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Applied Optics

Applied Optics


  • Vol. 39, Iss. 8 — Mar. 10, 2000
  • pp: 1279–1289

Coherent and incoherent off-axis Hermite–Gaussian beam combinations

Baida Lü and Hong Ma  »View Author Affiliations

Applied Optics, Vol. 39, Issue 8, pp. 1279-1289 (2000)

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A detailed study of the coherent and the incoherent combinations of two-dimensional off-axis Hermite–Gaussian beams with rectangular symmetry is made. The closed-form propagation formulas of the resulting beam are derived, and the resulting beam quality in terms of the M2 factor and power in the bucket is discussed and compared for the coherent and the incoherent combinations. In addition, it is shown that the resulting astigmatic beam can be symmetrized in the sense of the second-moment definition of beam width. However, the symmetrizing transformation of the resulting astigmatic beams is incomplete, because there exist different irradiance profiles.

© 2000 Optical Society of America

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(140.3300) Lasers and laser optics : Laser beam shaping
(220.4830) Optical design and fabrication : Systems design

Original Manuscript: August 10, 1999
Revised Manuscript: November 29, 1999
Published: March 10, 2000

Baida Lü and Hong Ma, "Coherent and incoherent off-axis Hermite–Gaussian beam combinations," Appl. Opt. 39, 1279-1289 (2000)

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  1. R. A. Chodzko, J. M. Bernard, H. Mirels, “Coherent combination of multiline lasers,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 239–253 (1990). [CrossRef]
  2. B. Ozygus, H. Laabs, “Gain-induced coupling of solid-state lasers,” Chaos, Solitons, Fractals 4, 1559–1572 (1994).
  3. J. R. Andrews, “Interferometric power amplifiers,” Opt. Lett. 14, 33–35 (1989). [CrossRef] [PubMed]
  4. J. R. Andrews, G. L. Schuster, “High-power and high-spatial-coherence broad-area power amplifier,” Opt. Lett. 16, 913–915 (1991). [CrossRef] [PubMed]
  5. G. L. Schuster, J. R. Andrews, “Coherent summation of saturated AlGaAs amplifiers,” Opt. Lett. 18, 619–621 (1993). [CrossRef] [PubMed]
  6. M. Brunel, A. L. Floch, F. Bretenaker, J. Marty, E. Molva, “Coherent addition of adjacent laser by forked eigenstate operation,” Appl. Opt. 37, 2402–2406 (1998). [CrossRef]
  7. J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, “Beam propagation constants for a radial laser array,” Appl. Opt. 37, 1045–1048 (1998). [CrossRef]
  8. G. L. Schuster, J. R. Andrews, “Coherent beam combining: optical loss effects on power scaling,” Appl. Opt. 34, 6801–6805 (1995). [CrossRef] [PubMed]
  9. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues, M. W. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 184–199.
  10. A. E. Siegman, “New development in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990). [CrossRef]
  11. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970). [CrossRef]
  12. C. Palma, “Decentered Gaussian beams, ray bundles, and Bessel–Gauss beams,” Appl. Opt. 36, 1116–1120 (1997). [CrossRef] [PubMed]
  13. H. Weber, “Some historical and technical aspects of beam quality,” Opt. Quant. Electron. 24, 861–864 (1992). [CrossRef]
  14. D. Zhao, Q. Lin, S. Wang, “Symmetrizing transformation of general astigmatic Gaussian beams,” Opt. Quantum Electron. 26, 903–910 (1994).
  15. B. Eppich, A. T. Friberg, C. Gao, H. Weber, “Twist of coherent field and beam quality,” in Third International Workshop on Laser Beam and Optics Characterization, M. Morin, A. Giesen, eds., Proc. SPIE2870, 260–267 (1996). [CrossRef]
  16. P. A. Belanger, “Beam propagation and the ABCD ray matrix,” Opt. Lett. 16, 196–198 (1991). [CrossRef]

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