## Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs

Optics Express, Vol. 18, Issue 9, pp. 9164-9172 (2010)

http://dx.doi.org/10.1364/OE.18.009164

Acrobat PDF (1067 KB)

### Abstract

We demonstrate planar structures that can provide simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical (or phoxonic) crystal slabs. Different phoxonic crystal (PxC) structures, composed of square, hexagonal (honeycomb), or triangular arrays of void cylindrical holes embedded in silicon (Si) slabs with a finite thickness, are investigated. Photonic band gap (PtBG) maps and the complete phononic band gap (PnBG) maps of PxC slabs with different radii of the holes and thicknesses of the slabs are calculated using a three-dimensional plane wave expansion code. Simultaneous phononic and photonic band gaps with band gap to midgap ratios of more than 10% are shown to be readily obtainable with practical geometries in both square and hexagonal lattices, but not for the triangular lattice.

© 2010 OSA

## 1. Introduction

1. E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. **58**(20), 2059–2062 (1987). [CrossRef] [PubMed]

2. M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. **77**(13), 1937–1939 (2000). [CrossRef]

3. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature **425**(6961), 944–947 (2003). [CrossRef] [PubMed]

4. M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. **19**(12), 1970–1975 (2001). [CrossRef]

5. M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. **158**(2), 377–382 (1992). [CrossRef]

6. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. **94**(22), 223902 (2005). [CrossRef] [PubMed]

7. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature **459**(7246), 550–555 (2009). [CrossRef] [PubMed]

8. A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. **101**(3), 033902–033905 (2008). [CrossRef] [PubMed]

9. P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. **2**(6), 388–392 (2006). [CrossRef]

10. M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B **83**(4), 595–600 (2006). [CrossRef]

11. M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. **88**(25), 251907 (2006). [CrossRef]

_{3}with optimization of the size of the gap have been recently reported [12

12. S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. **106**(7), 074912 (2009). [CrossRef]

13. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **74**(4), 046610 (2006). [CrossRef]

14. S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. **43**(16), 898–899 (2007). [CrossRef]

15. S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. **92**(22), 221905 (2008). [CrossRef]

16. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs,” in Proceedings of *2008 IEEE International Frequency Control Symposium,* 2008 IEEE International Frequency Control Symposium, FCS (IEEE, 2008), 768–772.

17. R. H. Olsson III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. **145-146**, 87–93 (2008). [CrossRef]

2. M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. **77**(13), 1937–1939 (2000). [CrossRef]

3. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature **425**(6961), 944–947 (2003). [CrossRef] [PubMed]

2. M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. **77**(13), 1937–1939 (2000). [CrossRef]

3. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature **425**(6961), 944–947 (2003). [CrossRef] [PubMed]

14. S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. **43**(16), 898–899 (2007). [CrossRef]

16. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs,” in Proceedings of *2008 IEEE International Frequency Control Symposium,* 2008 IEEE International Frequency Control Symposium, FCS (IEEE, 2008), 768–772.

13. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **74**(4), 046610 (2006). [CrossRef]

17. R. H. Olsson III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. **145-146**, 87–93 (2008). [CrossRef]

10. M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B **83**(4), 595–600 (2006). [CrossRef]

12. S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. **106**(7), 074912 (2009). [CrossRef]

## 2. Method of simulation and simulation assumptions

19. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. **65**(25), 3152–3155 (1990). [CrossRef] [PubMed]

20. M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B **49**(4), 2313–2322 (1994). [CrossRef]

*ε*is the position-dependent dielectric permittivity and

*H*is the magnetic field intensity vector. Equation (1) is then converted to an eigenvalue problem by expanding the magnetic field intensity using a plane wave basis and the dielectric permittivity using Fourier transform [19

19. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. **65**(25), 3152–3155 (1990). [CrossRef] [PubMed]

21. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B **60**(8), 5751–5758 (1999). [CrossRef]

*x*,

*y*, and

*z*directions of the coordinate system. The anisotropy of the mechanical parameters of the Si is fully considered in our simulations. The material parameters of Si are assumed to be ε

_{r}= 12.25,

*c*= 16.7 × 10

_{11}^{10}N/m

^{2},

*c*= 6.39 × 10

_{12}^{10}N/m

^{2},

*c*= 7.956 × 10

_{44}^{10}N/m

^{2}, and

*ρ*= 2332 kg/m

^{3}, where ε

_{r}is the relative permittivity,

*c*are the independent components of the stiffness tensor, and

_{11}, c_{12,}c_{44}*ρ*is the mass density of Si.

## 3. Comparison of the band structures of 2D PxCs and PxC slabs

*a*is the spacing between the centers of the nearest holes (or the lattice constant) and

*r*is the radius of the holes. The normalized radius of the holes is

*r/a*= 0.45. As can be seen in Fig. 1(a), a PnBG exists in this PxC and covers a frequency range of 2430 m/s <

*f × a*< 3619 m/s. Figure 1(b) shows the band structure of elastic waves in a square-lattice Si PxC slab calculated using 3D PWE. A schematic of the structure is shown in the inset of Fig. 1(b), where

*a*is the lattice constant,

*r*is the radius of the holes, and

*d*is the thickness of the slab. The normalized radius of the holes in the structure is the same as that of the structure in Fig. 1(a) (i.e.,

*r/a*= 0.45), and the normalized thickness of the structure is

*d/a*= 0.5 rather than infinite. The PnBG for this structure extends in the frequency range of 3000 m/s <

*f × a*< 3260 m/s. As can be seen, the band structure and the PnBG of the structure with a finite thickness [shown in Fig. 1(b)] are considerably different from those of the structure with infinite thickness [shown in Fig. 1(a)].

*r/a*= 0.45 as in the case of Fig. 1(a). As can be seen in Fig. 1(c), there are both TE and TM PtBGs in the photonic band structure.

21. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B **60**(8), 5751–5758 (1999). [CrossRef]

*r/a*= 0.45, and

*d/a*= 0.5, respectively [as in the case of Fig. 1(b)]. Since the photonic modes of the structure are lossy above the light line, only the guided modes that reside below the light line are considered [21

21. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B **60**(8), 5751–5758 (1999). [CrossRef]

*r/a*= 0.45 and

*d/a*= 0.5.

## 4. Phononic and photonic band gap maps for the square-lattice PxC slab

*r/a*) and a fixed normalized thickness of

*d/a*= 0.5 [Fig. 2(a) , Fig. 2(c)], and for varying normalized thickness (

*d/a*) and constant normalized hole radii of

*r/a*= 0.45 [Fig. 2(b), Fig. 2(d)] are shown in Fig. 2. Such band gap maps are beneficial for designing PxC slabs with simultaneous PnBG/PtBGs for different applications and conditions.

*d/a*= 0.5, the PnBG of the square-lattice PxC slab opens up at approximately

*r/a*= 0.43 at frequency of

*f × a*= 3150 m/s; it widens up as the normalized radius increases. At normalized radius of

*r/a*= 0.49, the PnBG extends to the frequency range of 2170 m/s <

*f × a*< 3380 m/s. The PnBG map of the same PxC for constant normalized radius of

*r/a*= 0.45 and as a function of the slab thickness is shown in Fig. 2(b). As is visualized in this figure, the PnBGs, opens up at

*d/a*~0.4 at frequency of 3750 m/s; by increasing the thickness, the PnBG widens up to 2970 m/s <

*f × a*< 3400 m/s at

*d/a*= 0.55 and closes at

*d/a*= 0.7 at

*f × a*~2800 m/s.

*d/a*= 0.5 is shown in Fig. 2(c). The PtBG maps are calculated considering the band structure of the PtC under the light line of the slab. PtBG regions of narrower than 5% of the center frequency and higher than the sixth band are not considered since such gaps have limitations for realizing practical devices. The band numbers between which each PtBG occurs are shown close to each region. As can be seen in Fig. 2(c), three even PtBGs are present in this PtBG map. The first even PtBG is between 1st and 2nd bands and starts expanding at

*r/a*= 0.33 at

*f × a / c*= 0.295, where

*c*is the phase velocity of light in vacuum. This even PtBG expands to a PtBG to mid gap ratio (or PtBG ratio) of more than 10% and closes at

*r/a*= 0.47. The second even PtBG occurs between the 2nd and 3rd even bands and opens up at

*r/a*= 0.22 and closes at

*r/a*~0.36 with a relatively small bandwidth (less than 7% PtBG ratio). Finally, the third even PtBG occurs between the 4th and the 5th bands. It starts at

*r/a*~0.33 at

*f × a / c*= 0.465 and expands up to 0.57 <

*f × a / c*< 0.66 at

*r/a*= 0.49 with a maximum PtBG ratio of approximately 15% at this point. The only present odd PtBG region starts at

*r/a*= 0.3 between the 3rd and 4th odd bands at

*f × a / c*= 0.42 and expands as the normalized radius increases to

*r/a*= 0.49 at which, 0.51 <

*f × a / c*< 0.67 with a PtBG ratio of 27%. It is instructive to note that if there are no imperfections in the slab structure, even and odd modes are decoupled from each other and can be separately excited and detected; therefore, several large simultaneous (even or odd) PtBGs and PnBGs can be obtained in this type of PxC for several geometrical parameters.

*r/a*= 0.44 at

*f × a / c*= 0.52 and expands to 0.57 <

*f × a / c*< 0.66 at

*r/a*= 0.49. Interestingly, this common PtBG for even and odd modes overlaps with the PnBG of the PxC at the same range of geometrical parameters. This makes a structure with simultaneous band gaps for all guided optical modes and all elastic waves possible. As an example, for

*d/a*= 0.5 and

*r/a*> 0.45, a PnBG, and PtBGs for both even and odd modes exist. For a PtBG ratio of more than 8% for both even and odd PtBGs, an

*r/a*of 0.47 or larger is required. For

*r/a*= 0.47, to have the center of the PtBG at λ = 1.55µm (i.e., the most desired optical communication wavelength),

*a*and

*r*are calculated to be 890 nm and 418.3 nm, respectively. The spacing between the perimeters of the holes, which is a major parameter dictating the fabrication limitations, is 53.4 nm. This feature size is readily achievable using the advanced fabrication techniques. These geometrical parameters correspond to a PnBG in the frequency range of 2700 m/s <

*f × a*< 3300 m/s or 3 GHz <

*f*< 3.7 GHz (a PnBG ratio of 21%), and PtBG ratios of 19% and 13% for the individual even and odd PtBGs, respectively.

*r/a*= 0.45 and variable

*d/a*are also shown in Fig. 2(d) confirming the existence of the simultaneous PtBGs and PnBGs in the square-lattice PxC slabs.

## 5. Phononic and photonic band gap maps for the triangular-lattice PxC slab

**77**(13), 1937–1939 (2000). [CrossRef]

**425**(6961), 944–947 (2003). [CrossRef] [PubMed]

**60**(8), 5751–5758 (1999). [CrossRef]

*r/a*< 0.49 with a step size of 0.02 and for each normalized radius we calculated the PnBG in the normalized thickness range of 0.1 <

*d/a*< 2, with a 0.1 step size. However, no sizable PnBG was obtained for this structure despite our extensive simulations. The PtBG maps of the triangular-lattice PxC slab have already been extensively studied before [23

23. L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. **38**(7), 891–898 (2002). [CrossRef]

## 6. Phononic and photonic band gap maps for the hexagonal-lattice PxC slab

14. S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. **43**(16), 898–899 (2007). [CrossRef]

*a*is the distance between the centers of the two nearest holes,

*d*is the thickness of the slab, and

*r*is the radius of the holes. The PnBG map for varying radius of the holes with a constant thickness of

*d/a*= 1 is shown in Fig. 3(a). The PnBG map is also derived for a varying slab thickness and a constant normalized radius of

*r/a*= 0.45 in Fig. 3(b). These values for the normalized radius and thickness are chosen as they can attain large PnBGs. The PnBG for this PxC slab structure of

*d/a*= 1 opens up at

*r/a*= 0.36 and expands as the normalized radius increases. As shown in Fig. 3(b), four different regions of PnBGs exist in the PnBG map. The range of geometrical parameters of the hexagonal-lattice PxC required for achieving PnBGs corresponds to values that are more practical from the structure stability and fabrication points of view compared to the square-lattice PxCs.

*r/a*< 0.42. However, the PtBG ratio of this overlapping PtBG region is limited to about 5%, which may not be sufficient for wide-band applications; rather, the PtBG of the odd modes can be made large enough by increasing the normalized radius and can be used for many of the envisioned applications.

*f × a/c*< 0.254) can be obtained for

*r/a*= 0.42 and

*d/a*= 1, at which the PnBG is obtained in frequency range of 1780 m/s <

*f × a*< 2249 m/s (~23%), which is appropriate for wide bandwidth applications of PxC structures. For

*λ*= 1.55 µm, the required value of

*a*would be 371.2 nm, which corresponds to a center phonon frequency of 5.4 GHz. Other parameters of this structure are

*r*= 155.9 nm,

*d*= 371.2 nm, and spacing between hole perimeters of 59.4 nm, which falls into practical fabrication conditions. Such geometrical parameters impose similar fabrication limitations compared to the square-lattice PxCs; however, due to a smaller volume ration of void compared to the square lattice, the hexagonal lattice can have a better mechanical stability.

*r/a*= 0.45. There are four regions (two odd and two even) of PtBG in Fig. 3(d). The band numbers between which the PtBGs are formed are also indicated in this figure. As can be seen by comparing Fig. 3(b) and Fig. 3(d), simultaneous PnBGs and either even or odd PtBGs exist for several values of

*d/a*; Therefore, based on the intended applications, any of such simultaneous band gaps can be utilized. As can be seen in Fig. 3(d), there are two common even and odd PtBG regions. Both of these regions have PtBG ratios of less than 5%, which may be too small for some of the envisioned applications.

## 7. Comparison of the structures

## 8. Concluding remarks

## Acknowledgements

## References and links

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

2. | M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. |

3. | Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature |

4. | M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. |

5. | M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. |

6. | T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. |

7. | M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature |

8. | A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. |

9. | P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. |

10. | M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B |

11. | M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. |

12. | S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. |

13. | A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

14. | S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. |

15. | S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. |

16. | S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs,” in Proceedings of |

17. | R. H. Olsson III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. |

18. | S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . |

19. | K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. |

20. | M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B |

21. | S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B |

22. | W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. |

23. | L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. |

**OCIS Codes**

(160.5293) Materials : Photonic bandgap materials

(050.5298) Diffraction and gratings : Photonic crystals

(120.4880) Instrumentation, measurement, and metrology : Optomechanics

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: February 9, 2010

Revised Manuscript: April 5, 2010

Manuscript Accepted: April 7, 2010

Published: April 16, 2010

**Citation**

Saeed Mohammadi, Ali A. Eftekhar, Abdelkrim Khelif, and Ali Adibi, "Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs," Opt. Express **18**, 9164-9172 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9164

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### References

- E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]
- M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000). [CrossRef]
- Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]
- M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. 19(12), 1970–1975 (2001). [CrossRef]
- M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992). [CrossRef]
- T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005). [CrossRef] [PubMed]
- M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]
- A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902–033905 (2008). [CrossRef] [PubMed]
- P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006). [CrossRef]
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