OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7929–7945

Curvature effects on optical emission of flexible organic light-emitting diodes

Ariel Epstein, Nir Tessler, and Pinchas D. Einziger  »View Author Affiliations

Optics Express, Vol. 20, Issue 7, pp. 7929-7945 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2078 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an analytical model for the optical emission of a two-dimensional source in a flexible organic light-emitting diode formation with arbitrary curvature. The formulation rigorously produces closed-form analytical expressions which clearly relate the emission pattern and the device configuration, in particular, the radius of curvature. We investigate the optical properties of a prototype model through the resultant expressions, revealing that the bending induces a dramatic enhancement of emission to large angles, allowing for large viewing angle and reduced total internal reflection losses. These effects, shown to arise from geometrical considerations, demonstrate the unique advantages which curved flexible devices offer with respect to their planar counterparts. To the best of our knowledge, this is the first time that a rigorous analytical investigation of the optical characteristics of these novel devices is conducted. The resultant analytical formulae provide a robust basis for future analysis, as well as a set of design rules for efficient device engineering.

© 2012 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.3670) Optical devices : Light-emitting diodes
(250.3680) Optoelectronics : Light-emitting polymers
(310.6845) Thin films : Thin film devices and applications

ToC Category:
Optical Devices

Original Manuscript: December 22, 2011
Revised Manuscript: March 7, 2012
Manuscript Accepted: March 8, 2012
Published: March 21, 2012

Ariel Epstein, Nir Tessler, and Pinchas D. Einziger, "Curvature effects on optical emission of flexible organic light-emitting diodes," Opt. Express 20, 7929-7945 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Gustafsson, Y. Cao, G. M. Treacy, F. Klavetter, N. Colaneri, A. J. Heeger, “Flexible light-emitting diodes made from soluble conducting polymers,” Nature 357, 477–479 (1992). [CrossRef]
  2. G. Gu, P. E. Burrows, S. Venkatesh, S. R. Forrest, M. E. Thompson, “Vacuum-deposited, nonpolymeric flexible organic light-emitting devices,” Opt. Lett. 22, 172–174 (1997). [CrossRef] [PubMed]
  3. N. Tessler, G. J. Denton, R. H. Friend, “Lasing from conjugated-polymer microcavities,” Nature 382, 695–697 (1996). [CrossRef]
  4. D. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. Lüssem, K. Leo, “White organic light-emitting diodes with fluorescent tube efficiency,” Nature 459, 234–238 (2009). [CrossRef] [PubMed]
  5. B. Park, C. H. Park, M. Kim, M. Han, “Polarized organic light-emitting device on a flexible giant birefringent optical reflecting polarizer substrate,” Opt. Express 17, 10136–10143 (2009). [CrossRef] [PubMed]
  6. T. Sekitani, H. Nakajima, H. Maeda, T. Fukushima, T. Aida, K. Hata, T. Someya, “Stretchable active-matrix organic light-emitting diode display using printable elastic conductors,” Nat. Mater. 8, 494–499 (2009). [CrossRef] [PubMed]
  7. C.-J. Chiang, C. Winscom, S. Bull, A. Monkman, “Mechanical modeling of flexible OLED devices,” Org. Electron. 10, 1268–1274 (2009). [CrossRef]
  8. C.-J. Chiang, C. Winscom, A. Monkman, “Electroluminescence characterization of FOLED devices under two type of external stresses caused by bending,” Org. Electron. 11, 1870–1875 (2010). [CrossRef]
  9. B. Park, H. G. Jeon, “Spontaneous buckling in flexible organic light-emitting devices for enhanced light extraction,” Opt. Express 19, A1117–A1125 (2011). [CrossRef] [PubMed]
  10. H.-J. Kwon, H. Shim, S. Kim, W. Choi, Y. Chun, I. Kee, S. Lee, “Mechanically and optically reliable folding structure with a hyperelastic material for seamless foldable displays,” Appl. Phys. Lett. 98, 151904 (2011). [CrossRef]
  11. Z. B. Wang, M. G. Helander, J. Qiu, D. P. Puzzo, M. T. Greiner, Z. M. Hudson, S. Wang, Z. W. Liu, Z. H. Lu, “Unlocking the full potential of organic light-emitting diodes on flexible plastic,” Nat. Photonics 5, 753–757 (2011). [CrossRef]
  12. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).
  13. P. Einziger, L. Felsen, “Rigorous asymptotic analysis of transmission through a curved dielectric slab,” IEEE Trans. Antennas Propag. 31, 863–870 (1983). [CrossRef]
  14. W. Wasylkiwskyj, “Diffraction by a concave perfectly conducting circular cylinder,” IEEE Trans. Antennas Propag. 23, 480–492 (1975). [CrossRef]
  15. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions : with Formulas, Graphs, and Mathematical Tables (Dover Publications, New York, 1970).
  16. A. Epstein, N. Tessler, P. D. Einziger, “The impact of spectral and spatial exciton distributions on optical emission from thin-film weak-microcavity organic light-emitting diodes,” IEEE J. Quantum Electron. 46, 1388–1395 (2010). [CrossRef]
  17. A. Epstein, N. Tessler, P. D. Einziger, “Analytical extraction of the recombination zone location in organic light-emitting diodes from emission pattern extrema,” Opt. Lett. 35, 3366–3368 (2010). [CrossRef] [PubMed]
  18. P. Einziger, L. Felsen, “Ray analysis of two-dimensional radomes,” IEEE Trans. Antennas Propag. 31, 870–884 (1983). [CrossRef]
  19. A. Cherkassky, “Optimization of electromagnetic power absorption in a lossy circular cylinder,” Master’s thesis, Technion - Israel Institute of Technology (2006).
  20. M. Flämmich, M. C. Gather, N. Danz, D. Michaelis, A. H. Bräuer, K. Meerholz, A. Tünnermann, “Orientation of emissive dipoles in OLEDs: Quantitative in situ analysis,” Org. Electron. 11, 1039–1046 (2010). [CrossRef]
  21. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2006). [CrossRef]
  22. T. Tsutsui, M. Yahiro, H. Yokogawa, K. Kawano, M. Yokoyama, “Doubling coupling-out efficiency in organic light-emitting devices using a thin silica aerogel layer,” Adv. Mater. 13, 1149–1152 (2001). [CrossRef]
  23. M. Ma, F. W. Mont, X. Yan, J. Cho, E. F. Schubert, G. B. Kim, C. Sone, “Effects of the refractive index of the encapsulant on the light-extraction efficiency of light-emitting diodes,” Opt. Express 19, A1135–A1140 (2011). [CrossRef] [PubMed]
  24. S. Nowy, B. C. Krummacher, J. Frischeisen, N. A. Reinke, W. Brutting, “Light extraction and optical loss mechanisms in organic light-emitting diodes: Influence of the emitter quantum efficiency,” J. Appl. Phys. 104, 123109 (2008). [CrossRef]
  25. R. Meerheim, M. Furno, S. Hofmann, B. Lussem, K. Leo, “Quantification of energy loss mechanisms in organic light-emitting diodes,” Appl. Phys. Lett. 97, 253305 (2010). [CrossRef]
  26. S. Mladenovski, K. Neyts, D. Pavicic, A. Werner, C. Rothe, “Exceptionally efficient organic light emitting devices using high refractive index substrates,” Opt. Express 17, 7562–7570 (2009). [CrossRef] [PubMed]
  27. K.-Y. Chen, Y.-T. Chang, Y.-H. Ho, H.-Y. Lin, J.-H. Lee, M.-K. Wei, “Emitter apodization dependent angular luminance enhancement of microlens-array film attached organic light-emitting devices,” Opt. Express 18, 3238–3243 (2010). [CrossRef] [PubMed]
  28. Y. Sun, S. R. Forrest, “Enhanced light out-coupling of organic light-emitting devices using embedded low-index grids,” Nat. Photonics 2, 483–487 (2008). [CrossRef]
  29. T. Sekitani, U. Zschieschang, H. Klauk, T. Someya, “Flexible organic transistors and circuits with extreme bending stability,” Nat. Mater. 9, 1015–1022 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited