Abstract

A photonic and phononic crystal (phoxonic crystal PxC) is a periodically patterned material that can at the same time localize optical and mechanical modes. Here we theoretically model one-dimensional PxC in diamond and find high quality mechanical resonances with very high frequencies > 10 GHz and optical properties comparable to those of PxC in other materials. The simultaneous confinement of photons and phonons leads to an optomechanical interaction that we calculate in a perturbation approach. The optomechanical coupling strengths reach values in the MHz range. We identify design rules to simultaneously achieve high optical and mechanical quality factors along with strong optomechanical coupling.

© 2014 Optical Society of America

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2014

M. Davanço, S. Ates, Y. Liu, K. Srinivasan, “Si3N4 optomechanical crystals in the resolved-sideband regime,” Appl. Phys. Lett. 104, 041101 (2014).
[CrossRef]

M. Leifgen, T. Schröder, F. Gädeke, R. Riemann, V. Métillon, E. Neu, C. Hepp, C. Arend, C. Becher, K. Lauritsen, O. Benson, “Evaluation of nitrogen- and silicon-vacancy defect centres as single photon sources in quantum key distribution,” New J. Phys. 16, 023021 (2014).
[CrossRef]

T. Müller, C. Hepp, B. Pingault, E. Neu, S. Gsell, M. Schreck, H. Sternschulte, D. Steinmüller-Nethl, C. Becher, M. Atatüre, “Optical signatures of silicon-vacancy spins in diamond,” Nature Commun. 5, 3328 (2014).
[CrossRef]

2013

M. Lesik, P. Spinicelli, S. Pezzagna, P. Happel, V. Jacques, O. Salord, B. Rasser, A. Delobbe, P. Sudraud, A. Tallaire, J. Meijer, J.-F. Roch, “Maskless and targeted creation of arrays of colour centres in diamond using focused ion beam technology,” Phys. Stat. Sol. A 210, 2055–2059 (2013).
[CrossRef]

M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, L. C. Hollenberg, “The nitrogen-vacancy colour centre in diamond,” Phys. Rep. 528, 1–45 (2013).
[CrossRef]

K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, P. Rabl, “Phonon cooling and lasing with nitrogen-vacancy centers in diamond,” Phys. Rev. B 88, 064105 (2013).
[CrossRef]

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
[CrossRef] [PubMed]

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, M. Loncr, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[CrossRef] [PubMed]

Y. Liu, M. Davanço, V. Aksyuk, K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[CrossRef] [PubMed]

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, W. H. Pernice, “Diamond-integrated optomechanical circuits,” Nat. Commun. 4, 1690 (2013).
[CrossRef] [PubMed]

M. J. Burek, D. Ramos, P. Patel, I. W. Frank, M. Lončar, “Nanomechanical resonant structures in single-crystal diamond,” Appl. Phys. Lett. 103, 131904 (2013).
[CrossRef]

2012

J. Riedrich-Möller, L. Kipfstuhl, C. Hepp, E. Neu, C. Pauly, F. Mücklich, A. Baur, M. Wandt, S. Wolff, M. Fischer, S. Gsell, M. Schreck, C. Becher, “One- and two-dimensional photonic crystal micro-cavities in single crystal diamond,” Nature Nanotech. 7, 69–74 (2012).
[CrossRef]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[CrossRef] [PubMed]

P. Ovartchaiyapong, L. M. A. Pascal, B. A. Myers, P. Lauria, A. C. B. Jayich, “High quality factor single-crystal diamond mechanical resonators,” Appl. Phys. Lett. 101, 163505 (2012).
[CrossRef]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef] [PubMed]

E. Gavartin, P. Verlot, T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nature Nanotech. 7, 509–515 (2012).
[CrossRef]

C. Xiong, X. Sun, K. Y. Fong, H. X. Tang, “Integrated high frequency aluminum nitride optomechanical resonators,” Appl. Phys. Lett. 100, 171111 (2012).
[CrossRef]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[CrossRef]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Leveque, B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101, 061109 (2012).
[CrossRef]

M. Nomura, “GaAs-based air-slot photonic crystal nanocavity for optomechanical oscillators,” Opt. Express 20, 5204–5212 (2012).
[CrossRef] [PubMed]

E. Neu, M. Agio, C. Becher, “Photophysics of single silicon vacancy centers in diamond: implications for single photon emission,” Opt. Express 20, 19956–19971 (2012).
[CrossRef] [PubMed]

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20, 24394–24410 (2012).
[CrossRef] [PubMed]

2011

T. Antoni, A. G. Kuhn, T. Briant, P.-F. Cohadon, A. Heidmann, R. Braive, A. Beveratos, I. Abram, L. L. Gratiet, I. Sagnes, I. Robert-Philip, “Deformable two-dimensional photonic crystal slab for cavity optomechanics,” Opt. Lett. 36, 3434–3436 (2011).
[CrossRef] [PubMed]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef] [PubMed]

I. Aharonovich, A. D. Greentree, S. Prawer, “Diamond photonics,” Nature Photon. 5, 397–405 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B 84, 205211 (2011).
[CrossRef]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[CrossRef] [PubMed]

M. K. Zalalutdinov, M. P. Ray, D. M. Photiadis, J. T. Robinson, J. W. Baldwin, J. E. Butler, T. I. Feygelson, B. B. Pate, B. H. Houston, “Ultrathin single crystal diamond nanomechanical dome resonators,” Nano Lett. 11, 4304–4308 (2011).
[CrossRef] [PubMed]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys. 13, 025012 (2011).
[CrossRef]

2010

S. Pezzagna, D. Wildanger, P. Mazarov, A. D. Wieck, Y. Sarov, I. Rangelow, B. Naydenov, F. Jelezko, S. W. Hell, J. Meijer, “Nanoscale engineering and optical addressing of single spins in diamond,” Small 6, 2117–2121 (2010).
[CrossRef] [PubMed]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. OBrien, “Quantum computers,” Nature 464, 45–53 (2010).
[CrossRef] [PubMed]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82, 174303 (2010).
[CrossRef]

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101 (2010).
[CrossRef]

Q. Quan, P. B. Deotare, M. Lončar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

J. Riedrich-Möller, E. Neu, C. Becher, “Design of microcavities in diamond-based photonic crystals by fourier- and real-space analysis of cavity fields,” Photon. Nanostruc.: Fundam. Appl. 8, 150–162 (2010).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in optomechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
[CrossRef] [PubMed]

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Nature

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Nature Commun.

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Nature Nanotech.

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Opt. Express

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Phys. Rev. E

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Science

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Figures (5)

Fig. 1
Fig. 1

(a) Design of the unit cell with hole radius r, structure height h, width w and lattice constant a. (b),(c) Profile of the Ex- and Ey-component of the electromagnetic field of the first order optical mode.

Fig. 2
Fig. 2

(a) Phononic band structure for a PxC cavity with a unit cell length of a = 223 nm. The width w = 1.6 a and height h = 1.7 a are chosen according to the optimized optical cavity (see Tab. 1). The hole radius is r0 = 0.42 a corresponding to the holes in the center of the structure. The modes are sorted according to symmetry conditions where +(−) y/z denotes even (odd) mirror symmetry with respect to the y/z-direction. (b) Mechanical modes associated to the band edges of the second and third phononic band at the Γ-point G2 and G3 and of the first and second phononic bands at the X-point X1 and X2. The mechanical displacement is depicted in a color scale where red represents maximal elongation and blue unperturbed regions. (c) Frequencies of the band edges at the Γ-point for different hole radii r. (d) Frequencies of the band edges at the X-point for different hole radii r.

Fig. 3
Fig. 3

Mechanical displacement field of the localized mechanical mode arising from the guided mode G2.

Fig. 4
Fig. 4

(a) PxC structure with mirror section where the hole radii are only decreasing to the hole K = 10 and the outer holes are being kept constant. The hole radius in the mirror section is identical with the radius of the K-th hole. (b) Optical quality factor Qopt as a function of the number of holes K that have a non-constant radius. (c) Mechanical quality factor Qmech as a function of the number of holes K that have a non-constant radius. Note the logarithmic scale of the graph. The inset shows the frequency of the localized mechanical mode and the band gap of the mirror section for different values of K.

Fig. 5
Fig. 5

(a) Profile of the Ey-component of the electromagnetic field of the first order optical cavity mode of structure 2. (b),(c) Mechanical displacement field of the fundamental mechanical cavity mode of structure 2.

Tables (1)

Tables Icon

Table 1 Parameter values for the optimized photonic crystal cavity

Equations (8)

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× × E = ( ω opt c ) 2 ε E
( C _ : s u ) = 4 π 2 ρ f mech 2 u
m eff = ρ ( | u | max ( | u | ) ) 2 d V
d ω opt d α = ω opt ( 0 ) 2 E ( 0 ) | d ε d α | E ( 0 ) E ( 0 ) | ε | E ( 0 )
E ( 0 ) | d ε d α | E ( 0 ) = ( u n ^ ) ( Δ ε | E | | | 2 Δ ε 1 | D | 2 ) d S
E ( 0 ) | d ε d α | E ( 0 ) = ε 0 n 4 [ p 44 i j E i E j S i j + 1 2 i j k | E i | 2 ( p 11 S i i + p 12 ( S j j + S k k ) ) ] d V
g 0 = x Z P F d ω opt d α | α = α 0
x Z P F = h ¯ 2 m eff ω mech

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