Theoretical analysis of the order to disorder phase transition in random photonic crystals

Shimpei Hamada, Seiji Takeda, Pierre Viktorovitch, Mitsuhiro Terakawa, Minoru Obara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The effect of structural randomness introduction into ordered photonic crystals on the behavior of the Bloch-mode and defect mode is presented. In order to induce strong localization of optical waves in nanostructures, there are two kinds of schemes: to utilize the defect mode in photonic crystals and Anderson localization modes in random structures. Recently, the intermediate state between the two above structures has been remarkably noticed. Despite its potential advantage, however, the modal characteristic of these merged structures, random photonic crystals, has not been revealed systematically yet. The aim is to figure out the appropriate degree of randomness to induce highly localized modes. We investigate an impulse response of the random photonic crystals by 2D FDTD method. We array air holes with triangular lattice shape into silicon substrate based material, and set a defect area in the center. The randomness is introduced into the structure by randomly dislocating the positions of the air holes. After the impulse illumination, we acquire the temporal evolution of the electric amplitudes over the system. By employing DFT on the sampled signals, we achieve the frequency spectrum and Q factors of the modes. We confirmed the optical phase transition of the system: with the increase of the randomness, the propagating Bloch-modes become localized and achieve higher Q factors. Slight spectrum shifts are also confirmed. The confinement efficiency of optical waves in the photonic crystals is greatly improved as well.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume7946
DOIs
Publication statusPublished - 2011
EventPhotonic and Phononic Properties of Engineered Nanostructures - San Francisco, CA, United States
Duration: 2011 Jan 242011 Jan 27

Other

OtherPhotonic and Phononic Properties of Engineered Nanostructures
CountryUnited States
CitySan Francisco, CA
Period11/1/2411/1/27

Fingerprint

Photonic crystals
Photonic Crystal
Disorder
Theoretical Analysis
Phase Transition
Phase transitions
Randomness
disorders
photonics
Random Structure
Defects
crystals
Q factors
FDTD Method
Anderson Localization
impulses
defects
Frequency Spectrum
Triangular Lattice
Silicon

Keywords

  • Anderson localization
  • photonic crystal
  • random photonic crystal

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Hamada, S., Takeda, S., Viktorovitch, P., Terakawa, M., & Obara, M. (2011). Theoretical analysis of the order to disorder phase transition in random photonic crystals. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7946). [79460J] https://doi.org/10.1117/12.873483

Theoretical analysis of the order to disorder phase transition in random photonic crystals. / Hamada, Shimpei; Takeda, Seiji; Viktorovitch, Pierre; Terakawa, Mitsuhiro; Obara, Minoru.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7946 2011. 79460J.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hamada, S, Takeda, S, Viktorovitch, P, Terakawa, M & Obara, M 2011, Theoretical analysis of the order to disorder phase transition in random photonic crystals. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7946, 79460J, Photonic and Phononic Properties of Engineered Nanostructures, San Francisco, CA, United States, 11/1/24. https://doi.org/10.1117/12.873483
Hamada S, Takeda S, Viktorovitch P, Terakawa M, Obara M. Theoretical analysis of the order to disorder phase transition in random photonic crystals. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7946. 2011. 79460J https://doi.org/10.1117/12.873483
Hamada, Shimpei ; Takeda, Seiji ; Viktorovitch, Pierre ; Terakawa, Mitsuhiro ; Obara, Minoru. / Theoretical analysis of the order to disorder phase transition in random photonic crystals. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7946 2011.
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