Skip to main content
SpringerLink
Log in

Non-Euclidean Ideal Spectrometry

  • General and Applied Physics
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. G.P. Alexander, R.D. Kamien, R.A. Mosna, Conformal smectics and their many metrics. Phys. Rev. E. 85, 050701(R) (2012)

    Article  ADS  Google Scholar 

  2. H.G. Beutler, The theory of the concave grating. J. Opt. Soc. Am. 35(5), 311–350 (1945)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. W. Cai, V. Shalaev, D.K. Paul, Optical metamaterials: fundamentals and applications. Phys Today. 63 (9), 57 (2010)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

  6. J James. Spectrograph Design Fundamentals (Cambridge University Press, 2007)

  7. BBC Kyotoku, Applications of optical coherence tomography and advances into a photonic integrated device, Ph.D. Thesis (2011)

  8. U. Leonhardt, Optical conformal mapping. Science. 312(5781), 1777–1780 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. J. Li, J.B. Pendry, Hiding under the carpet: a new strategy for cloaking. Phys. Rev. Lett. 101(20), 203901 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. R. Marz, C. Cremer, On the theory of planar spectrographs. J. Lightw. Technol. 10(12), 2017–2022 (1992)

    Article  ADS  Google Scholar 

  12. T. Namioka, Theory of the concave grating. J. Opt. Soc. Am. 49(5), 446–460 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  13. J.B. Pendry, D. Schurig, D.R. Smith, Controlling electromagnetic fields. Science. 312(5781), 1780–1782 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. H.A. Rowland, On concave gratings for optical purposes. Philos. Mag. 16(99), 197–210 (1883)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  16. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58 (20), 2059 (1987)

    Article  ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing (Imecc), University of Campinas (Unicamp), Campinas, Brazil

    Henrique N. Sá Earp & Vladmir Sicca

  2. ‘Gleb Wataghin’ Institute of Physics (IFGW), University of Campinas (Unicamp), Campinas, Brazil

    Bernardo B. C. Kyotoku

Authors
  1. Henrique N. Sá Earp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladmir Sicca
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bernardo B. C. Kyotoku
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Henrique N. Sá Earp.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sá Earp, H.N., Sicca, V. & Kyotoku, B.B.C. Non-Euclidean Ideal Spectrometry. Braz J Phys 46, 683–688 (2016). https://doi.org/10.1007/s13538-016-0452-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-016-0452-1

Keywords

Search

Navigation