efficient TEM00 operation of transversely diode-pumped Nd:YAG lasers,” Opt. Lett. 17, 186–188 (1992).
    [CrossRef] [PubMed]
  8. A. D. Hays, R. Burnham, “Quasi-CW diode-array side pumped 946-nm neodymium laser,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 4.
  9. R. Burnham, “High-power transverse diode-pumped solid-state lasers,” Opt. Photon. News 1(1), 4–8 (1990).
    [CrossRef]
  10. T. H. Allik, W. W. Hovis, D. P. Caffey, V. King, “Efficient diode-array-pumped Nd:YAG and Nd:Lu:YAG lasers,” Opt. Lett. 14, 116–118 (1989).
    [CrossRef] [PubMed]
  11. Throughout this study the absorption distribution is calculated for a number of pump cavities with diode pump sources. The gain distribution is directly related to the absorption distribution by multiplication of the quantum defect value (e.g., for diode pumping at 810 nm of Nd:YAG, this value is approximately 0.8).
  12. We assume that matching the gain distribution to the cavity TEM00 mode profile is optimum. Some authors claim that the optimum transverse gain profile is a delta function along the mode axis of the gain medium, although these authors account for neither the effects of amplified spontaneous emission and optical damage nor diffraction. See, e.g., D. G. Hall, R. J. Smith, R. R. Rice, “Pump-size effects in Nd:YAG lasers,” Appl. Opt. 19, 3041–3043 (1980).
    [CrossRef] [PubMed]
  13. M. K. Reed, W. J. Kozlovsky, R. L. Byer, G. L. Harnagel, P. S. Cross, “Diode-laser-array-pumped neodymium slab oscillators,” Opt. Lett. 13, 204–206 (1988).
    [CrossRef] [PubMed]
  14. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4.
  15. Ref. 14, Chap. 9.
  16. O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), p. 354. The parallel junction is typically three to five times larger; therefore, the divergence angle in the perpendicular direction is three to five times larger than the divergence angle in the parallel direction.
  17. The full standard deviation angle is twice the standard deviation angle of the Gaussian curve in both the tangential and the sagittal directions. The relation between these angles and the FWHM divergence angles of the individual diodes is θFWHM = 2.35482 (σt,s).
  18. Other ray-tracing angle selection algorithms were considered, but because of the small dimensionality of the space and a deterministic result in question, a deterministic ray set was chosen. For example, a Monte Carlo ray-tracing method would give results similar to those of these deterministic ray sets. It is also noted that, because the cavity is cylindrical in nature, the three-dimensional ray trace offers little advantage over the two-dimensional trace; however, the three-dimensional trace was performed for completeness. The accuracy of the deterministic ray trace in two-dimensional space is proportional to one over the square root of the number of rays. To back up this claim we traced ray sets larger by 1 order of magnitude and found that there are no appreciable differences between the determined absorption distributions.
  19. I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentrators,” in Progress in Optics, E. Wolf, ed. (Elsevier, London, 1989) Chap. III, p. 171.
  20. Refractive imaging systems are available with a N.A. of 0.85, which corresponds to an object-space angle of approximately 58°; therefore the maximum possible C2D is not obtained. Further, these systems are microscope objectives with a focal length of approximately 3 mm. This length gives a lens radius of approximately 5 mm, so the lens system is small and cannot be enlarged easily without introducing a large amount of aberration. Therefore refractive imaging systems cannot be scaled up to permit large-area pump sources.
  21. Ref. 14, Chap. 1.
  22. P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).
  23. A. Rabl, “Solar concentrators with maximal concentrations for cylindrical absorbers,” Appl. Opt. 15, 1871–1873 (1976).
    [CrossRef] [PubMed]
  24. Ref. 14, App. H.
  25. J. D. Kuppenheimer, “Design of multilamp nonimaging laser pump cavities,” Opt. Eng. 27, 1067–1071 (1988).
  26. P. Gleckman, “Achievement of ultrahigh solar concentration with potential for efficient laser pumping,” Appl. Opt. 27, 4385–4391 (1988).
    [CrossRef] [PubMed]
  27. R. M. J. Benmair, J. Kagan, Y. Kalisky, Y. Noter, M. Oron, Y. Shimony, A. Yogev, “Solar-pumped Er, Tm, Ho:YAG laser,” Opt. Lett. 15, 36–38 (1990).
    [CrossRef] [PubMed]
  28. R. J. Koshel, I. A. Walmsley, “Diode pumping of solid-state lasers with nonimaging optics: a theoretical study,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 126.
  29. The parameterization of the CPC for a circular absorber follows Rabl23; however, in Eqs. (8) and (9) of Sec. II in Rabl one reads that δ = π/2, when this substitution for δ is not supposed to be done until Sec. III (specific to a circular absorber). Welford and Winston complete the theory in the correct order, but the notation of Rabl is used throughout this study.
  30. Ref. 14, Chap. 9.
  31. R. Winston, “Ideal flux concentrators with reflector gaps,” Appl. Opt. 17, 1668–1669 (1978).
    [CrossRef] [PubMed]
  32. W. R. McIntire, “New reflector design, which avoids losses through gaps between tubular absorbers and reflectors,” Sol. Energy 25, 215–220 (1980).
    [CrossRef]
  33. W. R. McIntire, R. Winston, “Design considerations for reducing optical losses due to gaps between absorber and reflector,” in Proceedings of the 1981 Annual Meeting of the American Section of the International Solar Energy Society, B. H. Glenn, G. E. Franta, eds. (American Section, International Solar Energy Society, Newark, Del., 1981), pp. 211–273.
  34. An effective absorption coefficient of the solid-state material is used by comparing the overlap of the absorption-bandwidth profile of the solid-state medium (Nd:YAG) and the emission-bandwidth profile of the diode array. This comparison also gives an effective index of refraction, but the index is fairly constant over the emission bandwidth of a diode laser (typically 2–4 nm). The diode parameters used in this study were taken from the literature and were assumed to have a bandwidth of 2 nm centered at 809 nm.
  35. This is not a requirement but provides symmetry of the absorption distribution. For an example of off-axis diode pump sources see M. Kuzumoto, K. Kuba, S. Yaga, “Continuous-wave operation of a YAG laser by off-centered LD side-pumping,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 414.
  36. D. G. Burkhard, D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Sol. Energy 17, 221–227 (1975).
    [CrossRef]
  37. M. J. J. B. Maes, A. J. E. M. Janssen, “A note on cylindrical reflector design,” Optik (Stuttgart) 88, 177–181 (1991).
  38. The critical angle radius is the radius of the caustic formed by rays that strike the rod surface tangentially. These rays are analogous to the rays that enter the CPC pump cavity at the acceptance angle of θa. This radius is the interior circle of the gray-scale plots of the CPC and elliptical pump cavities (see Figs. 11 and 12).

1992 (1)

1991 (2)

T. Y. Fan, “Efficient coupling of multiple diode laser arrays to an optical fiber by geometric multiplexing,” Appl. Opt. 30, 620 (1991).
[CrossRef]

M. J. J. B. Maes, A. J. E. M. Janssen, “A note on cylindrical reflector design,” Optik (Stuttgart) 88, 177–181 (1991).

1990 (3)

R. M. J. Benmair, J. Kagan, Y. Kalisky, Y. Noter, M. Oron, Y. Shimony, A. Yogev, “Solar-pumped Er, Tm, Ho:YAG laser,” Opt. Lett. 15, 36–38 (1990).
[CrossRef] [PubMed]

R. Burnham, “High-power transverse diode-pumped solid-state lasers,” Opt. Photon. News 1(1), 4–8 (1990).
[CrossRef]

T. Y. Fan, “Diode-pumped solid state lasers,” Line. Lab. J. 3, 413–425 (1990).

1989 (1)

1988 (3)

1980 (2)

1978 (1)

1976 (1)

1975 (1)

D. G. Burkhard, D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Sol. Energy 17, 221–227 (1975).
[CrossRef]

1974 (1)

Allik, T. H.

Baer, T. M.

T. M. Baer, D. F. Head, M. Sakamoto, “High efficiency diode-bar pumped solid state laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical, Digest Series (Optical Society of America, Washington, D.C., 1989), p. 416.

T. M. Baer, D. F. Head, P. Gooding. “High peak power Q-switched Nd:YLF laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

As of February 1992, the maximum reported output powers for the tightly folded resonator was 10 W when fiber coupling was used: M. S. Keirstead, T. M. Baer, “10 W, TEM00 output from a diode-pumped, solid-state laser,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 490. In a geometric multiplex end-pump design, a 15-W multimode and a 6-W TEM00 have been obtained: S. C. Todwell, J. F. Seamans, C. E. Hamilton, C. H. Muller, D. D. Lowenthal, “Efficient, 15-W output power, diode-end pumped Nd:YAG laser,” Opt. Lett. 16, 584–586 (1991).
[CrossRef]

Bassett, I. M.

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentrators,” in Progress in Optics, E. Wolf, ed. (Elsevier, London, 1989) Chap. III, p. 171.

Benmair, R. M. J.

Burkhard, D. G.

D. G. Burkhard, D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Sol. Energy 17, 221–227 (1975).
[CrossRef]

Burnham, R.

R. Burnham, “High-power transverse diode-pumped solid-state lasers,” Opt. Photon. News 1(1), 4–8 (1990).
[CrossRef]

A. D. Hays, R. Burnham, “Quasi-CW diode-array side pumped 946-nm neodymium laser,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 4.

Burnham, R. L.

Byer, R. L.

Caffey, D. P.

Conant, L. C.

Cross, P. S.

Fan, T. Y.

T. Y. Fan, “Efficient coupling of multiple diode laser arrays to an optical fiber by geometric multiplexing,” Appl. Opt. 30, 620 (1991).
[CrossRef]

T. Y. Fan, “Diode-pumped solid state lasers,” Line. Lab. J. 3, 413–425 (1990).

Gleckman, P.

P. Gleckman, “Achievement of ultrahigh solar concentration with potential for efficient laser pumping,” Appl. Opt. 27, 4385–4391 (1988).
[CrossRef] [PubMed]

P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).

Gooding, P.

T. M. Baer, D. F. Head, P. Gooding. “High peak power Q-switched Nd:YLF laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

Hall, D. G.

Harnagel, G. L.

Hays, A. D.

A. D. Hays, R. Burnham, “Quasi-CW diode-array side pumped 946-nm neodymium laser,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 4.

Head, D. F.

T. M. Baer, D. F. Head, P. Gooding. “High peak power Q-switched Nd:YLF laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

T. M. Baer, D. F. Head, M. Sakamoto, “High efficiency diode-bar pumped solid state laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical, Digest Series (Optical Society of America, Washington, D.C., 1989), p. 416.

Holman, R. L.

P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).

Hovis, W. W.

Janssen, A. J. E. M.

M. J. J. B. Maes, A. J. E. M. Janssen, “A note on cylindrical reflector design,” Optik (Stuttgart) 88, 177–181 (1991).

Kagan, J.

Kalisky, Y.

Kaz, A.

Keirstead, M. S.

As of February 1992, the maximum reported output powers for the tightly folded resonator was 10 W when fiber coupling was used: M. S. Keirstead, T. M. Baer, “10 W, TEM00 output from a diode-pumped, solid-state laser,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 490. In a geometric multiplex end-pump design, a 15-W multimode and a 6-W TEM00 have been obtained: S. C. Todwell, J. F. Seamans, C. E. Hamilton, C. H. Muller, D. D. Lowenthal, “Efficient, 15-W output power, diode-end pumped Nd:YAG laser,” Opt. Lett. 16, 584–586 (1991).
[CrossRef]

King, V.

Koshel, R. J.

R. J. Koshel, I. A. Walmsley, “Diode pumping of solid-state lasers with nonimaging optics: a theoretical study,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 126.

Kozlovsky, W. J.

Kuba, K.

This is not a requirement but provides symmetry of the absorption distribution. For an example of off-axis diode pump sources see M. Kuzumoto, K. Kuba, S. Yaga, “Continuous-wave operation of a YAG laser by off-centered LD side-pumping,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 414.

Kuppenheimer, J. D.

J. D. Kuppenheimer, “Design of multilamp nonimaging laser pump cavities,” Opt. Eng. 27, 1067–1071 (1988).

Kuzumoto, M.

This is not a requirement but provides symmetry of the absorption distribution. For an example of off-axis diode pump sources see M. Kuzumoto, K. Kuba, S. Yaga, “Continuous-wave operation of a YAG laser by off-centered LD side-pumping,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 414.

Lacovara, P.

P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).

Maes, M. J. J. B.

M. J. J. B. Maes, A. J. E. M. Janssen, “A note on cylindrical reflector design,” Optik (Stuttgart) 88, 177–181 (1991).

Marshall, L. R.

McIntire, W. R.

W. R. McIntire, “New reflector design, which avoids losses through gaps between tubular absorbers and reflectors,” Sol. Energy 25, 215–220 (1980).
[CrossRef]

W. R. McIntire, R. Winston, “Design considerations for reducing optical losses due to gaps between absorber and reflector,” in Proceedings of the 1981 Annual Meeting of the American Section of the International Solar Energy Society, B. H. Glenn, G. E. Franta, eds. (American Section, International Solar Energy Society, Newark, Del., 1981), pp. 211–273.

Noter, Y.

Oron, M.

Rabl, A.

Reed, M. K.

Reno, C. W.

Rice, R. R.

Sakamoto, M.

T. M. Baer, D. F. Head, M. Sakamoto, “High efficiency diode-bar pumped solid state laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical, Digest Series (Optical Society of America, Washington, D.C., 1989), p. 416.

Shealy, D. L.

D. G. Burkhard, D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Sol. Energy 17, 221–227 (1975).
[CrossRef]

Shimony, Y.

Smith, R. J.

Svelto, O.

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), p. 354. The parallel junction is typically three to five times larger; therefore, the divergence angle in the perpendicular direction is three to five times larger than the divergence angle in the parallel direction.

Walmsley, I. A.

R. J. Koshel, I. A. Walmsley, “Diode pumping of solid-state lasers with nonimaging optics: a theoretical study,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 126.

Welford, W. T.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4.

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentrators,” in Progress in Optics, E. Wolf, ed. (Elsevier, London, 1989) Chap. III, p. 171.

Winston, R.

R. Winston, “Ideal flux concentrators with reflector gaps,” Appl. Opt. 17, 1668–1669 (1978).
[CrossRef] [PubMed]

W. R. McIntire, R. Winston, “Design considerations for reducing optical losses due to gaps between absorber and reflector,” in Proceedings of the 1981 Annual Meeting of the American Section of the International Solar Energy Society, B. H. Glenn, G. E. Franta, eds. (American Section, International Solar Energy Society, Newark, Del., 1981), pp. 211–273.

P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentrators,” in Progress in Optics, E. Wolf, ed. (Elsevier, London, 1989) Chap. III, p. 171.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4.

Yaga, S.

This is not a requirement but provides symmetry of the absorption distribution. For an example of off-axis diode pump sources see M. Kuzumoto, K. Kuba, S. Yaga, “Continuous-wave operation of a YAG laser by off-centered LD side-pumping,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 414.

Yogev, A.

Appl. Opt. (6)

Line. Lab. J. (1)

T. Y. Fan, “Diode-pumped solid state lasers,” Line. Lab. J. 3, 413–425 (1990).

Opt. Eng. (1)

J. D. Kuppenheimer, “Design of multilamp nonimaging laser pump cavities,” Opt. Eng. 27, 1067–1071 (1988).

Opt. Lett. (4)

Opt. Photon. News (1)

R. Burnham, “High-power transverse diode-pumped solid-state lasers,” Opt. Photon. News 1(1), 4–8 (1990).
[CrossRef]

Optik (Stuttgart) (1)

M. J. J. B. Maes, A. J. E. M. Janssen, “A note on cylindrical reflector design,” Optik (Stuttgart) 88, 177–181 (1991).

Sol. Energy (2)

D. G. Burkhard, D. L. Shealy, “Design of reflectors which will distribute sunlight in a specified manner,” Sol. Energy 17, 221–227 (1975).
[CrossRef]

W. R. McIntire, “New reflector design, which avoids losses through gaps between tubular absorbers and reflectors,” Sol. Energy 25, 215–220 (1980).
[CrossRef]

Other (22)

W. R. McIntire, R. Winston, “Design considerations for reducing optical losses due to gaps between absorber and reflector,” in Proceedings of the 1981 Annual Meeting of the American Section of the International Solar Energy Society, B. H. Glenn, G. E. Franta, eds. (American Section, International Solar Energy Society, Newark, Del., 1981), pp. 211–273.

An effective absorption coefficient of the solid-state material is used by comparing the overlap of the absorption-bandwidth profile of the solid-state medium (Nd:YAG) and the emission-bandwidth profile of the diode array. This comparison also gives an effective index of refraction, but the index is fairly constant over the emission bandwidth of a diode laser (typically 2–4 nm). The diode parameters used in this study were taken from the literature and were assumed to have a bandwidth of 2 nm centered at 809 nm.

This is not a requirement but provides symmetry of the absorption distribution. For an example of off-axis diode pump sources see M. Kuzumoto, K. Kuba, S. Yaga, “Continuous-wave operation of a YAG laser by off-centered LD side-pumping,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 414.

The critical angle radius is the radius of the caustic formed by rays that strike the rod surface tangentially. These rays are analogous to the rays that enter the CPC pump cavity at the acceptance angle of θa. This radius is the interior circle of the gray-scale plots of the CPC and elliptical pump cavities (see Figs. 11 and 12).

Throughout this study the absorption distribution is calculated for a number of pump cavities with diode pump sources. The gain distribution is directly related to the absorption distribution by multiplication of the quantum defect value (e.g., for diode pumping at 810 nm of Nd:YAG, this value is approximately 0.8).

Ref. 14, App. H.

R. J. Koshel, I. A. Walmsley, “Diode pumping of solid-state lasers with nonimaging optics: a theoretical study,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 126.

The parameterization of the CPC for a circular absorber follows Rabl23; however, in Eqs. (8) and (9) of Sec. II in Rabl one reads that δ = π/2, when this substitution for δ is not supposed to be done until Sec. III (specific to a circular absorber). Welford and Winston complete the theory in the correct order, but the notation of Rabl is used throughout this study.

Ref. 14, Chap. 9.

A. D. Hays, R. Burnham, “Quasi-CW diode-array side pumped 946-nm neodymium laser,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 4.

As of February 1992, the maximum reported output powers for the tightly folded resonator was 10 W when fiber coupling was used: M. S. Keirstead, T. M. Baer, “10 W, TEM00 output from a diode-pumped, solid-state laser,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 490. In a geometric multiplex end-pump design, a 15-W multimode and a 6-W TEM00 have been obtained: S. C. Todwell, J. F. Seamans, C. E. Hamilton, C. H. Muller, D. D. Lowenthal, “Efficient, 15-W output power, diode-end pumped Nd:YAG laser,” Opt. Lett. 16, 584–586 (1991).
[CrossRef]

T. M. Baer, D. F. Head, M. Sakamoto, “High efficiency diode-bar pumped solid state laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1989 OSA Technical, Digest Series (Optical Society of America, Washington, D.C., 1989), p. 416.

T. M. Baer, D. F. Head, P. Gooding. “High peak power Q-switched Nd:YLF laser using a tightly folded resonator,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 24.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4.

Ref. 14, Chap. 9.

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), p. 354. The parallel junction is typically three to five times larger; therefore, the divergence angle in the perpendicular direction is three to five times larger than the divergence angle in the parallel direction.

The full standard deviation angle is twice the standard deviation angle of the Gaussian curve in both the tangential and the sagittal directions. The relation between these angles and the FWHM divergence angles of the individual diodes is θFWHM = 2.35482 (σt,s).

Other ray-tracing angle selection algorithms were considered, but because of the small dimensionality of the space and a deterministic result in question, a deterministic ray set was chosen. For example, a Monte Carlo ray-tracing method would give results similar to those of these deterministic ray sets. It is also noted that, because the cavity is cylindrical in nature, the three-dimensional ray trace offers little advantage over the two-dimensional trace; however, the three-dimensional trace was performed for completeness. The accuracy of the deterministic ray trace in two-dimensional space is proportional to one over the square root of the number of rays. To back up this claim we traced ray sets larger by 1 order of magnitude and found that there are no appreciable differences between the determined absorption distributions.

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentrators,” in Progress in Optics, E. Wolf, ed. (Elsevier, London, 1989) Chap. III, p. 171.

Refractive imaging systems are available with a N.A. of 0.85, which corresponds to an object-space angle of approximately 58°; therefore the maximum possible C2D is not obtained. Further, these systems are microscope objectives with a focal length of approximately 3 mm. This length gives a lens radius of approximately 5 mm, so the lens system is small and cannot be enlarged easily without introducing a large amount of aberration. Therefore refractive imaging systems cannot be scaled up to permit large-area pump sources.

Ref. 14, Chap. 1.

P. Lacovara, P. Gleckman, R. L. Holman, R. Winston, “Nonimaging concentrators for diode-pumped slab lasers,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. In-strum. Eng.1528, 135–141 (1991).

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Figures (13)

Fig. 1
Fig. 1

Three-dimensional view of the proposed pump cavity.

Fig. 2
Fig. 2

Radiation-emission pattern of individual diode lasers, comprising a Gaussian distribution in the angle in the tangential direction (perpendicular direction of the diode) and two equally offset Gaussian distributions in the angle in the sagittal direction (parallel direction of the diode).

Fig. 3
Fig. 3

Gaussian radiation pattern in the angle of an individual diode laser. The ray-angle set is determined by setting A i = A for i = ±1, ±2,…, ±(M − 1)/2; the angles θ i , are set at the midpoints of each of these regions along the θ axis.

Fig. 4
Fig. 4

Cross section of the CPC pump cavity. The cavity is designed with the edge-ray principle of nonimaging optics; θ a is the acceptance angle of the cavity and a is the radius of the laser rod.

Fig. 5
Fig. 5

Cross-sectional view of the laser rod. The rod is divided into N a angular zones and N r radial zones. The angular zones are measured counterclockwise from the positive x axis, whereas the radial zones are measured from the surface of the rod toward its center.

Fig. 6
Fig. 6

Radial gain density distribution for the close-coupled side-pumping design when six diodes are used to pump. The horizontal axis is the ratio of the radius of the radial zones to the radius of the rod.

Fig. 7
Fig. 7

Angular gain distribution for the close-coupled side-pumping design when six diodes are used to pump. The horizontal axis is the angle in radians measured counterclockwise from the positive x axis of the laser rod.

Fig. 8
Fig. 8

Gray-scale gain density distribution for the close-coupled side-pumping design when six diodes are used to pump. Black signifies near or at maximum absorption for this plot, whereas white signifies little or no absorption.

Fig. 9
Fig. 9

Radial gain density distribution for the CPC side-pumping design of Section 3 and the truncated elliptical side-pumping design of Section 4.

Fig. 10
Fig. 10

Angular gain distribution for the CPC side-pumping design of Section 3 and the truncated elliptical side-pumping design of Section 4.

Fig. 11
Fig. 11

Gray-scale gain density distribution for the CPC side-pumping design.

Fig. 12
Fig. 12

Gray-scale gain density distribution for the truncated elliptical side-pumping design.

Fig. 13
Fig. 13

Effect on the power absorbed in the laser rod when an individual diode laser is moved off axis for the CPC and truncated elliptical side-pumping cavities. The horizontal axis, x/a, signifies the position of the diode in units of rod radii.

Tables (1)

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Table 1 Merit Values for the Various Cavity Designs

Equations (9)

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M s ( θ t ) = M t σ s ( 1 θ t 2 / θ t , m 2 ) 1 / 2 σ t ,
P diode = 2 i = 1 M t M s ( θ t , i ) .
C = A / A ,
C 2 D = n / n sin θ a .
ρ = a θ for | θ | θ a + π / 2 ,
= a θ + θ a + π / 2 cos ( θ θ a ) 1 + sin ( θ θ a ) for θ a + π / 2 | θ | 3 π / 2 θ a .
rad = i = 1 N r | P r , i P G ( r i ) | ,
ang = j = 1 N a | P a , j P U ( ϕ j ) | .
FOM = w pow ( 1 P abs P in ) + w rad rad P ¯ rad + w ang ang P ¯ ang = FOM pow + FOM rad + FOM ang ,

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