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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1297–1304

Optimization of planar self-collimating photonic crystals

Raymond C. Rumpf and Javier J. Pazos  »View Author Affiliations


JOSA A, Vol. 30, Issue 7, pp. 1297-1304 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001297


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Abstract

Self-collimation in photonic crystals has received a lot of attention in the literature, partly due to recent interest in silicon photonics, yet no performance metrics have been proposed. This paper proposes a figure of merit (FOM) for self-collimation and outlines a methodical approach for calculating it. Performance metrics include bandwidth, angular acceptance, strength, and an overall FOM. Two key contributions of this work include the performance metrics and identifying that the optimum frequency for self-collimation is not at the inflection point. The FOM is used to optimize a planar photonic crystal composed of a square array of cylinders. Conclusions are drawn about how the refractive indices and fill fraction of the lattice impact each of the performance metrics. The optimization is demonstrated by simulating two spatially variant self-collimating photonic crystals, where one has a high FOM and the other has a low FOM. This work gives optical designers tremendous insight into how to design and optimize robust self-collimating photonic crystals, which promises many applications in silicon photonics and integrated optics.

© 2013 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(130.0130) Integrated optics : Integrated optics
(130.1750) Integrated optics : Components
(130.2790) Integrated optics : Guided waves
(130.5296) Integrated optics : Photonic crystal waveguides
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Integrated Optics

History
Original Manuscript: March 7, 2013
Manuscript Accepted: April 25, 2013
Published: June 3, 2013

Citation
Raymond C. Rumpf and Javier J. Pazos, "Optimization of planar self-collimating photonic crystals," J. Opt. Soc. Am. A 30, 1297-1304 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-7-1297


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References

  1. S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005). [CrossRef]
  2. R. Iliew, C. Etrich, and F. Lederer, “Self-collimation of light in three-dimensional photonic crystals,” Opt. Express 13, 7076–7085 (2005). [CrossRef]
  3. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004). [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999). [CrossRef]
  5. Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96, 173902 (2006). [CrossRef]
  6. J. Shin and S. Fan, “Conditions for self-collimation in three-dimensional photonic crystals,” Opt. Lett. 30, 2397 (2005). [CrossRef]
  7. J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002). [CrossRef]
  8. T.-T. Kim, S.-G. Lee, H. Y. Park, J.-E. Kim, and C.-S. Kee, “Asymmetric Mach-Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express 18, 5384–5389 (2010). [CrossRef]
  9. A. F. Matthews, S. K. Morrison, and Y. S. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279, 313–319 (2007). [CrossRef]
  10. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004). [CrossRef]
  11. Y. Zhang, Y. Zhang, and B. Li, “Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals,” Opt. Express 15, 9287–9292 (2007). [CrossRef]
  12. D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystal,” J. Phys. D 41, 115108 (2008). [CrossRef]
  13. X. Chen, Z. Qiang, D. Zhao, H. Li, Y. Qiu, W. Yang, and W. Zhou, “Polarization-independent drop filters based on photonic crystal self-collimation ring resonators,” Opt. Express 17, 19808–19813 (2009). [CrossRef]
  14. Y. Wang, H. Wang, Q. Xue, and W. Zheng, “Photonic crystal self-collimation sensor,” Opt. Express 20, 12111–12118 (2012). [CrossRef]
  15. D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D 40, 2635 (2007). [CrossRef]
  16. Z. Fang and C. Z. Zhao, “Recent progress in silicon photonics: a review,” ISRN Opt. 2012, 1–27 (2012).
  17. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006). [CrossRef]
  18. R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20, 15263–15274 (2012). [CrossRef]
  19. M. I. Hussein, “Reduced Bloch mode expansion for periodic media band structure calculations,” Proc. Roy. Soc. Lond. Ser. A 465, 2825–2848 (2009). [CrossRef]
  20. S. Guo and S. Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167–175 (2003). [CrossRef]
  21. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef]
  22. M. J. Lax, Symmetry Principles in Solid State and Molecular Physics (Wiley, 1974), p. 449.
  23. H. Anton, Elementary Linear Algebra (Wiley, 2010), pp. 303–305.
  24. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), pp. 673–690.
  25. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, 6th ed. (McGraw-Hill, 2010), Vol. 2, pp. 852–887.

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