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Band gaps and cavity modes in dual phononic and photonic strip waveguides
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Figures

Image of FIG. 1.

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FIG. 1.

(a) Schematic view of the periodic silicon strip waveguide. (b) Representation of the unit cell which contains one hole in the middle of the waveguide and two symmetric stubs on each side.

Image of FIG. 2.

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FIG. 2.

(a) Phononic dispersion diagram for the stubbed waveguide of figure 1 with parameters we/Λ=3.0, wi/Λ=0.5, h/Λ=0.44, and r/Λ=0.3. (b, c, d and e) Evolution of band gap edges as a function of each geometrical parameter, the others being kept constant: (b) we/Λ, (c) wi/Λ, (d) h/Λ and (e) r/Λ. The vertical blue dashed lines give the values of the parameters used in the calculation of the dispersion diagram presented in (a).

Image of FIG. 3.

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FIG. 3.

Photonic dispersion diagrams for the same parameters (h/Λ=0.44, wi/Λ=0.5 and we/Λ=3.0) as in figure 2(a), but for three different radii: (a) r/Λ=0.0, (b) r/Λ=0.3 and (c) r/Λ=0.45. In figure (b), modes are labeled as odd (o) or even (e) with respect to the symmetry planes Π and Π of the structure. The reduced frequency is given by Ω=ωΛ/2πc=Λ/λ, where c is the velocity of light in vacuum.

Image of FIG. 4.

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FIG. 4.

Map of the x component of the electric field for the lowest four modes in Fig. 3(b) at the reduced wavenumber kΛ/2π=0.414.

Image of FIG. 5.

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FIG. 5.

(a) Geometry of the cavity defined by the length Δ. (b) Phononic dispersion diagram along the ΓX direction of the strip waveguide, for a cavity of length Δ/Λ=0.4. (c) Modulus of the displacement field calculated at the points A, B, C, and D of the dispersion curves.

Image of FIG. 6.

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FIG. 6.

(a) Schematic view of the (x,z) section of the structure used for the 3D-FDTD calculation of transmission, with Δ/Λ=0.4. (b) Left: Transmission coefficients for the electric and magnetic fields displaying a resonant peak inside the gap. Right: Magnification of the resonant peak. The inset shows the evolution of the peak frequency as a function of Δ.

Image of FIG. 7.

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FIG. 7.

(a) Maps of the electric and magnetic fields in the strip waveguide structure containing a cavity with length Δ/Λ=0.4 at the monochromatic frequency 0.3172. (b) 3D map of the magnetic field.

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/content/aip/journal/adva/1/4/10.1063/1.3675799
2011-12-23
2014-04-17

Abstract

We discuss theoretically the simultaneous existence of phoxonic, i.e., dual phononic and photonic,band gaps in a periodic silicon strip waveguide. The unit-cell of this one-dimensional waveguide contains a hole in the middle and two symmetric stubs on the sides. Indeed, stubs and holes are respectively favorable for creating a phononic and a photonic band gap. Appropriate geometrical parameters allow us to obtain a complete phononic gap together with a photonic gap of a given polarization and symmetry. The insertion of a cavity inside the perfect structure provides simultaneous confinement of acoustic and optical waves suitable to enhance the phonon-photon interaction.

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Scitation: Band gaps and cavity modes in dual phononic and photonic strip waveguides
http://aip.metastore.ingenta.com/content/aip/journal/adva/1/4/10.1063/1.3675799
10.1063/1.3675799
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