Skip to main content
Log in

Curie’s Symmetry Principle for Selection Rule of Photonic Crystal Defect Modes

  • Published:
Plasmonics Aims and scope Submit manuscript

Abstract

Symmetry, which defines invariant properties under a group of transformations, provides a frame of generalization uncovering regularities from given quantitative descriptions. Based on the Curie’s symmetry principle, connecting between causality and symmetry, we formulate the intuitive but formal selection rules and apply to determine the excitable resonant modes of a photonic crystal defect cavity, which is an important element for plasmonic applications. Quantitative agreement with the numerical simulations demonstrates the effectiveness of the fundamental principle in finding the critical symmetry conditions for the available localized defect states within photonic crystals. Moreover, the principle facilitates analysis of the higher-order or even forbidden modes in the asymmetric excitation configurations regarding the polarizations or positions of the light source, which typically require heavy computations. Our results may be extended similarly to develop the qualitative selection rules in other physical systems with a geometric symmetry.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Curie P (1894) Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique. J Phys Theor Appl 3(1):393–415. doi:10.1051/jphystap:018940030039300

    Article  Google Scholar 

  2. Brading K, Castellani E (2003) Symmetries in physics. Symmetries in Physics, Edited by Katherine Brading and Elena Castellani, pp 458 ISBN 0521821371 Cambridge. Cambridge University Press, UK, p 1

    Google Scholar 

  3. Jaeger FM (1920) Lectures on the Principles of Symmetry and Its Application in All Natural Sciences, 2nd edn. Elsevier, Amsterdam. doi:10.1002/bbpc.192400056

    Google Scholar 

  4. Ismael J (1997) Curie’s principle. Synthese 110(2):167–190. doi:10.1023/A:1004929109216

    Article  Google Scholar 

  5. Earman J (2004) Curie’s Principle and spontaneous symmetry breaking. Int Stud Philos Sci 18(2-3):173–198. doi:10.1080/0269859042000311299

    Article  Google Scholar 

  6. Fan S, Joannopoulos J, Winn JN, Devenyi A, Chen J, Meade RD (1995) Guided and defect modes in periodic dielectric waveguides. JOSA B 12(7):1267–1272. doi:10.1364/JOSAB.12.001267

    Article  CAS  Google Scholar 

  7. Akahane Y, Asano T, Song B-S, Noda S (2003) High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature 425(6961):944–947. doi:10.1038/nature02063

    Article  CAS  Google Scholar 

  8. Zhang Z, Qiu M (2004) Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs. Opt Express 12(17):3988–3995. doi:10.1364/OPEX.12.003988

    Article  Google Scholar 

  9. Yanik MF, Fan S, Soljačić M (2003) High-contrast all-optical bistable switching in photonic crystal microcavities. Appl Phys Lett 83(14):2739–2741. doi:10.1063/1.1615835

    Article  CAS  Google Scholar 

  10. Soljačić M, Luo C, Joannopoulos JD, Fan S (2003) Nonlinear photonic crystal microdevices for optical integration. Opt Lett 28(8):637–639. doi:10.1364/OL.28.000637

    Article  Google Scholar 

  11. Asakawa K, Sugimoto Y, Watanabe Y, Ozaki N, Mizutani A, Takata Y, Kitagawa Y, Ishikawa H, Ikeda N, Awazu K (2006) Photonic crystal and quantum dot technologies for all-optical switch and logic device. J Phys 8(9):208. doi:10.1088/1367-2630/8/9/208

    Google Scholar 

  12. Xu Q, Lipson M (2007) All-optical logic based on silicon micro-ring resonators. Opt Express 15(3):924–929. doi:10.1364/OE.15.000924

    Article  Google Scholar 

  13. Andalib P, Granpayeh N (2009) All-optical ultracompact photonic crystal AND gate based on nonlinear ring resonators. JOSA B 26(1):10–16. doi:10.1364/JOSAB.26.000010

    Article  CAS  Google Scholar 

  14. Liu Y, Qin F, Meng Z-M, Zhou F, Mao Q-H, Li Z-Y (2011) All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs. Opt Express 19(3):1945–1953. doi:10.1364/OE.19.001945

    Article  CAS  Google Scholar 

  15. Yanik MF, Fan S, Soljačić M (2003) High-contrast all-optical bistable switching in photonic crystal microcavities. Appl Phys Lett 83(14):2739–2741. doi:10.1063/1.1615835

    Article  CAS  Google Scholar 

  16. Tanabe T, Notomi M, Mitsugi S, Shinya A, Kuramochi E (2005) All-optical switches on a silicon chip realized using photonic crystal nanocavities. Appl Phys Lett 87(15):151112. doi:10.1063/1.2089185

    Article  Google Scholar 

  17. Ren H, Jiang C, Hu W, Gao M, Wang J (2006) Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity. Opt Express 14(6):2446–2458. doi:10.1364/OE.14.002446

    Article  Google Scholar 

  18. Akahane Y, Asano T, Takano H, Song B-S, Takana Y, Noda S (2005) Two-dimensional photonic-crystal-slab channeldrop filter with flat-top response. Opt Express 13(7):2512–2530. doi:10.1364/OPEX.13.002512

    Article  Google Scholar 

  19. Chhipa MK, Rewar E (2014) Effect of variable dielectric constant of Si material rods on 2-D photonic crystal ring resonator based channel drop filter for ITU. T. 694.2 CWDM system 2014 International Conference on Computer and Communication Technology (ICCCT). IEEE, , pp 257–262. doi:10.1109/ICCCT.2014.7001501

  20. Bahabady AM, Olyaee S (2015) Two-curve-shaped biosensor for detecting glucose concentration and salinity of seawater based on photonic crystal nano-ring resonator. Sens Lett 13(9):774–777. doi:10.1166/sl.2015.3517

    Article  Google Scholar 

  21. Lee MR, Fauchet PM (2007) Two-dimensional silicon photonic crystal based biosensing platform for protein detection. Optics express 15(8):4530–4535. doi:10.1364/OE.15.004530

    Article  CAS  Google Scholar 

  22. Fan X, White IM, Shopova SI, Zhu H, Suter JD, Sun Y (2008) Sensitive optical biosensors for unlabeled targets: A review. Analytica Chimica Acta 620(1):8–26. doi:10.1016/j.aca.2008.05.022

    Article  CAS  Google Scholar 

  23. Chutinan A, Noda S (2000) Waveguides and waveguide bends in two-dimensional photonic crystal slabs. Phys Rev B 62(7):4488. doi:10.1103/PhysRevB.62.4488

    Article  CAS  Google Scholar 

  24. Qiu M (2001) Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method. Microw Opt Technol Lett 30(5):327–330. doi:10.1002/mop.1304

    Article  Google Scholar 

  25. Lončar M, Doll T, Vučković J, Scherer A (2000) Design and fabrication of silicon photonic crystal optical waveguides. J Light Technol 18(10):1402. doi:10.1109/50.887192

    Article  Google Scholar 

  26. Kuzmiak V, Maradudin AA (2000) Symmetry analysis of the localized modes associated with substitutional and interstitial defects in a two-dimensional triangular photonic crystal. Phys Rev B 61(16):10750. doi:10.1103/PhysRevB.61.10750

    Article  CAS  Google Scholar 

  27. Lin L-L, Li Z-Y, Ho K-M (2003) Lattice symmetry applied in transfer-matrix methods for photonic crystals. J Appl Phys 94(2):811–821. doi:10.1063/1.1587011

    Article  CAS  Google Scholar 

  28. Painter O, Srinivasan K (2003) Localized defect states in two-dimensional photonic crystal slab waveguides: A simple model based upon symmetry analysis. Phys Rev B 68(3):035110. doi:10.1103/PhysRevB.68.035110

    Article  Google Scholar 

  29. Robertson W, Arjavalingam G, Meade R, Brommer K, Rappe A, Joannopoulos J (1993) Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays. JOSA B 10(2):322–327. doi:10.1364/JOSAB.10.000322

    Article  Google Scholar 

  30. Yeung KY, Chee J, Yoon H, Song Y, Kong J, Ham D (2014) Far-infrared graphene plasmonic crystals for plasmonic band engineering. Nano Lett 14(5):2479–2484. doi:10.1021/nl500158y

    Article  CAS  Google Scholar 

  31. Yeung KY, Chee J, Song Y, Kong J, Ham D (2015) Symmetry Engineering of Graphene Plasmonic Crystals. Nano Lett 15(8):5001–5009. doi:10.1021/acs.nanolett.5b00970

    Article  CAS  Google Scholar 

  32. Painter O, Srinivasan K, Barclay PE (2003) Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals. Physical Review B 68(3):035214. doi:10.1103/PhysRevB.68.035214

    Article  Google Scholar 

  33. Oskooi AF, Roundy D, Ibanescu M, Bermel P, Joannopoulos J, Johnson SG (2010) MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput Phys Commun 181(3):687–702. doi:10.1016/j.cpc.2009.11.008

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wonho Jhe.

Additional information

This work was supported in part by the National Research Foundation of Korea grant funded by the Korea government (MSIP) (No. 2016R1A3B1908660).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Park, J., Choi, W., Song, T. et al. Curie’s Symmetry Principle for Selection Rule of Photonic Crystal Defect Modes. Plasmonics 13, 393–402 (2018). https://doi.org/10.1007/s11468-017-0523-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11468-017-0523-3

Keywords

Navigation