## Enhanced spontaneous emission observed at one-dimensional photonic band edges

JOSA B, Vol. 27, Issue 1, pp. 45-50 (2010)

http://dx.doi.org/10.1364/JOSAB.27.000045

Acrobat PDF (497 KB)

### Abstract

We recently reported experimental evidence for double enhancement of spontaneous emission due to increased photon density of states and small group velocity at photonic band-edge frequencies by observing angle-resolved emission and excitation spectra of photoluminescence [
K. Kuroda et al., Opt. Express
17, 13168 (2009)
]. The specimen we used was a one-dimensional photonic crystal composed of periodic multilayers of

© 2009 Optical Society of America

## 1. INTRODUCTION

3. K. Sakoda, “Optics of photonic crystals,” Opt. Rev. **6**, 381–392 (1999). [CrossRef]

4. M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. **83**, 2841–2844 (1999). [CrossRef]

5. E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, “Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells,” Phys. Rev. B **70**, 195106 (2004). [CrossRef]

6. K. Kuroda, T. Sawada, T. Kuroda, K. Watanabe, and K. Sakoda, “Doubly enhanced spontaneous emission due to increased photon density of states at photonic band edge frequencies,” Opt. Express **17**, 13168–13177 (2009). [CrossRef] [PubMed]

6. K. Kuroda, T. Sawada, T. Kuroda, K. Watanabe, and K. Sakoda, “Doubly enhanced spontaneous emission due to increased photon density of states at photonic band edge frequencies,” Opt. Express **17**, 13168–13177 (2009). [CrossRef] [PubMed]

7. P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature **430**, 654–657 (2004). [CrossRef] [PubMed]

8. M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A **53**, 2799–2803 (1996). [CrossRef] [PubMed]

*et al.*and Scalora

*et al.*presented detailed calculations on finite one-dimensional PCs [9

9. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. **75**, 1896–1899 (1994). [CrossRef]

11. Y. Matsuhisa, Y. Huang, Y. Zhou, S.-T. Wu, Y. Takao, A. Fujii, and M. Ozaki, “Cholesteric liquid crystal laser in a dielectric mirror cavity upon band-edge excitation,” Opt. Express **15**, 616–622 (2007). [CrossRef] [PubMed]

12. M. Astic, Ph. Delaye, R. Frey, G. Roosen, R. André, N. Belabas, I. Sagnes, and R. Raj, “Time resolved nonlinear spectroscopy at the band edge of 1D photonic crystals,” J. Phys. D **41**, 224005 (2008). [CrossRef]

6. K. Kuroda, T. Sawada, T. Kuroda, K. Watanabe, and K. Sakoda, “Doubly enhanced spontaneous emission due to increased photon density of states at photonic band edge frequencies,” Opt. Express **17**, 13168–13177 (2009). [CrossRef] [PubMed]

## 2. THEORY

### 2A. Photonic Band Calculation

*a*is the lattice constant of the one-dimensional PC (the dielectric multilayers),

*θ*is the observation angle, and

*ω*and

*k*are the angular frequency and wave number of emitted photons.

*p*polarization for which the electric field is pointing in the

*s*polarization for which the electric field is pointing in the

*z*direction, which is perpendicular to the

*z*component of the magnetic field,

*p*polarization and that of the electric field,

*s*polarization. From the Maxwell equations, we obtain the following eigen equations: where

*c*is the velocity of light in free space and

*y*direction, spatial variation of the eigenfunctions in the

*y*direction is simply described by a phase factor

*y*component of the wave vector,

*x*direction is described by the Bloch theorem because of the periodicity of the structure. Thus the eigenfunctions of the

*p*and

*s*polarizations should have the following forms, respectively: whereis the reciprocal lattice constant and

*x*component of the wave vector.

*p*polarization first. By substituting Eqs. (3, 4) into Eq. (1) and comparing the Fourier component of the same order, we obtainFrom this equation, we can find that

*s*polarization, we substitute Eqs. (3, 5) into Eq. (2) and obtainIn the same conditions as given in Eq. (8), we obtain the following coupled equations for

*p*and

*s*polarizations:So, there is no eigenmode in the frequency range ofIf

*a*,

### 2B. Enhancement Factor

*θ*. Thus the two dimensions are reduced by these two experimental conditions, and it is sufficient to take into consideration the one-dimensional volume

*s*polarization and thin lines denote the

*p*polarization. Taking into account the lifetime of the eigenmodes in the actual specimen of a finite thickness

*s*and

*p*polarizations, whereas its width is wider for the

*s*polarization. In Section 4, we show that these features are actually observed in the experiment.

## 3. EXPERIMENTAL

**17**, 13168–13177 (2009). [CrossRef] [PubMed]

## 4. RESULTS AND DISCUSSION

### 4A. Excitation Power Dependence

### 4B. Polarization Dependence

*θ*from 0° to 45°, where thick and thin lines denote

*s*- and

*p*-polarized emissions. The overall features of this figure agree well with Fig. 2. First, the PBG and two emission peaks shift to the shorter wavelength with increasing detection angle. Second, the center wavelength of the PBG is nearly the same for the

*s*and

*p*polarizations. Third, the distance between the two peaks is larger for the

*s*polarization than for the

*p*polarization.

*θ*, the observed linewidth in the averaged spectrum becomes larger with increasing

*θ*.

*s*and

*p*polarizations as a function of the detection angle. Figures 6a, 6b show a magnified view of the two peaks of the

*s*-(thick curve) and

*p*-polarized (thin curve) emissions at

## 5. CONCLUSION

*s*and

*p*polarizations were calculated analytically in the weak modulation approximation, which was justified by the small PBG width of the specimen. The enhancement factor of spontaneous emission derived from the band structure was shown to be divergent at the band-edge frequencies.

## ACKNOWLEDGMENTS

1. | J. D. Joannopoulos, R. D. Meade, and J. N. Winn, |

2. | K. Sakoda, |

3. | K. Sakoda, “Optics of photonic crystals,” Opt. Rev. |

4. | M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. |

5. | E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, “Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells,” Phys. Rev. B |

6. | K. Kuroda, T. Sawada, T. Kuroda, K. Watanabe, and K. Sakoda, “Doubly enhanced spontaneous emission due to increased photon density of states at photonic band edge frequencies,” Opt. Express |

7. | P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature |

8. | M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A |

9. | J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. |

10. | M. Scalora, J. P. Dowling, M. Tocci, M. J. Bloemer, C. M. Bowden, and J. W. Haus, “Dipole emission rates in one-dimensional photonic band-gap materials,” Appl. Phys. B |

11. | Y. Matsuhisa, Y. Huang, Y. Zhou, S.-T. Wu, Y. Takao, A. Fujii, and M. Ozaki, “Cholesteric liquid crystal laser in a dielectric mirror cavity upon band-edge excitation,” Opt. Express |

12. | M. Astic, Ph. Delaye, R. Frey, G. Roosen, R. André, N. Belabas, I. Sagnes, and R. Raj, “Time resolved nonlinear spectroscopy at the band edge of 1D photonic crystals,” J. Phys. D |

**OCIS Codes**

(160.2540) Materials : Fluorescent and luminescent materials

(260.3800) Physical optics : Luminescence

(160.5298) Materials : Photonic crystals

**ToC Category:**

Physical Optics

**History**

Original Manuscript: September 14, 2009

Revised Manuscript: October 23, 2009

Manuscript Accepted: October 30, 2009

Published: December 17, 2009

**Citation**

Keiji Kuroda, Tsutomu Sawada, Takashi Kuroda, Kenji Watanabe, and Kazuaki Sakoda, "Enhanced spontaneous emission observed at one-dimensional photonic band edges," J. Opt. Soc. Am. B **27**, 45-50 (2010)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-1-45

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### References

- J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).
- K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer, 2004).
- K. Sakoda, “Optics of photonic crystals,” Opt. Rev. 6, 381-392 (1999). [CrossRef]
- M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841-2844 (1999). [CrossRef]
- E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, “Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells,” Phys. Rev. B 70, 195106 (2004). [CrossRef]
- K. Kuroda, T. Sawada, T. Kuroda, K. Watanabe, and K. Sakoda, “Doubly enhanced spontaneous emission due to increased photon density of states at photonic band edge frequencies,” Opt. Express 17, 13168-13177 (2009). [CrossRef] [PubMed]
- P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004). [CrossRef] [PubMed]
- M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53, 2799-2803 (1996). [CrossRef] [PubMed]
- J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75, 1896-1899 (1994). [CrossRef]
- M. Scalora, J. P. Dowling, M. Tocci, M. J. Bloemer, C. M. Bowden, and J. W. Haus, “Dipole emission rates in one-dimensional photonic band-gap materials,” Appl. Phys. B 60, S57-S61 (1995).
- Y. Matsuhisa, Y. Huang, Y. Zhou, S.-T. Wu, Y. Takao, A. Fujii, and M. Ozaki, “Cholesteric liquid crystal laser in a dielectric mirror cavity upon band-edge excitation,” Opt. Express 15, 616-622 (2007). [CrossRef] [PubMed]
- M. Astic, Ph. Delaye, R. Frey, G. Roosen, R. André, N. Belabas, I. Sagnes, and R. Raj, “Time resolved nonlinear spectroscopy at the band edge of 1D photonic crystals,” J. Phys. D 41, 224005 (2008). [CrossRef]

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