Two-Dimensional Phononic-Photonic Band Gap Optomechanical Crystal Cavity

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Two-Dimensional Phononic-Photonic Band Gap Optomechanical Crystal Cavity

Amir H. Safavi-Naeini, Jeff T. Hill, Seán Meenehan, Jasper Chan, Simon Gröblacher, and Oskar Painter

Phys. Rev. Lett. 112, 153603 – Published 14 April 2014

See Viewpoint: “Snowflake Crystal” Traps Light and Sound

Abstract

We present the fabrication and characterization of an artificial crystal structure formed from a thin film of silicon that has a full phononic band gap for microwave $X$ -band phonons and a two-dimensional pseudo-band gap for near-infrared photons. An engineered defect in the crystal structure is used to localize optical and mechanical resonances in the band gap of the planar crystal. Two-tone optical spectroscopy is used to characterize the cavity system, showing a large coupling ( $g_{0} / 2 π \approx 220 kHz$ ) between the fundamental optical cavity resonance at $ω_{o} / 2 π = 195 THz$ and colocalized mechanical resonances at frequency $ω_{m} / 2 π \approx 9.3 GHz$ .

Received 7 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.153603

Viewpoint

“Snowflake Crystal” Traps Light and Sound

Published 14 April 2014

Experimentalists trap optical and acoustic oscillations together in a two dimensional structure that will make it easier to study their coupled behavior.

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Authors & Affiliations

Amir H. Safavi-Naeini^1,2,*, Jeff T. Hill^1,2,†, Seán Meenehan^1,2, Jasper Chan^1,2, Simon Gröblacher^1,2, and Oskar Painter^1,2,‡

¹Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
²Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

^*Present address: Department of Physics, ETH Zürich, CH-8093 Zürich, Switzerland.
^†Present address: Edward L. Ginzton Laboratory, Stanford University, Stanford CA 94305, USA.
^‡opainter@caltech.edu

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Vol. 112, Iss. 15 — 18 April 2014

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Images

Figure 1
(a) Snowflake crystal unit cell. (b) Photonic and (c) phononic band structure of a silicon planar snowflake crystal with $(d, r, w, a) = (220, 200, 75, 500) nm$ . Photonic band structures are computed with the MPB [24] mode solver, and phononic band structures are computed with the comsol [25] finite-element method (FEM) solver. In the photonic band structure, only the fundamental even-parity optical modes (solid blue curves) of the silicon slab are shown and the gray shaded area indicates the region above the light line of the vacuum cladding. The dashed gray curves are leaky resonances above the light line. (d) Unit cell schematic of a linear waveguide formed in the snowflake crystal, in which a row of snowflake holes are removed and the surrounding holes are moved inwards by $W$ , yielding a waveguide width $Δ_{y} = \sqrt{3} a - 2 W$ . Guided modes of the waveguide propagate along $x$ . (e) Photonic and (f) phononic band structure of the linear waveguide with $(d, r, w, a, W) = (220, 210, 75, 500, 200) nm$ . The solid blue curves are waveguide bands of interest; dashed lines are the other guided modes; shaded light blue regions are band gaps of interest; green tick mark indicates the cavity mode frequencies; gray regions denote the continua of propagating modes outside of the snowflake crystal band gap. (g) FEM simulated mode profile of the fundamental optical resonance at $ω_{o} / 2 π = 195 THz$ ( $λ_{o} = 1530 nm$ ). The $E_{y}$ component of the electric field is plotted here, with red (blue) corresponding to positive (negative) field amplitude. (h) FEM simulated mechanical resonance displacement profile for mode with $ω_{m} / 2 π = 9.35 GHz$ and $g_{0} / 2 π = 250 kHz$ . Here, the magnitude of the displacement is represented by color (large displacement in red, zero displacement in blue).
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Figure 2
(a) SEM image of the fabricated snowflake crystal structure. (b) Schematic showing the fiber-taper-coupling method used to optically excite and probe the snowflake cavity. (c) Experimental setup for optical and mechanical spectroscopy of the snowflake cavity; $PD \equiv photodetector$ , $VOA \equiv variable$ optical attenuator, $FPC \equiv fiber$ polarization controller, $λ meter \equiv optical$ wave meter, $EOM \equiv electro-optic$ modulator, and $VNA \equiv vector$ network analyzer.
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Figure 3
(a) Low ( $n_{c} = 550$ ) and (b) high ( $n_{c} = 2.2 \times 10^{4}$ ) power EIT spectra of the snowflake cavity with nominal parameters described in the text. The insets show a zoom in of the interference resulting from the optomechanical interaction between the optics and mechanics. The fits shown in the insets are used to extract the optomechanical coupling ( $γ_{OM}$ ) and intrinsic mechanical loss rate ( $γ_{i}$ ) for every optical power. (c) Plot of the resulting fit mechanical damping rates versus $n_{c}$ . $γ_{i}$ data are shown as squares, and $γ_{OM}$ are shown as circles, with the low (high) frequency mode shown in green (purple). Dashed lines correspond to linear fits to the $γ_{OM}$ data.
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Figure 4
(a) Plot of the linear acoustic energy density profile $u_{a} (x)$ , for the localized mechanical resonances with strong optomechanical coupling to the fundamental optical resonance. The top black curve corresponds to the unperturbed structure. Each pair of red and blue curves corresponds to the mechanical resonance with the largest and second largest magnitude of optomechanical coupling, respectively, for a different disordered structure; $u_{a} (x)$ is computed by integrating the acoustic energy density across the transverse $y$ and $z$ dimensions. (b) Plot of the corresponding mechanical frequency difference and (c) optomechanical rate $g_{0}$ for the two most strongly coupled mechanical resonances. Here, we show results for a representative eight of the simulated disordered structures.
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