## Effects of resonant absorption and inhomogeneous broadening on reflection and absorption spectra of optical lattices in diamond NV centers

Optics Express, Vol. 14, Issue 24, pp. 11727-11735 (2006)

http://dx.doi.org/10.1364/OE.14.011727

Acrobat PDF (2447 KB)

### Abstract

Using the transfer-matrix method, the effects of absorption and inhomogeneous broadening, in one-dimensional optical lattice constructed from inhomogeneously broadened spin transitions of nitrogen-vacancy color centers in single crystal diamond (NV diamond), on the reflection and absorption spectrum are presented. Further analysis show that, in realistic periodic stacks of the NV diamond, modulating the geometrical configuration of the external optical potential, the absorption lineshape scale, and the inhomogeneous broadening, one could easily access the diverse gap structures and a high band-gap reflectivity. These pretty useful calculations hold more potential for effective control of the light-matter interaction and realization in practice.

© 2006 Optical Society of America

## 1. Introduction

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. **58**, 2059–2062 (1987). [CrossRef] [PubMed]

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. **58**, 2486–2489 (1987). [CrossRef] [PubMed]

3. S. Harris, “Electromagnetically induced transparency,” Physics Today **50**, 36–42 (1997). [CrossRef]

4. A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. **89**, 143602 (2002). [CrossRef] [PubMed]

7. Q. Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J. H. Xu, and J. Y. Gao, “Coherently induced stop-bands in resonantly absorbing and inhomogeneously broadened doped crystals,” Phys. Rev. B **73**, 195124 (2006). [CrossRef]

8. Q. Y. He, J. H. Wu, T. J. Wang, and J. Y. Gao, “Dynamic control of the photonic stop bands formed by a standing wave in inhomogeneous broadening solids,” Phys. Rev. A **73**, 053813 (2006). [CrossRef]

10. M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, and K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B **48**, 14121–14126 (1993). [CrossRef]

14. M. Hubner, 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]

18. M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E **72**, 046604 (2005). [CrossRef]

18. M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E **72**, 046604 (2005). [CrossRef]

## 2. The model and equations

*W*

^{cb}≃ 30 KHz is the inhomogeneous widths of the optic transition |

*c*→|

*b*〉, where the Raman transition frequency (120 MHz) is determined by the spacing between the S=0 (|

*b*〉) and S=-1 (|

*c*〉) ground-state spin sublevels. This spacing is controlled by the magnitude of the applied magnetic field (~1 KG along the (111) direction is applied) [19

19. X. F. He, N. B. Manson, and P. T. H. Fisk, “Paramagnetic resonance of photoexcited N-V defects in diamond. I. Level anticrossing in the ^{3}*A* ground state,” Phys. Rev. B **47**, 8809 (1993). [CrossRef]

*a*〉 and |

*b*〉, where the relevant optical transition at 637 nm has an inhomogeneous width

*W*

^{ab}≃ 375 GHz, are coupled by a weak probe beam with frequency

*ω*, the reflection and absorption of which are the physical quantities we are interested in. All relevant parameters we used come from the published experiment [20

20. P. R. Hemmer, A. V. Turukhin, M. S. Shahriar, and J. Musser, “Raman excited spin coherence in NV-Diamond,” Opt. Lett. **26**, 361–363 (2001). [CrossRef]

22. E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A **66**, 063802 (2002). [CrossRef]

23. A. Javan, O. Kocharovskaya, Hwang Lee, and M. O. Scully, “Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A **66**, 013805 (2002). [CrossRef]

*ω*

_{ij}are the frequencies of the corresponding transitions, Δ

*ω*

_{ij}represents the detuning of the inhomogeneous broadened line center from an isolated atom line center, and χ̕(

*ω*,

*ω*

_{ab(cb)}) corresponds to a single ion with specific detunings

*ω*

_{ab}and

*ω*

_{cb}determined by its position within its host, which is from the off diagonal density matrix elements oscillating

*ρ*

_{ab(ω)}[25]. Finally, the optical properties of the single slab are specified by the complex dielectric function

*M*

_{N}(

*ω*) (

*N*is the number of the periods) for the whole periodic dissipative solid layers, with optical properties specified by the complex dielectric function (3) and otherwise separated by vacuum, is obtained by multiplying together the transfer matrix

*M*(

*ω*) of a single period [6–8

6. M. Artoni and G. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. **96**, 073905 (2006). [CrossRef] [PubMed]

*i.e.*, the dependence of the complex Bloch wavevector

*κ*associated with a given incident frequency

*ω*

*E*

^{+}and

*E*

^{-}are the electric field amplitudes of the forward and backward (Bragg reflected) propagating probe,

*a*is the periodicity of this structure [27–29

27.
In typical experimental configurations *a* is set by the periodicity of the standing wave and it is just half the wavelength of the two counter-propagating laser beams creating the optical potential as described in following Ref. [28, 29]. Each slab has a thickness *d* sufficiently smaller than the periodicity.

*R*

_{N}|

^{2}) and transmissivity (|

*T*

_{N}|

^{2}) for the

*L*length, namely,

*A*=1-|

*R*

_{N}|

^{2}-|

*T*

_{N}|

^{2}.

## 3. Numerical results and discussion

*ε*=

*ε*

_{0}(

*constant*),

*ε*=

*ε*′(

*ω*), and

*ε*=

*ε*′(

*ω*) +

*iε*″(

*ω*). The curves in Fig. 1(a) correspond to two antithetic cases:

*ε*

_{1}=

*ε*

_{vacuum}- Δ

*ε*

_{1}and

*ε*

_{2}=

*ε*

_{vacuum}+ Δ

*ε*

_{2}(

*ε*

_{vacuum}=1), where the NV diamond has frequency independent dielectric constant,

*i.e.*, non dissipative. It is evident that the band-gaps appear to be symmetric with respect to resonant frequency when Δ

*ε*

_{1}=Δ

*ε*

_{2}, in addition, with the value of Δ

*ε*increasing, the width of gap will be larger. In the presence of dissipation the situation becomes more complicated. The blue curves in Fig. 1(b) correspond to cases where the imaginary part of the frequency-dependent dielectric constants is equal to zero (nonabsorbent materials). We can obtain a perfect traditional photonic band-gap that split right at resonance; in other words, gaps are symmetrically located at both sides of the resonance frequency as shown in [11

11. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B **49**, 11080–11087 (1994). [CrossRef]

18. M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E **72**, 046604 (2005). [CrossRef]

*α*term of the damping [30], what will happen? Answer is clearly shown in Fig. 2: (a) the gap could survive in the presence of strong dissipation except for the width of gap decreasing; (b) for narrow absorption profile (blue) the reflectivity within the resonance region is higher than the ones in broadened cases (red and black), which is due to the corresponding higher refractive index (

*η*)shown under Fig. 2(a). This effect will be remarkable for the whole gap developing within the NV resonance region, which may be achieved through appreciable modifications of the NV lattice periodicity a as shown in Fig. 2(c) [31

31.
It could be realized by using a rather large misalignment between the two beams. While in Fig. 2(b) the periodicity *a* ≃ 318.5 nm is the situation in which the two beams are exactly counter propagating, because it is just equal to the half-wavelength of the resonant transition from the excited state |*a*〉 to the ground-state spin sublevel |*c*〉 in NV diamond.

^{3}GHz, rather larger than ~ 10

^{3}MHz in atomic, due to its large inhomogeneous broadening line width. And besides, shorter sample length is needed to stop the probe restricted within the gap. The other side, thus even a weak dissipation in the gap (black curve shown in Fig. 2(c)) leads to a rounding or “smoothing” of the edge of the forbidden zone. Because of this it should be rather difficult to resolve narrow gaps experimentally. However fortunately, the periodicity of the standing wave needed in the experiment should be almost equal to the half-wavelength of the resonant transition from the excited state to the ground-state spin sublevel in NV diamond color centers,

*i.e.*,

*a*≃ 318.5 nm, which is just our case shown in Fig. 2(b). Then even for the black curve, it’s feasible to realize the band-gap and the high reflectivity.

*a*. Symmetric band-gap splitting is obtained from a solid stack with periodicity

*a*≃ 318.5 nm that equal to the half-wavelength of the exciton radiation. When

*a*is lager than that one, the gap will move to the frequency region below resonance (Δ

_{p}> 0) - the so-called red detuning, while moving to above resonance (Δ

_{p}< 0) - the so-called blue detuning when the period

*a*is reduced. That result does accord with the character of the typical period material. The steep profile for red/blue detuning is due to the resonance absorption, and the other gap is symmetric around mid-gap because of falling far from resonance making the solid periodic structure essentially non-dissipative. The corresponding band-gap reflectivity and absorption spectrum with an array of length

*L*≃ 6.55×10

^{3}

*a*are shown in Fig. 3(b).

*d*/

*a*) of single layer. It is clear that the reflectivity is zero and most probe is absorbed when (

*d*/

*a*)=1 that corresponding to a continuous NV diamond sample without period. While when the ratio of the slab and the period is reduced,

*i.e.*, the thickness of solid dielectric slab is decreased, two symmetric band-gaps appear. The more reduced the ratio is, the closer the two band-gap reflectivity spectra are to approach to the resonance frequency, even combined to make one gap.

32. B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. **144**, 227–230 (1997). [CrossRef]

33. According to the experiment done by Ham in Ref. [32], we know that inhomogeneous line broadening can be effectively reduced up to the magnitude of the laser beam jitter using an optical repump scheme, corresponding reduction in the effective atomic density. As for the use of a repumper in Ref. [20], the authors explicitly say that for NV diamond this procedure is not frequency selective, however in Ref. [22, 23] the discrepancy in the transparency value (bigger in experiment than in theory) is attributed to possible effects of the repumper. Maybe that the use of the repumper in NV diamond leads to a minor correction of the broadening compared to the case of Pr:YSO.

*W*

^{ab}≃ 375 GHz corresponding to the density of centers

*N*=3×10

^{18}cm

^{-3}(case 1), we can properly estimate:

*W*

^{ab}≃ Δ

*v*

_{jit}=100 MHz corresponding to the effective density

*N*=1×10

^{15}cm

^{-3}(case 2). A typical reflectivity and absorption spectrum of such a modification in broadened system is shown in Fig. 5.

*L*≃ 6.55×10

^{4}

*a*(2 cm), is also plotted in Fig. 5(c, d). Now, case 2 shows a distinct predominance in the spectral response,

*i.e.*, the perfect band-gap (reflectivity in the gap goes up to unity) appears to be symmetric with respect to resonance within the inhomogeneous width of NV. Whereas case 1 exhibits the same behavior as ones in Fig. 5(a) except for the region outside its wide gap where the absorption is increasing due to the longer sample. One can understand this phenomenon by calculating the typical values of absorption (

*l*

_{abs}) and the extinction (

*l*

_{ext}) length decided by their Bloch modes shown in Fig. 6 [34]. Either of both above cases for NV diamond has its merits.

## 4. Conclusion

*m*

_{s}=± 1 states so that the spacing of 120 MHz can be got. The fabrication of diamond single crystal layers is difficult but not unfeasible. For example, one can use CVD or MPCVD to grow high quality single crystal diamond film [35, 36

36. C. Tavares, F. Omnes, J Pernot, and E. Bustarret, “Electronic properties of boron-doped 111-oriented homoepitaxial diamond layers,” Diamond Relat. Mater. **15**, 582–585 (2006). [CrossRef]

37. S. Tomljenovic-Hanic, M. J. Steel, and C. Martijn de Sterke, “Diamond based photonic crystal microcavities,” Opt. Express **14**, 3556 (2006). [CrossRef] [PubMed]

38. M. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. **75**, 457 (2003). [CrossRef]

39. A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. **94**, 063902 (2005). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. |

2. | S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. |

3. | S. Harris, “Electromagnetically induced transparency,” Physics Today |

4. | A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. |

5. | H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. |

6. | M. Artoni and G. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. |

7. | Q. Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J. H. Xu, and J. Y. Gao, “Coherently induced stop-bands in resonantly absorbing and inhomogeneously broadened doped crystals,” Phys. Rev. B |

8. | Q. Y. He, J. H. Wu, T. J. Wang, and J. Y. Gao, “Dynamic control of the photonic stop bands formed by a standing wave in inhomogeneous broadening solids,” Phys. Rev. A |

9. | X. M. Su and B. S. Ham, “Dynamic control of the photonic band gap using quantum coherence,” Phys. Rev. A |

10. | M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, and K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B |

11. | M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B |

12. | A. A. Krokhin and P. Halevi, “Influence of weak dissipation on the photonic band structure of periodic composites,” Phys. Rev. B |

13. | A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of polaritonic crystal slab,” Phys. Stat. Sol. (a) |

14. | M. Hubner, 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. |

15. | J. P. Prineas, C. Ell, E. S. L EE, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Exciton-polariton eigenmodes in light-coupled in 0.04Ga0.96As/GaAs semiconductor multiple-quantum-well periodic structures,” Phys. Rev. B |

16. | L. I. Deych, M. V. Erementchouk, and A. A. Lisyansky, “Effects of inhomogeneous broadening on reflection spectra of Bragg multiple quantum well structures with a defect,” Phys. Rev. B |

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

18. | M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E |

19. | X. F. He, N. B. Manson, and P. T. H. Fisk, “Paramagnetic resonance of photoexcited N-V defects in diamond. I. Level anticrossing in the |

20. | P. R. Hemmer, A. V. Turukhin, M. S. Shahriar, and J. Musser, “Raman excited spin coherence in NV-Diamond,” Opt. Lett. |

21. | M. Born and E. Wolf, |

22. | E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A |

23. | A. Javan, O. Kocharovskaya, Hwang Lee, and M. O. Scully, “Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A |

24. |
The use of Lorentzian line shapes allows us to obtain analytical results for |

25. |
Here, ω,ω_{ab}(_{cd}))=ρab/(2h̅Ω_{p}) the density equations and all parameters are shown in detail in our earlier work [7, 8]. |

26. | F. Bassani and G. Pastori Parravicini, |

27. |
In typical experimental configurations |

28. | I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, and W. D. Phillips, “Photonic band gaps in optical lattices,” Phys. Rev. A |

29. | M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature |

30. |
The scaling affects both the resonant absorption ( |

31. |
It could be realized by using a rather large misalignment between the two beams. While in Fig. 2(b) the periodicity |

32. | B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. |

33. | According to the experiment done by Ham in Ref. [32], we know that inhomogeneous line broadening can be effectively reduced up to the magnitude of the laser beam jitter using an optical repump scheme, corresponding reduction in the effective atomic density. As for the use of a repumper in Ref. [20], the authors explicitly say that for NV diamond this procedure is not frequency selective, however in Ref. [22, 23] the discrepancy in the transparency value (bigger in experiment than in theory) is attributed to possible effects of the repumper. Maybe that the use of the repumper in NV diamond leads to a minor correction of the broadening compared to the case of Pr:YSO. |

34. | M. Artoni, G. La Rocca, and F. Bassani have described the detail about |

35. | T. Shibata, “Micromachining of diamond thin film,” New Diamond Front. Carbon Technol. |

36. | C. Tavares, F. Omnes, J Pernot, and E. Bustarret, “Electronic properties of boron-doped 111-oriented homoepitaxial diamond layers,” Diamond Relat. Mater. |

37. | S. Tomljenovic-Hanic, M. J. Steel, and C. Martijn de Sterke, “Diamond based photonic crystal microcavities,” Opt. Express |

38. | M. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. |

39. | A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. |

**OCIS Codes**

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(290.5830) Scattering : Scattering, Brillouin

(300.6250) Spectroscopy : Spectroscopy, condensed matter

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 26, 2006

Revised Manuscript: October 3, 2006

Manuscript Accepted: October 4, 2006

Published: November 27, 2006

**Citation**

Qiongyi He, Tiejun Wang, Jinhui Wu, and Jinyue Gao, "Effects of resonant absorption and inhomogeneous broadening on reflection and absorption spectra of optical lattices diamond NV centers," Opt. Express **14**, 11727-11735 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-24-11727

Sort: Year | Journal | Reset

### References

- E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58,2059-2062 (1987). [CrossRef] [PubMed]
- S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58,2486-2489 (1987). [CrossRef] [PubMed]
- S. Harris, "Electromagnetically induced transparency," Phys. Today 50,36-42 (1997). [CrossRef]
- A. Andre and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89,143602 (2002). [CrossRef] [PubMed]
- H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93,073601 (2004). [CrossRef] [PubMed]
- M. Artoni and G. La Rocca, "Optically tunable photonic stop bands in homogeneous absorbing media," Phys. Rev. Lett. 96,073905 (2006). [CrossRef] [PubMed]
- Q. Y. He, Y. Xue, M. Artoni, G. C. La Rocca, J. H. Xu, and J. Y. Gao, "Coherently induced stop-bands in resonantly absorbing and inhomogeneously broadened doped crystals," Phys. Rev. B 73,195124 (2006). [CrossRef]
- Q. Y. He, J. H. Wu, T. J. Wang, and J. Y. Gao, "Dynamic control of the photonic stop bands formed by a standing wave in inhomogeneous broadening solids," Phys. Rev. A 73,053813 (2006). [CrossRef]
- X. M. Su and B. S. Ham, "Dynamic control of the photonic band gap using quantum coherence," Phys. Rev. A 71,013821 (2005). [CrossRef]
- M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, and K. M. Ho, "Photonic band gaps and defects in two dimensions: studies of the transmission coefficient," Phys. Rev. B 48,14121-14126 (1993). [CrossRef]
- M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, "Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials," Phys. Rev. B 49,11080-11087 (1994). [CrossRef]
- A. A. Krokhin and P. Halevi, "Influence of weak dissipation on the photonic band structure of periodic composites," Phys. Rev. B 53,1205-1214 (1996). [CrossRef]
- A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of polaritonic crystal slab," Phys. Stat. Solidi A 190,413-419 (2002). [CrossRef]
- M. Hubner, 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]
- J. P. Prineas, C. Ell, E. S. L EE, G. Khitrova, H. M. Gibbs, and S. W. Koch, "Exciton-polariton eigenmodes in light-coupled in 0.04Ga0.96As/GaAs semiconductor multiple-quantum-well periodic structures," Phys. Rev. B 61,13863-13872 (2000). [CrossRef]
- L. I. Deych, M. V. Erementchouk, and A. A. Lisyansky, "Effects of inhomogeneous broadening on reflection spectra of Bragg multiple quantum well structures with a defect," Phys. Rev. B 69,075308 (2004). [CrossRef]
- E. L. Ivchenko, M. M. Voronov, M. V. Eremetchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-wellbased photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70,195106 (2004). [CrossRef]
- M. Artoni, G. La Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Phys. Rev. E 72,046604 (2005). [CrossRef]
- X. F. He, N. B. Manson, and P. T. H. Fisk, "Paramagnetic resonance of photoexcited N-V defects in diamond. I. Level anticrossing in the 3A ground state," Phys. Rev. B 47,8809 (1993). [CrossRef]
- P. R. Hemmer, A. V. Turukhin, M. S. Shahriar, and J. Musser, "Raman excited spin coherence in NV-Diamond," Opt. Lett. 26,361-363 (2001). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, 6th Edition (Cambridge University Press, Cambridge, 1980).
- E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, "Atomic interference phenomena in solids with a long-lived spin coherence," Phys. Rev. A 66,063802 (2002). [CrossRef]
- A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, "Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium," Phys. Rev. A 66,013805 (2002). [CrossRef]
- The use of Lorentzian line shapes allows us to obtain analytical results for χ as described in detail in Ref. [22].
- Here, χ (ω,ωab(cb)_ = Nμ2 abρab/(2¯hΩp) the density equations and all parameters are shown in detail in our earlier work [7, 8].
- F. Bassani and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon Press, Oxford, 1975).
- In typical experimental configurations a is set by the periodicity of the standing wave and it is just half the wavelength of the two counter-propagating laser beams creating the optical potential as described in following Ref. [28, 29]. Each slab has a thickness d sufficiently smaller than the periodicity.
- I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, and W. D. Phillips, "Photonic band gaps in optical lattices," Phys. Rev. A 52,1394-1410 (1995). [CrossRef] [PubMed]
- M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003). [CrossRef] [PubMed]
- The scaling affects both the resonant absorption (κ) and the refractive index (η) as shown in Fig. 2(c) for NV diamond. α → 1 corresponds to the actual linewidth profile, smaller α yield a linewidth narrowing with a concomitant peak absorption increase.
- It could be realized by using a rather large misalignment between the two beams. While in Fig. 2(b) the periodicity a ≃ 318.5 nm is the situation in which the two beams are exactly counter propagating, because it is just equal to the half-wavelength of the resonant transition from the excited state |ai to the ground-state spin sublevel |ci in NV diamond.
- B. S. Ham, P. R. Hemmer, and M. S. Shahriar, "Efficient electromagnetically induced transparency in a rare-earth doped crystal," Opt. Commun. 144,227-230 (1997). [CrossRef]
- According to the experiment done by Ham in Ref. [32], we know that inhomogeneous line broadening can be effectively reduced up to the magnitude of the laser beam jitter using an optical repump scheme, corresponding reduction in the effective atomic density. As for the use of a repumper in Ref. [20], the authors explicitly say that for NV diamond this procedure is not frequency selective, however in Ref. [22, 23] the discrepancy in the transparency value (bigger in experiment than in theory) is attributed to possible effects of the repumper. Maybe that the use of the repumper in NV diamond leads to a minor correction of the broadening compared to the case of Pr:YSO.
- M. Artoni, G. La Rocca, and F. Bassani have described the detail about labs and lext for atom stacks in Ref. [18].
- T. Shibata, "Micromachining of diamond thin film," New Diamond Front. Carbon Technol. 10,161-175 (2000).
- C. Tavares, F. Omnes, J Pernot, and E. Bustarret, "Electronic properties of boron-doped 111-oriented homoepitaxial diamond layers," Diamond Relat. Mater. 15,582-585 (2006). [CrossRef]
- S. Tomljenovic-Hanic, M. J. Steel, and C. Martijn de Sterke, "Diamond based photonic crystal microcavities," Opt. Express 14,3556 (2006). [CrossRef] [PubMed]
- M. Lukin, "Colloquium: trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75,457 (2003). [CrossRef]
- A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Nonlinear optics with stationary pulses of light," Phys. Rev. Lett. 94,063902 (2005). [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.

« Previous Article | Next Article »

OSA is a member of CrossRef.