Abstract

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

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References

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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]

1995 (3)

K. A. McGreer, “Diffraction from concave gratings in planar waveguides,” IEEE Photon. Technol. Lett. 7, 324–326 (1995).
[Crossref]

T. Onoka, “Aberration-corrected concave grating for the midinfrared spectrometer aboard the infrared telescope in space,” Appl. Opt. 34, 659–666 (1995).
[Crossref]

K. A. McGreer, “A flat-field broadband spectrograph design,” IEEE Photon. Technol. Lett. 7, 397–399 (1995).
[Crossref]

1994 (2)

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]

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]

1993 (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]

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]

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]

1992 (3)

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]

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]

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2022 (1992).
[Crossref]

1991 (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]

1982 (1)

R. Güther, S. Polze, “The construction of stigmatic points for concave gratings,” Opt. Acta 29, 659–665 (1982).
[Crossref]

1981 (1)

J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).

1980 (1)

1978 (1)

1976 (1)

1974 (1)

1970 (1)

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).

1945 (1)

1883 (1)

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).
[Crossref]

Andreadakis, N. C.

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]

Barber, R.

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]

Beranek, M. W.

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]

Beutler, H. G.

Bhat, R.

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]

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]

Caneau, C.

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]

Capron, B. A.

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]

Chambers, R. L.

J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).

Chang-Hasnain, C.

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]

Chatenoud, F.

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]

Chen, Y. J.

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]

Cremer, C.

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]

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2022 (1992).
[Crossref]

Delage, A.

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]

Deri, R. J.

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]

Dijaili, S. P.

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]

Ebbinghaus, G.

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]

Emeis, N.

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]

Fallahi, M.

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]

Gersimov, F. M.

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).

Güther, R.

R. Güther, S. Polze, “The construction of stigmatic points for concave gratings,” Opt. Acta 29, 659–665 (1982).
[Crossref]

Harada, T.

Hayes, J. R.

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]

Heise, G.

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]

Huggins, R. W.

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]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).

Kallman, J. S.

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]

Kastner, S. O.

Kita, T.

Koshelev, B. V.

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).

Koshinz, D. G.

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]

Koza, M. A.

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]

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]

LeBlanc, H. P.

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]

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]

Lerner, J. M.

J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).

März, R.

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2022 (1992).
[Crossref]

McGreer, K. A.

K. A. McGreer, “A flat-field broadband spectrograph design,” IEEE Photon. Technol. Lett. 7, 397–399 (1995).
[Crossref]

K. A. McGreer, “Diffraction from concave gratings in planar waveguides,” IEEE Photon. Technol. Lett. 7, 324–326 (1995).
[Crossref]

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]

Namioka, T.

Noda, H.

Onoka, T.

Passereau, G.

J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).

Peisakhson, I. V.

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).

Poguntke, K.

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]

Poguntke, K. R.

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]

Polze, S.

R. Güther, S. Polze, “The construction of stigmatic points for concave gratings,” Opt. Acta 29, 659–665 (1982).
[Crossref]

Rowland, H. A.

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).
[Crossref]

Scherer, A.

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]

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]

Schier, M.

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]

Seya, M.

Soole, J. B. D.

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]

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]

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]

Stoll, L.

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]

Templeton, I. M.

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]

Velzel, C. H. F.

Wade, C.

Wu, M.

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]

Yakovlev, E. A.

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).

Appl. Opt. (3)

Appl. Phys. Lett. (2)

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]

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]

IEEE Photon. Technol. Lett. (5)

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]

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]

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]

K. A. McGreer, “Diffraction from concave gratings in planar waveguides,” IEEE Photon. Technol. Lett. 7, 324–326 (1995).
[Crossref]

K. A. McGreer, “A flat-field broadband spectrograph design,” IEEE Photon. Technol. Lett. 7, 397–399 (1995).
[Crossref]

Imag. Spectrosc. (1)

J. M. Lerner, R. L. Chambers, G. Passereau, “Flat field imaging spectroscopy using aberration corrected holographic gratings,” Imag. Spectrosc. 268, 122–128 (1981).

J. Lightwave Technol. (4)

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]

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]

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]

R. März, C. Cremer, “On the theory of planar spectrographs,” J. Lightwave Technol. 10, 2017–2022 (1992).
[Crossref]

J. Opt. Soc. Am. (3)

Opt. Acta (1)

R. Güther, S. Polze, “The construction of stigmatic points for concave gratings,” Opt. Acta 29, 659–665 (1982).
[Crossref]

Opt. Spectrosc. (USSR) (1)

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).

Philos. Mag. (1)

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).
[Crossref]

Other (1)

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).

Cited By

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Figures (7)

Fig. 1
Fig. 1

Grating curve is a smooth curve that goes through the centers of the facets; (xi, yi) is the center of the ith facet. The equations in the text make reference to an arbitrary point referred to as (x, y).

Fig. 2
Fig. 2

Path lengths used in the constraint function that gives a stigmatic point: r1, the distance between the stigmatic input point (a1, b1) and an arbitrary point (x, y); r2, the distance between the stigmatic output point (a2, b2) and (x, y); r1,0, the distance between (a1, b1) and the grating pole (x0, y0); and r2,0, the distance between (x0, y0) and (a2, b2).

Fig. 3
Fig. 3

For the Rowland circle grating, the input and output points lie on the Rowland circle that has radius R. The grating falls on a circular arc of radius 2R and has a center of curvature at (a0, b0). The grating curve is tangent to the Rowland circle at the grating pole.

Fig. 4
Fig. 4

Pitch of the Rowland circle grating is such that the projection of the facet centers onto the y axis is a series of points that are equally spaced by amount d.

Fig. 5
Fig. 5

Concave grating designed to serve as a spectrograph or a demultiplexer. All the wavelengths have a common point of incidence at (a1, b1). Light of the stigmatic wavelength is focused to the stigmatic output point (a2, b2). Light with an arbitrary wavelength λ is focused on the output focal curve at (a4, b4); r4 is the distance from (a4, b4) to an arbitrary point (x, y).

Fig. 6
Fig. 6

Concave grating designed to serve as a multiplexer. All the wavelengths have a common output point (a2, b2). Light of the stigmatic wavelength is designed to be incident at the stigmatic input point (a1, b1). Light with an arbitrary wavelength λ is designed to be incident on the input focal curve at (a3, b3); r1 is the distance from (a1, b1) to an arbitrary point (x, y).

Fig. 7
Fig. 7

For a multiorder grating, a facet can be chosen to lie closest to an electron-beam writer grid line. Each pair of adjacent facets can operate for a diffraction order that is different from that of an adjacent pair.

Equations (12)

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ɛ 1 , i ( x i , y i ) = 0 ,             ɛ 2 , i ( x i , y i ) = 0 ,
ɛ 1 , i ( x , y ) a 11 ( x - x i ) + a 12 ( y - y i ) , ɛ 2 , i ( x , y ) a 21 ( x - x i ) + a 22 ( y - y i ) ,
x i x - [ a 22 ɛ 1 , i ( x , y ) - a 12 ɛ 2 , i ( x , y ) ] / ( a 11 a 22 - a 21 a 12 ) , y i y - [ a 11 ɛ 2 , i ( x , y ) - a 21 ɛ 1 , i ( x , y ) ] / ( a 11 a 22 - a 21 a 12 ) .
ɛ 1 , i ( x , y ) = r 1 + r 2 + i m λ 0 / n - r 1 , 0 - r 2 , 0 .
F i ( λ ) = r 3 , i + r 4 , i + i m λ / n - r 3 , 0 - r 4 , 0 ,
m n ( λ u 2 ) i = ( r 4 , j - r 4 , i ) u 2 .
i m n ( λ u 2 ) 0 = k = 1 i m n ( λ u 2 ) k = ( r 4 , 0 - r 4 , i ) u 2 .
ɛ 2 , i ( x , y ) = ( r 4 , i - r 4 , 0 ) a 4 cos ( θ ) + ( r 4 , i - r 4 , 0 ) b 4 sin ( θ ) + i m n ( λ u 2 ) 0 ,
ɛ 2 , i ( x , y ) = ( F i λ ) ,
ɛ 2 , i ( x , y ) = ( r 3 , i - r 3 , 0 ) a 3 cos ( θ ) + ( r 3 , i - r 3 , 0 ) b 3 sin ( θ ) + i m n ( λ u 1 ) .
ɛ 1 , i ( x , y ) = r 1 + r 2 + M i λ 0 / n - r 1 , 0 - r 2 , 0 ,
ɛ 2 , i ( x , y ) = ( r 4 , i - r 4 , 0 ) a 4 cos ( θ ) + ( r 4 , i - r 4 , 0 ) b 4 sin ( θ ) + M i n ( λ u 2 ) 0 .

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