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Applied Optics

Applied Optics


  • Vol. 35, Iss. 30 — Oct. 20, 1996
  • pp: 5904–5910

Theory of concave gratings based on a recursive definition of facet positions

K. A. McGreer  »View Author Affiliations

Applied Optics, Vol. 35, Issue 30, pp. 5904-5910 (1996)

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A general theory for concave gratings is presented that is based on a recursion formula for the facet positions and that differs from previous theories that are based on a power-series expansion of the light path function. In the recursion formula approach the facet positions are determined from a numerical solution for the roots of two constraint functions. Facet positions are determined in sequence, starting from the grating pole. One constraint function may be chosen to give a stigmatic point. A variety of grating designs are discussed, including a design that cannot be generated with the power-series approach.

© 1996 Optical Society of America

Original Manuscript: May 24, 1995
Revised Manuscript: January 11, 1996
Published: October 20, 1996

K. A. McGreer, "Theory of concave gratings based on a recursive definition of facet positions," Appl. Opt. 35, 5904-5910 (1996)

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  1. J. B. D. Soole, A. Scherer, H. P. LeBlanc, N. C. Andreadakis, R. Bhat, M. A. Koza, “Monolithic InP/InGaAsP/InP grating spectrometer for the 1.48–1.56 μm wavelength range,” Appl. Phys. Lett. 58, 1949–1951 (1991). [CrossRef]
  2. C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP/InGaAs/InP,” IEEE Photon. Technol. Lett. 4, 108–110 (1992). [CrossRef]
  3. M. Fallahi, K. A. McGreer, A. Delage, I. M. Templeton, F. Chatenoud, R. Barber, “Grating demultiplexer integrated with MSM detector array in InGaAs/AlGaAs/GaAs for WDM,” IEEE Photon. Technol. Lett. 5, 794–797 (1993). [CrossRef]
  4. J. B. D. Soole, K. Poguntke, A. Scherer, H. P. LeBlanc, C. Chang-Hasnain, J. R. Hayes, C. Caneau, R. Bhat, M. A. Koza, “Wavelength-selectable laser emission from a multi-stripe array grating integrated cavity (MAGIC) laser,” Appl. Phys. Lett. 61, 2750–2752 (1992). [CrossRef]
  5. R. J. Deri, J. S. Kallman, S. P. Dijaili, “Quantitative analysis of integrated optic waveguide spectrometers,” IEEE Photon. Technol. Lett. 6, 242–244 (1994). [CrossRef]
  6. K. A. McGreer, “Diffraction from concave gratings in planar waveguides,” IEEE Photon. Technol. Lett. 7, 324–326 (1995). [CrossRef]
  7. M. Wu, Y. J. Chen, “Design considerations for Rowland circle gratings used in photonic integrated devices for WDM applications,” J. Lightwave Technol. 12, 1939–1942 (1994). [CrossRef]
  8. C. H. F. Velzel, “General theory of the aberrations of diffraction gratings and gratinglike optical instruments,” J. Opt. Soc. Am. 66, 346–353 (1976). [CrossRef]
  9. H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974). [CrossRef]
  10. H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883). [CrossRef]
  11. H. G. Beutler, “The theory of concave grating,” J. Opt. Soc. Am. 35, 311–350 (1945). [CrossRef]
  12. M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).
  13. F. M. Gersimov, E. A. Yakovlev, I. V. Peisakhson, B. V. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. (USSR) 28, 423–426 (1970).
  14. T. Harada, T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980). [CrossRef] [PubMed]
  15. K. R. Poguntke, J. B. D. Soole, “Design of a multistripe array grating integrated cavity (MAGIC) laser,” J. Lightwave Technol. 11, 2191–2200 (1993). [CrossRef]
  16. T. Onoka, “Aberration-corrected concave grating for the midinfrared spectrometer aboard the infrared telescope in space,” Appl. Opt. 34, 659–666 (1995). [CrossRef]
  17. S. O. Kastner, C. Wade, “Aspheric grating for extreme ultraviolet astronomy,” Appl. Opt. 17, 1252–1258 (1978). [CrossRef] [PubMed]
  18. R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2022 (1992). [CrossRef]
  19. R. Güther, S. Polze, “The construction of stigmatic points for concave gratings,” Opt. Acta 29, 659–665 (1982). [CrossRef]
  20. B. A. Capron, M. W. Beranek, R. W. Huggins, D. G. Koshinz, “Design and performance of a multiple element slab waveguide spectrograph for multimode fiber-optic WDM systems,” J. Lightwave Technol. 11, 2009–2014 (1993). [CrossRef]
  21. J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).
  22. K. A. McGreer, “A flat-field broadband spectrograph design,” IEEE Photon. Technol. Lett. 7, 397–399 (1995). [CrossRef]

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