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2D Phononic Crystal Sensor with Normal Incidence of Sound
Available online at www.sciencedirect.com
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 25 (2011) 787 – 790
Procedia Engineering www.elsevier.com/locate/procedia
Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece
2D Phononic Crystal Sensor with Normal Incidence of Sound R. Lucklumaa*, M. Zubtsova, M. Kea,b, B. Henningc, U. Hempeld a
Institute of Micro and Sensor Systems (IMOS), Otto-von-Guericke-University Magdeburg, Germany b Department of Physics, Wuhan University, Wuhan, PR China c Faculty of Electrical Engineering, Computer Science and Mathematics, University of Paderborn, Germany d Institute for Automation and Communication (ifak), Magdeburg, Germany
Abstract This contribution shows the sensor application of a resonance-induced extraordinary transmission through a regular phononic crystal consisting of a metal plate with a periodic arrangement of holes in a square lattice at normal incidence of sound. The characteristic transmission peak has been found to strongly depend on liquid sound velocity. The respective peak maximum frequency can therefore serve as measure for liquid analysis. Experimental verification has been performed with mixtures of water and propanol as model system. Numerical calculations based on COMSOL and EFIT reveal more insides to the wave propagation characteristics. Experimental investigations with Schlieren method and laser interferometry support the theoretical findings.
© 2011 Published by Elsevier Ltd. Keywords: Phononic crystal sensor; Liquid sensor
1. Introduction Phononic Crystals (PnCs) have recently been introduced as a new sensor platform exploiting resonance modal effects at ultrasonic wave propagation in composite materials [1]. A traditional PnC consists of scattering centres, diameter d, with acoustic properties different to a t homogeneous matrix surrounding the scatters. The scatters are a d periodically arranged in two dimensions. The lattice constant, a, is the Fig. 1: Scheme of a regular phononic crystal. measure of the spatial modulation of the material properties.
* Corresponding author. Tel.: +49 391 671 8310; fax: +49 391 671 2609. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.12.193
788 2
R. Lucklum al. / Procedia Engineering 25 (2011) 787 – 790 Author name /etProcedia Engineering 00 (2011) 000–000
Interference of waves causes the most important feature of PnCs, frequency bands (stop bands) within which sound cannot propagate through the structure. In a sensor configuration the most appropriate measure is the frequency of maximum transmission of transmission peaks appearing within the band gap. Such features can be attributed to resonance phenomena, if appropriate designed some of them to a liquid confined in holes of the solid matrix. Since the lattice constant determines the acoustic wavelength in the stop band, PnC sensors can be designed for a wide range of the characteristic dimension of geometry by adjusting the probing frequency. For example, dimensions similar to those used in microfluidic devices require frequencies in the MHz-range. Here we analyze a specific version of the application of a PnC where the direction of incidence of the ultrasonic wave is perpendicular to the phononic crystal plate. The most apparent feature, a transmission peak having a theoretical transmission coefficient of 1 at a specific frequency (without losses), is the socalled extraordinary transmission phenomenon [2], Fig. 2. 2. Experimental We employ a thin steel plate whose thickness (t = 0.5 mm) is smaller than the minimum half wavelength of the scanned frequency range (thin plate limit). Holes having a diameter of 0.5 mm are arranged in square array having a lattice constant of 1.5 mm, Fig. 3. The PnC sample has been placed in a tank, together with immersion ultrasonic transducers in some distance to the PnC plate to avoid near field effects. The components are always carefully aligned with adjustment stages. The transmission curves have been obtained using a network analyzer together with a S-parameter test set. Transmission S21 has been measured with and without sample in place respectively. The transmission amplitude has been obtained by normalizing with the amplitude of the equivalent setup without the sample. The principle of Schlieren visualization of ultrasound wave fields is shown in Fig. 4. A digital micromirror device (DMD) is used as a variable filter for the signals in the Fourier plane. Sequential application of different filters together with methods of information fusion improves the quality of the sound field visualization in comparison with the classical Schlieren method [3]. Note, that the laser beam penetrates the whole width of the sound field above and below the PnC-plate; the image therefore delivers integral information. A Scanning Laser Doppler Vibrometer provides information about out-of-plane vibrations of a surface. Motion of the surface causes the Doppler shift appearing as modulation frequency in the received signal. steel water
Transmission
1.0
steel 1-propanol
0.8 0.6 0.4 0.2 0.0 0.0
0.5
1.0
f / MHz
Fig. 2: Transmission through regular phononic crystal at normal incidence of sound.
1.5
Fig. 3: Photo of the phononic crystal used throughout the experiments.
789 3
R. Lucklum et al./ /Procedia ProcediaEngineering Engineering00 25(20111) (2011) 787 – 790 Author name 000–000
Measurements are intended to experimentally verify plate modes; however, secured data are not available at the time of this proceedings paper. Measurements must be performed in a wide frequency range with frequency steps small enough to recover specific features of the plate mode spectrum (see Figs. 2,6,7). Different liquid properties are obtained by gradually changing the liquid in the holes and the surrounding from pure DI-water to pure 1-propanol via a series of liquid mixture with different molar ratios of 1-propanol. Density and sound velocity (see inset Fig. 5) have been taken from [4]. 3. Modeling The three-dimensional finite-difference time-domain (FDTD) method has been applied to calculate the transmission spectrum through the plate. A computational cell with dimension 3030300 grid points has been used. The faces of the computational cell normal to x and y axes are chosen to have Bloch boundary conditions, while the faces normal to z axis have Mur’s absorbing boundary conditions. The transmission coefficient is calculated by dividing the transmitted energy flux by the energy flux of the incident wave. EFIT relies on the Newton-Cauchy’s equation of motion and the equation of deformation rate. The underlying equations in integral form are discretized in the same dual grid complex in space and time which yields the so-called discrete grid equations. The discrete matrix equations represent a consistent one-to-one translation of the underlying field equations. COMSOL MultiphysicsTM simulations have been concentrating on coupled elements: liquid confined in the holes, regular set of portions of the plate surrounded by the holes and regular set of holes with adjacent portions of the plate. Each of these elements has its own set of modes and each of these modes can support either transmission or reflection.
Fig. 4: Scheme of the experimental setup for Schlieren visualization.
4. Results Simulation Experiment
900 850 800
1.6 Velocity (km/s)
950
Frequency(KHz)
Figure 5 compares the experimentally determined peak frequency with data extracted from FDTD simulation as function of molar ratio of 1-propanol in a water-propanol mixture. The inset shows the dependence of speed of sound. As one can see, speed of sound governs the frequency of extraordinary transmission which, in turn, can be exploited to determine the composition of the mixture. The sensitivity f/x2 in the concentration range between x2 = 0–0.035 is about 3 MHz The systematic deviation of the experimental data from simulation must be attributed to a small deviation in the lattice constant of the real sample rather than hole diameter.
1.5 1.4 1.3 1.2
0.0 0.2 0.4 0.6 0.8 1.0 Mol concentration of 1-Propanol
750 700 0.0
0.2
0.4
0.6
0.8
1.0
Mol concentration of 1-Propanol
Fig. 5: Peak frequency of extraordinary transmission.
790 4
R. Lucklum al. / Procedia Engineering 25 (2011) 787 – 790 Author name /etProcedia Engineering 00 (2011) 000–000
Fig. 6 shows an example result of EFIT and COMSOL simulations at the frequency of maximum transmission which agree very well. They display distinct pressure resonance pattern of the piston like movement inside the liquid aperture, accompanied by mechanical plate vibration. They do not support that elastic waves in the plate are involved in extraordinary transmission. Fig. 7 compares COMSOL simulations and their experimental verification with the Schlieren method at the frequency of extraordinary transmission as in Fig. 6 and above Wood’s anomaly (the minimum in the transmission curve, see Fig. 2) at 1.1 MHz. The transmitted signal is much weaker; however, the lowfrequency modulation of the reflected (simulation) and transmitted signal (simulation and experiment) is obvious. All kinds of interactions between propagating wave and periodic structure must be considered to understand this phenomenon, specifically diffraction of waves emanating from the wall of the liquid filled hole, mode conversion as well as coupling with resonant propagation through the plate.
a
b
c
d
Fig. 6: Simulation results of stress components T33 (a), T11 (b), T13 (c) (EFIT) and displacement (d) (COMSOL)
a
b
Fig. 7: Comparison between COMSOL and experiment Schlieren at the frequency of maximum transmission (a) and above (b).
Acknowledgements The work has been supported by a grant of the German Research Foundation (Lu 606/12-1) and the European Commission Seventh Framework Program (233883, TAILPHOX) which is gratefully acknowledged. References [1] R. Lucklum J. Li, "Phononic crystals for liquid sensor applications", Meas. Sci. Technol. 2009; 20:124014. [2] M.H. Lu, X.K. Liu, L. Feng, J. Li, C.P. Huang, Y.F. Chen, Y.Y. Zhu, S. N. Zhu, N.B. Ming, "Extraordinary Acoustic Transmission through a 1D Grating with Very Narrow Apertures" Phys. Rev. Lett. 2007; 99:174301. [3] B. Henning, J. Rautenberg, C. Unverzagt, A. Schröder, S. Olfert, “Computer assisted design of transducers for ultrasonic sensor systems”, Meas. Sci. Technol. 2009; 20:124012. [4] R. Kuhnkies, W. Schaaffs, Acustica 1963, 13:407.
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 25 (2011) 787 – 790
Procedia Engineering www.elsevier.com/locate/procedia
Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece
2D Phononic Crystal Sensor with Normal Incidence of Sound R. Lucklumaa*, M. Zubtsova, M. Kea,b, B. Henningc, U. Hempeld a
Institute of Micro and Sensor Systems (IMOS), Otto-von-Guericke-University Magdeburg, Germany b Department of Physics, Wuhan University, Wuhan, PR China c Faculty of Electrical Engineering, Computer Science and Mathematics, University of Paderborn, Germany d Institute for Automation and Communication (ifak), Magdeburg, Germany
Abstract This contribution shows the sensor application of a resonance-induced extraordinary transmission through a regular phononic crystal consisting of a metal plate with a periodic arrangement of holes in a square lattice at normal incidence of sound. The characteristic transmission peak has been found to strongly depend on liquid sound velocity. The respective peak maximum frequency can therefore serve as measure for liquid analysis. Experimental verification has been performed with mixtures of water and propanol as model system. Numerical calculations based on COMSOL and EFIT reveal more insides to the wave propagation characteristics. Experimental investigations with Schlieren method and laser interferometry support the theoretical findings.
© 2011 Published by Elsevier Ltd. Keywords: Phononic crystal sensor; Liquid sensor
1. Introduction Phononic Crystals (PnCs) have recently been introduced as a new sensor platform exploiting resonance modal effects at ultrasonic wave propagation in composite materials [1]. A traditional PnC consists of scattering centres, diameter d, with acoustic properties different to a t homogeneous matrix surrounding the scatters. The scatters are a d periodically arranged in two dimensions. The lattice constant, a, is the Fig. 1: Scheme of a regular phononic crystal. measure of the spatial modulation of the material properties.
* Corresponding author. Tel.: +49 391 671 8310; fax: +49 391 671 2609. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.12.193
788 2
R. Lucklum al. / Procedia Engineering 25 (2011) 787 – 790 Author name /etProcedia Engineering 00 (2011) 000–000
Interference of waves causes the most important feature of PnCs, frequency bands (stop bands) within which sound cannot propagate through the structure. In a sensor configuration the most appropriate measure is the frequency of maximum transmission of transmission peaks appearing within the band gap. Such features can be attributed to resonance phenomena, if appropriate designed some of them to a liquid confined in holes of the solid matrix. Since the lattice constant determines the acoustic wavelength in the stop band, PnC sensors can be designed for a wide range of the characteristic dimension of geometry by adjusting the probing frequency. For example, dimensions similar to those used in microfluidic devices require frequencies in the MHz-range. Here we analyze a specific version of the application of a PnC where the direction of incidence of the ultrasonic wave is perpendicular to the phononic crystal plate. The most apparent feature, a transmission peak having a theoretical transmission coefficient of 1 at a specific frequency (without losses), is the socalled extraordinary transmission phenomenon [2], Fig. 2. 2. Experimental We employ a thin steel plate whose thickness (t = 0.5 mm) is smaller than the minimum half wavelength of the scanned frequency range (thin plate limit). Holes having a diameter of 0.5 mm are arranged in square array having a lattice constant of 1.5 mm, Fig. 3. The PnC sample has been placed in a tank, together with immersion ultrasonic transducers in some distance to the PnC plate to avoid near field effects. The components are always carefully aligned with adjustment stages. The transmission curves have been obtained using a network analyzer together with a S-parameter test set. Transmission S21 has been measured with and without sample in place respectively. The transmission amplitude has been obtained by normalizing with the amplitude of the equivalent setup without the sample. The principle of Schlieren visualization of ultrasound wave fields is shown in Fig. 4. A digital micromirror device (DMD) is used as a variable filter for the signals in the Fourier plane. Sequential application of different filters together with methods of information fusion improves the quality of the sound field visualization in comparison with the classical Schlieren method [3]. Note, that the laser beam penetrates the whole width of the sound field above and below the PnC-plate; the image therefore delivers integral information. A Scanning Laser Doppler Vibrometer provides information about out-of-plane vibrations of a surface. Motion of the surface causes the Doppler shift appearing as modulation frequency in the received signal. steel water
Transmission
1.0
steel 1-propanol
0.8 0.6 0.4 0.2 0.0 0.0
0.5
1.0
f / MHz
Fig. 2: Transmission through regular phononic crystal at normal incidence of sound.
1.5
Fig. 3: Photo of the phononic crystal used throughout the experiments.
789 3
R. Lucklum et al./ /Procedia ProcediaEngineering Engineering00 25(20111) (2011) 787 – 790 Author name 000–000
Measurements are intended to experimentally verify plate modes; however, secured data are not available at the time of this proceedings paper. Measurements must be performed in a wide frequency range with frequency steps small enough to recover specific features of the plate mode spectrum (see Figs. 2,6,7). Different liquid properties are obtained by gradually changing the liquid in the holes and the surrounding from pure DI-water to pure 1-propanol via a series of liquid mixture with different molar ratios of 1-propanol. Density and sound velocity (see inset Fig. 5) have been taken from [4]. 3. Modeling The three-dimensional finite-difference time-domain (FDTD) method has been applied to calculate the transmission spectrum through the plate. A computational cell with dimension 3030300 grid points has been used. The faces of the computational cell normal to x and y axes are chosen to have Bloch boundary conditions, while the faces normal to z axis have Mur’s absorbing boundary conditions. The transmission coefficient is calculated by dividing the transmitted energy flux by the energy flux of the incident wave. EFIT relies on the Newton-Cauchy’s equation of motion and the equation of deformation rate. The underlying equations in integral form are discretized in the same dual grid complex in space and time which yields the so-called discrete grid equations. The discrete matrix equations represent a consistent one-to-one translation of the underlying field equations. COMSOL MultiphysicsTM simulations have been concentrating on coupled elements: liquid confined in the holes, regular set of portions of the plate surrounded by the holes and regular set of holes with adjacent portions of the plate. Each of these elements has its own set of modes and each of these modes can support either transmission or reflection.
Fig. 4: Scheme of the experimental setup for Schlieren visualization.
4. Results Simulation Experiment
900 850 800
1.6 Velocity (km/s)
950
Frequency(KHz)
Figure 5 compares the experimentally determined peak frequency with data extracted from FDTD simulation as function of molar ratio of 1-propanol in a water-propanol mixture. The inset shows the dependence of speed of sound. As one can see, speed of sound governs the frequency of extraordinary transmission which, in turn, can be exploited to determine the composition of the mixture. The sensitivity f/x2 in the concentration range between x2 = 0–0.035 is about 3 MHz The systematic deviation of the experimental data from simulation must be attributed to a small deviation in the lattice constant of the real sample rather than hole diameter.
1.5 1.4 1.3 1.2
0.0 0.2 0.4 0.6 0.8 1.0 Mol concentration of 1-Propanol
750 700 0.0
0.2
0.4
0.6
0.8
1.0
Mol concentration of 1-Propanol
Fig. 5: Peak frequency of extraordinary transmission.
790 4
R. Lucklum al. / Procedia Engineering 25 (2011) 787 – 790 Author name /etProcedia Engineering 00 (2011) 000–000
Fig. 6 shows an example result of EFIT and COMSOL simulations at the frequency of maximum transmission which agree very well. They display distinct pressure resonance pattern of the piston like movement inside the liquid aperture, accompanied by mechanical plate vibration. They do not support that elastic waves in the plate are involved in extraordinary transmission. Fig. 7 compares COMSOL simulations and their experimental verification with the Schlieren method at the frequency of extraordinary transmission as in Fig. 6 and above Wood’s anomaly (the minimum in the transmission curve, see Fig. 2) at 1.1 MHz. The transmitted signal is much weaker; however, the lowfrequency modulation of the reflected (simulation) and transmitted signal (simulation and experiment) is obvious. All kinds of interactions between propagating wave and periodic structure must be considered to understand this phenomenon, specifically diffraction of waves emanating from the wall of the liquid filled hole, mode conversion as well as coupling with resonant propagation through the plate.
a
b
c
d
Fig. 6: Simulation results of stress components T33 (a), T11 (b), T13 (c) (EFIT) and displacement (d) (COMSOL)
a
b
Fig. 7: Comparison between COMSOL and experiment Schlieren at the frequency of maximum transmission (a) and above (b).
Acknowledgements The work has been supported by a grant of the German Research Foundation (Lu 606/12-1) and the European Commission Seventh Framework Program (233883, TAILPHOX) which is gratefully acknowledged. References [1] R. Lucklum J. Li, "Phononic crystals for liquid sensor applications", Meas. Sci. Technol. 2009; 20:124014. [2] M.H. Lu, X.K. Liu, L. Feng, J. Li, C.P. Huang, Y.F. Chen, Y.Y. Zhu, S. N. Zhu, N.B. Ming, "Extraordinary Acoustic Transmission through a 1D Grating with Very Narrow Apertures" Phys. Rev. Lett. 2007; 99:174301. [3] B. Henning, J. Rautenberg, C. Unverzagt, A. Schröder, S. Olfert, “Computer assisted design of transducers for ultrasonic sensor systems”, Meas. Sci. Technol. 2009; 20:124012. [4] R. Kuhnkies, W. Schaaffs, Acustica 1963, 13:407.