Designing phononic crystal based tunable four-channel acoustic demultiplexer
Introduction
During the past three decades, periodic structures of inhomogeneous materials known as phononic crystals (PnCs) have attracted ample attention. A PnC is a periodic array of scatterers (inclusions) in a homogeneous host material (matrix) that can control the propagation of a specific mechanical wave [[1], [2], [3]]. Depending on the constituting materials, the lattice constant, the shape, and the size of the inclusions, the dispersion curve of a PnC may exhibit one or more acoustic band gaps, wherein the mechanical waves cannot propagate within the PnC structure [[4], [5], [6], [7], [8], [9]]. The Bragg reflections from the interfaces of the periodic structure explain the underlying mechanism. In other words, multiple scatterings of a mechanical wave at the interfaces between materials with different mechanical properties resulting in constructive reflections lead to phononic band gaps. Utilizing the potentials and properties of PnC based structures; researchers have designed different acoustic devices such as multi-band filters [10], waveguides [11,12], lenses [13,14], add-drop filter [15], demultiplexers [16,17], coupler [18], switch [19] and logic gate [20]. Furthermore, embedding one or more high quality factor (Q) acoustic cavities inside a PnC based device can add extra potentials to the structures, for various applications. To date, many acoustic devices based on high-Q cavities, such as acoustic filters [[21], [22], [23]], sources [24,25], and sensors [[26], [27], [28], [29]], have been proposed.
Jin et al. [30] have investigated the properties of a phononic crystal plate with hollow pillars and introduced the existence of whispering-gallery modes (WGMs). They have shown that by tuning the inner radius of the hollow pillars, these modes can merge inside both Bragg and low frequency band gaps, deserving phononic crystal, and acoustic metamaterial applications. These modes can be used as narrow passbands for which the quality factor can be greatly enhanced by the introduction of an additional cylinder between the hollow cylinder and the plate. They discussed some functionalities of these confined WGM in both Bragg and low frequency gaps for wavelength division in multiplexer devices using heteroradii pillars introduced into waveguide and cavity structures.
The eigenmodes selected by high-Q cavities can illustrate either narrow passing bands within the stop band of PnC structure or very narrow stopping bands in the passband of the waveguide. The signal energy can be constructively accumulated by exciting the resonant modes of the cavity. Therefore, a high-Q cavity may serve as an acoustic source. Moreover, a high-Q cavity made on a PnC platform can play a fundamental role in developing a micromechanical resonator [31].
Pennec et al. [16] have introduced the first 1 × 2 acoustic demultiplexer based on a 2-D PnC waveguide composed of a row of hollow cylinders of different inner radii. However, the operation of this cavity-less acoustic demultiplexer is limited to the two channels of fixed center frequencies set by the inner radii of the hollow cylinders along the waveguide. Moreover, the waveguide properties limit the bandwidths and hence quality factors of the operating channels. Later, to overcome these deficiencies we have taken advantage of the differences in the acoustic properties of methyl nonafluorobutyl ether (MNE) and ethyl fluorobutyl ether (ENE) and designed a two-channel switchable demultiplexer [17], based on a PnC characterized by a square lattice of cylindrical water inclusions in a mercury matrix. The two cylindrical resonant cavities of the same radii, filled with MNE and ENE and placed in correspondence of the throats of the output port have provided the demultiplexing functionality. Moreover, the different temperature dependencies of the sound velocities in MNE and ENE have enabled the demultiplexed channels to switch. Using the same T-shaped input PnC waveguide as in [17], in this work, we have designed a fork-shaped acoustic demultiplexer with four output ports (channels) coupled to the T-shaped waveguide arms, via four cylindrical resonant cavities. Unlike in [17], the cavities in the proposed structure are all filled with the same fluid (i.e., MNE) and have different radii. Hence, the center frequency of each demultiplexed channel is determined by its radius and the MNE acoustic properties. The aim of the earlier design was to switch the frequencies of the two output channels merely by tuning the cavities temperatures. Whereas, the main aim of the newly designed four-channel demultiplexer is to select four different frequencies from a broadband acoustic signal and demultiplex them throughout the output channels at a fixed temperature. The significance of this acoustic demultiplexer lies with its high-Q outputs and very low crosstalks. Furthermore, in a given structure, the demultiplexed frequencies are mainly affected by the acoustic properties of the cavity material, making the proposed structure useful as a temperature or pressure sensor.
Section snippets
The design procedure
Fig. 1 illustrates a general scheme of the proposed fork-shaped demultiplexer having four output channels (O1, O2, O3, and O4). There are four point-defect cavities (C1, C2, C3, and C4) of different radii (r1, r2, r3, and r4). Each cavity is placed at the throat of the corresponding output port. It selects and demultiplexes a narrow band signal from a given broadband acoustic signal, whose center frequency coincides with one of the cavity eigenmodes, and hence couples it to the corresponding
Characteristics of the proposed four-channel acoustic demultiplexer
Now, based on the resonant cavity characteristics described in Section 2, we propose a symmetric four-channel acoustics demultiplexer, as shown in Fig. 5(a). The proposed demultiplexer is a fork-shaped device with four output ports. There are four cylindrical cavities (O1–4) with different radii (rC1–4) filled with MNE, placed in correspondence of the throats of the output ports. Comparison of Fig. 5(a) with Fig. 3(a), reveals that in both cases each output port the corresponding cavity is
The temperature and pressure dependencies of the demultiplexed signals
Using data for the variations in the mass densities and the sound velocities of the demultiplexer constituents, given in [36] for MNE and in [40] for water and mercury, versus temperature at a given pressure and versus pressure for a given temperature, we have plotted the results. Fig. 6(a) shows the temperature dependence of the mass densities (solid symbols) of MNE (squares), water (circles), and mercury (diamonds), all for P = 0.1 MPa, while Fig. 6(b) shows the corresponding pressure
Conclusion
Exploiting the tunable characteristics of four cylindrical resonant cavities filled with the MNE, having different radii, we have designed and numerically investigated a four-channel demultiplexer for a particular range of acoustic frequency. The PnC platform can be characterized by a square lattice of cylindrical water inclusions of radii r in a mercury matrix. Each resonant cavity is placed in correspondence of the throat of one output port. Using the plane-wave expansion (PWE) method we have
Acknowledgments
The authors would like to acknowledge the partial financial support, received from Iran National Science Foundation (INSF).
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