## Luminescence properties of a Fibonacci photonic quasicrystal

Optics Express, Vol. 17, Issue 8, pp. 6636-6642 (2009)

http://dx.doi.org/10.1364/OE.17.006636

Acrobat PDF (160 KB)

### Abstract

An active one-dimensional Fibonacci photonic quasi-crystal is realized via spin coating. Luminescence properties of an organic dye embedded in the quasi-crystal are studied experimentally and compared to theoretical simulations. The luminescence occurs via the pseudo-bandedge mode and follows the dispersion properties of the Fibonacci crystal. Time resolved luminescence measurement of the active structure shows faster spontaneous emission rate, indicating the effect of the large photon densities available at the bandedge due to the presence of critically localized states. The experimental results are in good agreement with the theoretical calculations for steady-state luminescence spectra.

© 2009 Optical Society of America

1. M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. **81**, 2680 (2002);H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science **305**, 1444 (2004). [CrossRef]

3. G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. **60**, 1081 (1988) [CrossRef] [PubMed]

4. F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B **34**, 2207 (1986). [CrossRef]

5. T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B **40**, 7413 (1989). [CrossRef]

6. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. **58**, 2436 (1987);
B. Sutherland and M. Kohmoto, “Resistance of a one-dimensional quasicrystal: Power-law growth,” Phys. Rev. B **36**, 5877 (1987). [CrossRef] [PubMed]

7. R. Merlin, K. Bajema, R. Clarke, F. -Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs Heterostructures,” Phys. Rev. Lett. **55**, 1768 (1985). [CrossRef] [PubMed]

8. J. B. Sokoloff, “Anomalous Electrical Conduction in Quasicrystals and Fibonacci Lattices,” Phys. Rev. Lett. **58**, 2267 (1987). [CrossRef] [PubMed]

14. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Re v. Lett. **72**, 633 (1994). [CrossRef]

19. A. N. Poddubny, L. Pilozzi, M. M. Voronov, and E. L. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B , **77**, 113306, (2008). [CrossRef]

20. J, Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, “Excitonic polaritons in Fibonacci quasi-crystals,” Opt. Express **16**15382 (2008). [CrossRef] [PubMed]

21. L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. **86**, 261905 (2005). [CrossRef]

_{j+1}= {S

_{j-1}, S

_{j}} for j ≥1, where S

_{0}= {B} and S

_{1}= {A}, where S

_{j}is a structure obtained after

*j*iterations of the generation rule. In place of materials A and B we used Cellulose Acetate (CA) and Poly Vinyl Carbazole (PVK) respectively. The choice of the two polymers was dictated by their refractive index contrast and their solubility. The refractive indices of CA and PVK at 600 nm are 1.475 and 1.683, respectively. CA is soluble in polar solvents such as diacetone alcohol and PVK is soluble in non-polar solvent such as chlorobenzene. Similar approach using alternating layers of spin coated polymers has been previously used to realize Bragg mirrors for bandedge lasing, electro optical switching, enhanced spontaneous emission and microcavity lasing [22–25

22. H. Sakata, H. Takeuchi, K. Natsume, and S. Suzuki, “Vertical-cavity organic lasers with distributed-feedback structures based on active Bragg reflectors,” Opt. Exppress **14**, 11681 (2006). [CrossRef]

*j*=9 iterations was realized on a glass substrate using the polymers PVK with concentration of 0.5g in 20 ml of chlorobenzene and CA with concentration of 0.30g in 10 ml of diacetone alcohol. The {AA} layer was realized using a CA solution having twice the concentration. The CA polymer solutions were then infiltrated with

*sulforhodamine*dye, with an emission wavelength of 618 nm. The concentration of the dye in the CA solution was 1 mg in 10 ml of diacetone alcohol. The fabrication methodology involved spin coating process for every layer of polymer added onto the structure, which was subsequently heated on a hot plate for 15 minutes to remove the solvent. Cellulose acetate layers were heated at 120°C, while PVK layers were heated at 80°C. The desired thickness of the CA and PVK layers to yield a pseudo-bandgap around 600 nm were 132 nm and 109 nm and were realized by spin coating the layers at 1800 rpm and 2200 rpm, respectively. The {AA} layer was realized by spin coating the CA solution with double the concentration at 3000 rpm. The layer thicknesses were separately calibrated using reflectivity and surface profiling. Experiments revealed that the emission wavelength of the dye in CA was 594 nm, instead of bare dye’s emission wavelength (618 nm). This change introduced smaller overlap between the emission spectra and the bandedge state. Despite this detrimental effect, optical characterization of the system revealed interesting results which are discussed below.

26. L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, “Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach,” Phys. Rev. B **76**, 075350 (2007). [CrossRef]

*ε*(

*ω*,

*z*), When

*z*falls inside a passive PVK layer

*ε*(

*ω*,

*z*) =

*ε*=2.832, for values of

_{B}*z*inside CA layers embedded with dye the value of the dielectric constant isv

*A*. Frequency

*ω*corresponds to the maximum of the absorption of dye molecules dissolved in CA polymer layers. One should notice that we introduced two different resonance frequencies

_{abs}*ω*and

_{em}*ω*to describe emission and absorption properties of the dye molecules, which, is done to reflect a large experimentally observed Stokes shift between the emission and absorption spectra.

_{abs}24. N. Valappil, M. Luberto, V. M. Menon, I. Zeylikovich, T. K. Gayen, J. Franco, B. B. Das, and R. R. Alfano. “Solution processed microcavity structures with embedded quantum dots,” Photonics and Nanostructures: Fundamentals and Applications **5**, 184 (2007). [CrossRef]

*E*

_{-}

^{(m)}is the amplitude of the light emitted to the right of the structure,

*t*is its transmission coefficients, and two by two transfer matrices

*T*, and

_{R}*T*(

*N*,

*m*+ 1) describe propagation of light across the interface between the last layer of the structure and vacuum, and between the

*m*

^{th}and the last layer, respectively. Two dimensional bra and ket vectors appearing in Eq. (3) are given as ∣-〉 = (0 1), ∣

*V*

^{(m)}) = (

*V*

_{1}

^{(m)}

*V*

_{2}

^{(m)}), where

*z*

_{±}

^{(m)}are right and left coordinates of

*m*

^{th}active layer respectively. Total non-coherent emitted intensity is given as

*ω*and characterized by the second moment Δ. Neglecting the homogeneous broadening contribution to the susceptibility we assumed that the most of the width of the luminescence spectrum of pure dye is due to inhomogeneous broadening, thus we postulated that Δ =

_{em}*γ*. Our calculations showed that indeed, the inhomogeneous broadening results in appearance of the second peak in the spectra. Taking this into account results in a better agreement with experiment of not only the main feature, but also of the finer details of the spectra.

27. G. Bjork, “On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes,” IEEE J. Quantum Electron. **30**, 2314 (1994). [CrossRef]

*sulforhodamine*dye in CA showed PL lifetime of 4.57 ns independent of the wavelength. The dye showed decay time of 4.4 ns when observed off resonance from the bandedge state, while on resonance we observed noticeable reduction in the PL lifetime of 3.9 ns. This reduction in PL lifetime is attributed to the increased photon density of states available at the bandedge due to the presence of critically localized states.

## Acknowledgments

## References and links

1. | M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, “Low-threshold photonic crystal laser,” Appl. Phys. Lett. |

2. | T. Fujiwara and T. Ogawa, |

3. | G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. |

4. | F. Nori and J. P. Rodriguez, “Acoustic and electronic properties of one-dimensional quasicrystals,” Phys. Rev. B |

5. | T. Fujiwara, M. Kohmoto, and T. Tokihiro, “Multifractal wave functions on a Fibonacci lattice,” Phys. Rev. B |

6. | M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. |

7. | R. Merlin, K. Bajema, R. Clarke, F. -Y. Juang, and P. K. Bhattacharya, “Quasiperiodic GaAs-AlAs Heterostructures,” Phys. Rev. Lett. |

8. | J. B. Sokoloff, “Anomalous Electrical Conduction in Quasicrystals and Fibonacci Lattices,” Phys. Rev. Lett. |

9. | Ch. Wang and R. A. Barrio, “Theory of the Raman Response in Fibonacci Superlattices,” Phys. Rev. Lett. |

10. | E. Mad′a and F. Dom′inguez-Adame, “Physical Nature of Critical Wave Functions in Fibonacci Systems,” Phys. Rev. Lett. |

11. | F. Pi′echon, “Anomalous Diffusion Properties of Wave Packets on Quasiperiodic Chains,” Phys. Rev. Lett. |

12. | X. Huang and Ch. Gong, “Property of Fibonacci numbers and the periodiclike perfectly transparent electronic states in Fibonacci chains,” Phys. Rev. B |

13. | F. Steinbach, A. Ossipov, T. Kottos, and T. Geisel, “Statistics of Resonances and of Delay Times in Quasiperiodic Schrodinger Equations,” Phys. Rev. Lett. |

14. | W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Re v. Lett. |

15. | T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal,” Phys. Rev. B |

16. | D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. |

17. | E. Cojocaru, “Omnidirectional Reflection from Finite Periodic and Fibonacci Quasi-Periodic Multilayers of Alternating Isotropic and Birefringent Thin Films,” Appl. Opt. |

18. | L. dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light Transport through the Band-Edge States of Fibonacci Quasicrystals,” Phys. Rev. Lett. |

19. | A. N. Poddubny, L. Pilozzi, M. M. Voronov, and E. L. Ivchenko, “Resonant Fibonacci quantum well structures in one dimension,” Phys. Rev. B , |

20. | J, Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, “Excitonic polaritons in Fibonacci quasi-crystals,” Opt. Express |

21. | L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. |

22. | H. Sakata, H. Takeuchi, K. Natsume, and S. Suzuki, “Vertical-cavity organic lasers with distributed-feedback structures based on active Bragg reflectors,” Opt. Exppress |

23. | R. Katouf, T. Komikado, M. Itoh, T. Yatagai, and S. Umegaki, “Ultra-fast optical switches using 1D polymeric photonic crystals,” Photonics and Nanostructures - Fundamentals and Applications |

24. | N. Valappil, M. Luberto, V. M. Menon, I. Zeylikovich, T. K. Gayen, J. Franco, B. B. Das, and R. R. Alfano. “Solution processed microcavity structures with embedded quantum dots,” Photonics and Nanostructures: Fundamentals and Applications |

25. | V. M. Menon, M. Luberto, N. V. Valappil, and S. Chatterjee, “Lasing from quantum dots in a spin-coated flexible microcavity,” Opt. Express |

26. | L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, “Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach,” Phys. Rev. B |

27. | G. Bjork, “On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes,” IEEE J. Quantum Electron. |

**OCIS Codes**

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(050.5298) Diffraction and gratings : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: March 3, 2009

Revised Manuscript: April 5, 2009

Manuscript Accepted: April 5, 2009

Published: April 7, 2009

**Citation**

V. Passias, N. V. Valappil, Z. Shi, L. Deych, A. A. Lisyansky, and V. M. Menon, "Luminescence properties of a Fibonacci photonic quasicrystal," Opt. Express **17**, 6636-6642 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6636

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### References

- M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qiu, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680 (2002); H-G Park, S-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, "Electrically Driven Single-Cell Photonic Crystal Laser," Science 305, 1444 (2004). [CrossRef]
- T. Fujiwara and T. Ogawa, Quasicrystals (Springer Verlag, Berlin, 1990).
- G. Gumbs and M. K. Ali, "Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices," Phys. Rev. Lett. 60, 1081 (1988). [CrossRef] [PubMed]
- F. Nori and J. P. Rodriguez, "Acoustic and electronic properties of one-dimensional quasicrystals," Phys. Rev. B 34, 2207 (1986). [CrossRef]
- T. Fujiwara, M. Kohmoto, and T. Tokihiro, "Multifractal wave functions on a Fibonacci lattice," Phys. Rev. B 40, 7413 (1989). [CrossRef]
- M. Kohmoto, B. Sutherland, and K. Iguchi, "Localization of optics: Quasiperiodic media," Phys. Rev. Lett. 58, 2436 (1987);B. Sutherland and M. Kohmoto, "Resistance of a one-dimensional quasicrystal: Power-law growth," Phys. Rev. B 36, 5877 (1987). [CrossRef] [PubMed]
- R. Merlin, K. Bajema, R. Clarke, F. -Y. Juang, and P. K. Bhattacharya, "Quasiperiodic GaAs-AlAs Heterostructures," Phys. Rev. Lett. 55, 1768 (1985). [CrossRef] [PubMed]
- J. B. Sokoloff, "Anomalous Electrical Conduction in Quasicrystals and Fibonacci Lattices," Phys. Rev. Lett. 58, 2267 (1987). [CrossRef] [PubMed]
- Ch. Wang and R. A. Barrio, "Theory of the Raman Response in Fibonacci Superlattices," Phys. Rev. Lett. 61, 191 (1988). [CrossRef] [PubMed]
- E. Macia and F. Dom?nguez-Adame, "Physical Nature of Critical Wave Functions in Fibonacci Systems," Phys. Rev. Lett. 76, 2957 (1996). [CrossRef]
- F. Piechon, "Anomalous Diffusion Properties of Wave Packets on Quasiperiodic Chains," Phys. Rev. Lett. 76, 4372 (1996). [CrossRef]
- X. Huang and Ch. Gong, "Property of Fibonacci numbers and the periodiclike perfectly transparent electronic states in Fibonacci chains," Phys. Rev. B 58, 739 (1998). [CrossRef]
- F. Steinbach, A. Ossipov, T. Kottos, and T. Geisel, "Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations," Phys. Rev. Lett. 85, 4426 (2000). [CrossRef] [PubMed]
- W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1994). [CrossRef]
- T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, "Photonic dispersion relation in a one-dimensional quasicrystal," Phys. Rev. B 50, 4220, (1994). [CrossRef]
- D. Lusk, I. Abdulhalim, and F. Placido, "Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal," Opt. Commun. 198, 273 (2001). [CrossRef]
- E. Cojocaru, "Omnidirectional Reflection from Finite Periodic and Fibonacci Quasi-Periodic Multilayers of Alternating Isotropic and Birefringent Thin Films," Appl. Opt. 41, 747 (2002). [CrossRef] [PubMed]
- L. dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light Transport through the Band-Edge States of Fibonacci Quasicrystals," Phys. Rev. Lett. 90, 055501 (2003). [CrossRef]
- A. N. Poddubny, L. Pilozzi, M. M. Voronov, and E. L. Ivchenko, "Resonant Fibonacci quantum well structures in one dimension," Phys. Rev. B, 77, 113306, (2008). [CrossRef]
- J , Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, "Excitonic polaritons in Fibonacci quasi-crystals," Opt. Express 16, 15382 (2008). [CrossRef] [PubMed]
- L. Dal Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett. 86, 261905 (2005). [CrossRef]
- H. Sakata, H. Takeuchi, K. Natsume, and S. Suzuki, "Vertical-cavity organic lasers with distributed-feedback structures based on active Bragg reflectors," Opt. Exppress 14, 11681 (2006). [CrossRef]
- R. Katouf, T. Komikado, M. Itoh, T. Yatagai, and S. Umegaki, "Ultra-fast optical switches using 1D polymeric photonic crystals," Photonics and Nanostructures - Fundamentals and Applications 3, 116 (2005). [CrossRef]
- N. Valappil, M. Luberto, V. M. Menon, I. Zeylikovich, T. K. Gayen, J. Franco, B. B. Das, and R. R. Alfano. "Solution processed microcavity structures with embedded quantum dots," Photonics and Nanostructures: Fundamentals and Applications 5, 184 (2007). [CrossRef]
- V. M. Menon, M. Luberto, N. V. Valappil, and S. Chatterjee, "Lasing from quantum dots in a spin-coated flexible microcavity," Opt. Express 16, 19535 (2008). [CrossRef] [PubMed]
- L. I. Deych, M. V. Erementchouk, A. A. Lisyansky, E. L. Ivchenko, and M. M. Voronov, "Exciton luminescence in one-dimensional resonant photonic crystals: A phenomenological approach," Phys. Rev. B 76, 075350 (2007). [CrossRef]
- G. Bjork, "On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes," IEEE J. Quantum Electron. 30, 2314 (1994). [CrossRef]

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