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Brazilian Journal of Physics

, Volume 46, Issue 6, pp 683–688 | Cite as

Non-Euclidean Ideal Spectrometry

  • Henrique N. Sá Earp
  • Vladmir Sicca
  • Bernardo B. C. Kyotoku
General and Applied Physics
  • 73 Downloads

Abstract

We describe the mathematical scheme for an anomaly-free ideal spectrometer, based on a 2−dimensional plane medium with conical regions of bounded slope. Moreover, the construction may be realised in many different configurations.

Keywords

Integrated optics Spectrometers Geometric optical design 

Notes

Acknowledgments

We thank Professor Ricardo Mosna for the valuable ideas in the development of this project. HS is supported by the Fapesp research grant 2014/24727-0 and by the CNPq Productivity PQ2 grant 312390/2014-9. VS was supported by the Fapesp grant 2012/21923-7.

References

  1. 1.
    G.P. Alexander, R.D. Kamien, R.A. Mosna, Conformal smectics and their many metrics. Phys. Rev. E. 85, 050701(R) (2012)ADSCrossRefGoogle Scholar
  2. 2.
    H.G. Beutler, The theory of the concave grating. J. Opt. Soc. Am. 35(5), 311–350 (1945)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    W. Cai, V. Shalaev, D.K. Paul, Optical metamaterials: fundamentals and applications. Phys Today. 63 (9), 57 (2010)CrossRefGoogle Scholar
  4. 4.
    F. Horst, W.M.J. Green, B.J. Offrein, Y.A. Vlasov, Silicon-on-insulator echelle grating WDM demultiplexers with two stigmatic points. IEEE Photon. Technol. Lett. 21(23), 1743–1745 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Huang, J. Ma, S. Chang, Q. Zhao, S.-T. Ho, Aberration corrected ultra-compact ultra-large angle curved grating multiplexer and demultiplexer on SOI platform, CWP3 (2008)Google Scholar
  6. 6.
    J James. Spectrograph Design Fundamentals (Cambridge University Press, 2007)Google Scholar
  7. 7.
    BBC Kyotoku, Applications of optical coherence tomography and advances into a photonic integrated device, Ph.D. Thesis (2011)Google Scholar
  8. 8.
    U. Leonhardt, Optical conformal mapping. Science. 312(5781), 1777–1780 (2006)ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    J. Li, J.B. Pendry, Hiding under the carpet: a new strategy for cloaking. Phys. Rev. Lett. 101(20), 203901 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    R.A. Mosna, D.A. Beller, R.D. Kamien, Breaking the rules for topological defects: smectic order on conical substrates. Phys. Rev. E. 86, 011707 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    R. Marz, C. Cremer, On the theory of planar spectrographs. J. Lightw. Technol. 10(12), 2017–2022 (1992)ADSCrossRefGoogle Scholar
  12. 12.
    T. Namioka, Theory of the concave grating. J. Opt. Soc. Am. 49(5), 446–460 (1959)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    J.B. Pendry, D. Schurig, D.R. Smith, Controlling electromagnetic fields. Science. 312(5781), 1780–1782 (2006)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    H.A. Rowland, On concave gratings for optical purposes. Philos. Mag. 16(99), 197–210 (1883)CrossRefGoogle Scholar
  15. 15.
    Z. Shi, S. He, A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer. IEEE J. Sel. Top. Quant. Electron. 8(6), 1179–1185 (2002)CrossRefGoogle Scholar
  16. 16.
    E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58 (20), 2059 (1987)ADSCrossRefGoogle Scholar

Copyright information

© Sociedade Brasileira de Física 2016

Authors and Affiliations

  1. 1.Institute of Mathematics, Statistics and Scientific Computing (Imecc)University of Campinas (Unicamp)CampinasBrazil
  2. 2.‘Gleb Wataghin’ Institute of Physics (IFGW)University of Campinas (Unicamp)CampinasBrazil

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