Ultrasonics 57 (2015) 50–56
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
A plasmonic SAW transducer Ahmet Arca ⇑ Department of Electrical and Electronic Engineering, Faculty of Engineering, European University of Lefke, Gemikonagi, Mersin 10, Turkey
a r t i c l e
i n f o
Article history: Received 3 April 2014 Received in revised form 11 August 2014 Accepted 21 October 2014 Available online 13 November 2014 Keywords: Optical transducers SAW transducer GHz frequency SAW Plasmonic SAW transducer Optical detection of ultrahigh frequency SAW
a b s t r a c t In this work, an acoustic–optical transducer that is based on the utilization of plasmons is proposed to optically detect SAW of wavelength ( ko then diffraction based methods are viable such as knife-edge detection [2]. Another
⇑ Tel.: +90 3926602000. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ultras.2014.10.021 0041-624X/Ó 2014 Elsevier B.V. All rights reserved.
approach to the detection of SAWs involves using a transducer to maximise the change in the optical signal during the interaction of the acoustic signal with the transducer. Transducer based detection can be achieved through a grating structure whose period is equal to the SAW wavelength and whose finger height is carefully chosen to optimize the signal levels [6–8]. In the work of Stratoudaki et al. [6], the finger heights were chosen to be 1/8 of the optical wavelength, to obtain an in situ interferometer (CHOTs). The geometry of the devices looks like that in Fig. 1a. Transducer based techniques described in the literature rely on the diffraction of the optical waves due to the periodic disturbance caused by the SAW or the transducer. This requires that the disturbance wavelength i.e. SAW wavelength is in the vicinity of the optical wavelength used. As the SAW wavelength gets shorter than this value, the light no longer diffracts yielding no detection. This makes the utilization of ultrahigh frequency (GHz) SAWs very difficult. When ka < ko diffraction based techniques cannot be used, therefore interferometric methods and measurements of reflectivity due to acousto-optic effects can be used. The detection sub-optical-wavelength ultrasound, is mostly dominated by the interferometric techniques such as those demonstrated in [3] and scanning techniques such as [9]. These methods are difficult to use in the field and require sample removal and isolation. Transducer based detection techniques in the region where ka < ko , were investigated in [10]. As the wavelength of the SAW was decreased, approached and went below the optical wavelength, it was observed numerically that the reflected orders of the CHOT in [6] became evanescent and the energy trade was abolished. In this case, the transducers were optimized and
A. Arca / Ultrasonics 57 (2015) 50–56
another energy transfer mechanism was suggested, which relied on the modulation of the resistive heating taking place in a thin film placed underneath the grating [10]. Even though this device has the best possible signal for a grating of such structure, it still yielded low signal levels as compared with the original CHOTs. In this article, a new method for the optical detection of suboptical-wavelength SAWs is described. The operating principle depends on matching the total grating k-vector to that of the plasmon, whose coupling to the transducer is then modulated via the interaction with the SAW, thereby changing the overall reflectivity of the transducer. Three different designs are proposed that can utilize this operating principle. These are the Double Period Merged Gratings with Uniform Height (DPMG-UH), Double Period Superimposed Gratings (DPSG), and Double Period Merged Grating (DPMG). They are shown in Fig. 1b–d respectively. Samples are designed to be built on glass substrate (for modelling purposes), although substrate medium can be varied considering the SAW travel speed. They are Aluminium gratings, which can be fabricated using standard lithography/metallization techniques (see section 2.2). Transducers are all designed for 800 nm optical and 300 nm acoustic wavelengths (different wavelengths would require changes in the grating periodicity and parameter space). DPSG and DPMG use secondary grating periods (500 nm) multiplied by 3, in order to obtain a period which is greater than the optical wavelength, for easy fabrication using methods such as photolithography. Therefore the -3-order of the secondary grating is utilized to complete the k-vector to that of the plasmon (see Section 3.2). DPSG uses a direct superposition of two gratings, while DPMG merges the gratings by muting the primary grating fingers when it is to superimpose on the fingers of the secondary grating. The muting is done by making the primary grating finger
51
height equal to zero at the corresponding areas. The DPMG-UH combines two gratings whose periods are smaller than the optical wavelength (300 nm vs 500 nm). While the method of superposition is the same as in DPMG, all the grating heights are kept constant facilitating a single stage, e-beam lithography-metallization fabrication procedure. The -1-order of the secondary grating is used to complement the primary (detection) grating. 2. Methods 2.1. Description of the numerical model The numerical model has been developed using commercial software employing Finite Element Method (FEM) to simulate p-polarized 800 nm electromagnetic plane waves incident on a transducer from air. The incident side is on the right where a refractive index of 1 has been used to model air. The middle layer, i.e. the grating structure is modelled as Aluminium with a complex refractive index of, n = 2.8 j8.449. The transmission layer is set to be glass (n = 1.512), which is the leftmost medium in Fig. 1. Since the transmission medium is of no significance (metal layer is too thick), it is set to be glass for easier extraction of far field data. On the transmission and reflection sides, PMLs have been used to eliminate back reflections into the model. After the model is run, a separate script collects the transmitted and reflected far field from the transmitted side (glass) and reflected side (air). The numerical model is manipulated using scripts and multiple gratings can thus be introduced. Any two arbitrary grating can be simulated by finding their least common multiple and letting the simulation domain width be equal to this number so as to maintain periodicity. The acoustic wave propagation is modelled by a phase changing sinusoid which is superimposed onto the grating. The
Fig. 1. (a) The geometry for a grating based transducer whose period is ka-matched. The incident side is right hand side. The grating can be deposited on a glass or metal substrate. Rightmost medium is considered to be air. (b) The geometry for the DPMG design. (c) The geometry of the DPSG design. (d) The geometry of the DPMG-UH design.
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transducer is, thus, deformed by the sinusoid, i.e. the acoustic wave, so as to model the displacement caused by the acoustic wave. Reflections of the SAW from the grating walls are ignored, since the grating walls are small compared to half the acoustic wavelength. The photo-acoustic effect (refractive index change due to the SAW) was ignored, since the change in reflectivity due to this effect is negligible compared to the signal amplitude. The periodicity of this effect is also ignored, since the SAW wavelength is below the optical wavelength used for detection. The SAW amplitude was taken to be 10 nm for all simulations, although for lower values, the obtained signal amplitudes scaled linearly. For every phase of the SAW considered, a time harmonic optical simulation is run and the far field data are collected. Since the speed of the acoustic wave (2906 m/s) [11] is too small compared to the speed of light, the simulations associated with each SAW phase can be modelled as separate time-harmonic electromagnetic model. 2.2. Fabrication methods The transducer can be fabricated using a top to bottom approach. The first two designs (DPMG and DPSG) where the grating heights are not the same (see Fig. 1b and c) can be fabricated using a combination of photolithography-metallization and e-beam lithography-metallization techniques. In both of these designs, two approaches can be taken. If two sub-optical-wavelength-period gratings are to be produced successively, two stages of e-beam lithography may be necessary. This may be difficult since the first fabrication area may be too small to locate easily. However, the secondary grating period can be multiplied by an integer, and the grating heights readjusted, so as to make its fabrication possible using photolithography (see Fig. 1c). Since much bigger areas are possible using photolithography, the primary grating can then be fabricated on this template. The third design (DPMG-UH) can be fabricated with only one stage of e-beam lithography-metallization (see Fig. 1d). The difficulty in the fabrication of the structures that require two-stage lithography-metallization comes about when the alignment of the two gratings is considered. The alignment of the two gratings was found to affect the sensitivity of the transducer, for large misalignments. When the grating periods are small compared to the wavelength, such as 300 nm vs 500 nm, the alignment mistakes do reduce the sensitivity, but they do not deteriorate the signal. When the difference in grating periods is increased, the alignment does effect and deteriorate the sensitivity.
r: radius vector of the surface S (not a unit vector). Ep: calculated field at point p. The farfield is extracted from both sides of the model. For the DPMG-UH, the farfield pattern looks like those in Fig. 2a. Fig. 2b shows the farfield patterns obtained for the transducer with the grating that is ka-matched when the ka > ko . This corresponds to the CHOTs in [6]. Afterwards, the spectrum is sampled at appropriate locations to extract the desired reflected orders. The fields are normalized with the incident field and squared to give the reflectivity at desired far field angles. The difference between the maximum and the minimum reflectivity in the 0, +1, 1 orders or the sum of all orders (depending on the grating structure) yields a measure of signal amplitude of the sensor as SAW interacts with the transducer (details discussed in Sections 4.1, 4.2, 4.3). 3.2. Excitation of plasmons using grating k-vector matching Grating coupling of plasmons is well known [12]. The k-vector of plasmons travelling at an interface between semi-infinite media is given along with the grating equation in Eq. (2). 1
kp ¼ k0 ðee11þee22 Þ2 ð2Þ
kp ¼ kin sin h þ kg kg ¼ mkg1 þ nkg2
m; n 2 Z
where kp: k-vector of plasmons. k0: k-vector in free space of the excitation. e1: dielectric constant of the first medium. e2: dielectric constant of the first medium. h: angle of incidence (measured from surface normal). kin: k-vector of the incident radiation in medium 1. kg: grating k-vector. Presence of plasmons is ensured by using TM waves and complementing the detection grating k-vector to that of plasmon k-vector. The matching is shown in Eq. (2). Here the parallel component of the incoming k-vector is complemented by the k-vector due to the grating, kg. This k-vector can be obtained due to linear combination of various gratings. The detection (primary) grating is chosen so as to match the SAW wavelength. The secondary grating is there to complement the resulting k-vector to that of plasmons, kp.
3. Theory and calculations
4. Results and discussion
3.1. Farfield extraction
Using the model described in Section 0, three different scenarios involving the optical detection of SAWs have been modelled. In the first case, the acoustic wavelength is bigger than the optical wavelength, where a grating is used which is wavelength-matched to the acoustic wave (see Fig. 1a. In Fig. 1a the deformation due to the SAW is also demonstrated. This corresponds to the transducer described in [6]. The second case is when the acoustic wavelength is smaller than the optical wavelength. This corresponds to the transducer described in [10]. For the second scenario, the proposed idea of complementary gratings can be used. The proposed idea uses two gratings to modulate the excitation of surface plasmons on the transducer surface. Depending on the fabrication capabilities, 3 different designs are suggested and demonstrated. The three transducer designs are shown in Fig. 1b–d. These are ‘‘Double Period Superimposed Gratings (DPSG)’’ design, the ‘‘Double Period Merged Gratings (DPMG)’’ design, and the ‘‘Double Period Merged Gratings-Uniform Height (DPMG-UH)’’ design, where all the grating heights are kept at one level to facilitate easy fabrication.
The far field extraction uses the Stratton-Chu formulation, modified from its original form to incorporate media with refractive indices other than 1. Also the field is apodised to get rid of any possible cancellation effects inherent in plane waves passing through the extraction source unchanged. The Formulation is given in Eq. (1).
Ep ¼
jkn ro 4p
Z
½n Eap gn ro ðn H ap Þ expðjkn r r o ÞdS
where Eap: electric field on the aperture (apodised). Hap: magnetic field on the aperture (apodised). ro: unit vector pointing from origin to the field at p. n: unit normal to the surface S. gn: impedance of the ambient medium. kn: wave number in the ambient medium.
ð1Þ
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Fig. 2. (a) The reflected far field spectrum of the proposed DPMG-UH plasmonic transducer. The x-axis represents the far field extraction angle. The 0° is set to be the 0-order reflection, which corresponds to the outward surface normal measured from the transducer. (b) The farfield spectrum of the transducer whose period is wavelength-matched to the acoustic wave, when ka > ko .
4.1. ka-Matched grating transducer based surface acoustic wave detection for ka > ko When ka > ko , the grating period is larger than the optical wavelength, therefore diffraction of the incident EM wave is possible. A grating of period 1500 nm was deformed with a SAW of wavelength 1500 nm (geometry shown in Fig. 1a). The grating modelled had 0.5 duty cycle. The far field pattern for such a structure looks like Fig. 2b. In this figure it is clearly visible that the 0-order reflection is modulated as well as the ±1-orders. The signal amplitude, which is defined as the change in reflectivity, for this transducer, where ka ¼ 1500 nm; k0 ¼ 800 nm, was found to be around 0.18. Fig. 3a shows the plots of the relevant orders and demonstrates their modulation. As can be seen, the 0-order reflection undergoes significant modulation, which is facilitated by ±1-orders. 4.2. ka -matched grating transducer based surface acoustic wave detection for ka < ko As the ka approaches ko , the diffracted orders are expected to get closer toward 90° and to become evanescent when the limit is reached, where ka ¼ ko . For smaller values of ka , there is no diffraction and the signal amplitude deteriorates. A method based
on resistive heating can be used to raise signal amplitude by optimizing the grating parameters so as to facilitate transduction via resistive heating. The signal amplitude was found to be 0.084 for this grating transducer, whose period is ka-matched, when ka ¼ 300 nm; k0 ¼ 800 nm. Fig. 3b shows the extracted far field of the transducer when the ka < ko . There are no orders to plot other than the 0-order reflection. 4.3. The plasmonic transducer for ka < ko In this work, a double grating structure is proposed to successfully increase the signal levels for the optical detection of surface acoustic waves whose wavelength is smaller than the optical wavelength. In this paper, ka is assumed to be 300 nm and k0 = 800 nm. While one of the grating periods is designed so as to match the acoustic wavelength of interest (detection grating), the period of the secondary is designed to complement the former so as to match the total grating k-vector to those of plasmon as shown in Eq. (2). Three design suggestions are made utilizing the same principle with varying ease of fabrication (see Fig. 4). In the proposed mechanism, plasmons are launched on the surface and travel towards both sides of the transducer. As the acoustic waves interact with the transducer, the plasmon coupling
Fig. 3. (a) Plot for the orders of the grating based transducer for ka > ko where the grating period is k-matched to the SAW. (b) The reflected orders of the ka -matched grating when ka < ko . There is a change in the reflectivity of the 0-order reflection. As expected there are no ±1 – orders and the energy transfer is among the reflection and resistive heating. The modulation in the reflectivity, i.e. signal amplitude is 0.084.
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efficiency of the transducer changes with the perturbation, changing the overall reflectivity as measured from the 0-order reflection, +1 reflection, 1 reflection or their sum, depending on the design. Therefore, the operation mechanism of the proposed transducer differs greatly from that suggested in [6], i.e. energy transfer trade among orders, and [10] energy trade via resistive heating. 4.3.1. Double Period Superimposed Gratings (DPSG) The first design suggestion demonstrate the operating principle explicitly, where two gratings are superimposed directly (see Fig. 1c). The farfield patterns of such a grating where the secondary grating period is 500 nm is shown in Fig. 4a. This structure can be fabricated using two stage e-beam lithography-metallization. Fig. 4b shows the reflected orders where the secondary grating period is multiplied by 3 to make it 1500 nm. This structure can be built by photolithography-metallization followed by e-beam lithography-metallization. The 300 nm vs 500 nm transducer was measured to have 0.18 0-order reflection modulation. The 300 nm vs 1500 nm transducer had a similar, slightly lower, modulation of 0.16. However, the modulation was not only on the 0-order reflection, but was on the sum of all the reflected orders in the spectrum. 4.3.2. Double Period Merged Gratings (DPMG) The second design involves merging the gratings, rather than direct superposition. The geometry looks like that in Fig. 1b. The detection grating is ‘‘muted’’ when the secondary grating is on.
This structure can be fabricated in a similar fashion, two-stage lithography-metallization. The grating periods for this transducer are 300 nm vs 1500 nm. The reflected orders are shown in Fig. 5a, where the 0-order reflection modulation was around 0.22. The plasmonic nature can be seen in the farfield (see Fig. 5a and b) and in the near field of the structure (Fig. 6a and b) when the transducer was modelled in TM and TE modes (see Section 4.3.4). 4.3.3. Double Period Merged Gratings-Uniform Height (DPMG-UH) The transducer in Section 4.3.2 can be optimized to yield equal heights, which will simplify the fabrication process. If the grating heights are all equal, and the two gratings are merged, a single stage e-beam lithography-metallization could result in the final structure where 300 nm and 500 nm gratings were mixed (see Fig. 1d). The far field pattern of this design is also demonstrated in Fig. 2a). The 0-order reflection is modulated by 0.48, which is remarkable compared to the rest of the designs, even those where ka > ko . The reflected orders can be seen in Fig. 7a. 4.3.4. Parameter space for the plasmonic transducer The transducer is optimized for various grating parameters such as the height of both the grating fingers, the thickness of the background film. The models were run for TE and TM modes so as to verify the effect of plasmons in the operating principle. It was found that the device operation mechanism is based on the formation and modulation of surface plasmon waves in the transducer.
Fig. 4. (a) The reflected orders for the DPSG design. The 0-order reflection carries the signal. The difference in the reflectivity modulation is around 0.18, which is comparable to the transducers where ka > ko . (b) The reflected orders for the DPSG design where the secondary grating period is multiplied by an integer, to make it possible to fabricate using photolithography. In this case, all the light must be collected rather than a single order. The sum of all orders is modulated around 0.16.
Fig. 5. (a) The reflected orders for the DPMG plasmonic transducer when ka < ko . It can be seen that the modulation of the 0-order reflected light is much more pronounced (around 0.22) compared to the structure that is matched to the acoustic wavelength. (b) The reflected orders for the DPMG plasmonic transducer for TE modes when ka < ko . It can be seen that the reflected light is not modulated and hence there is no signal.
A. Arca / Ultrasonics 57 (2015) 50–56
Fig. 5a represents results obtained using TM waves, i.e. p-polarized incidence. When the same model was tested with s polarisation, ie TE incidence, no signal was found (see Fig. 5b). Fig. 6a shows the
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near field effects on the transducer during the interaction with the SAW when p-polarized waves are used as excitation. Here the field enhancements inherent to plasmons are visible. On the
Fig. 6. (a) The DPMG transducer when illuminated by TM polarized waves. Field enhancements are visible on the metallic surface. This demonstrates the presence of SPs on the surface. (b) The transducer when illuminated with TE polarized light. No field enhancements or confinements are visible. There is no evidence of plasmons.
Fig. 7. (a) The reflected orders obtained from the DPMG-UH plasmonic transducer. The primary grating period was chosen to be 300 nm and secondary grating period was 500 nm. The 0-order reflection is modulated by 0.48. (b) The parameter space of the DPMG-UH plasmonic transducer. The optimum grating height is 85 nm and the optimum background height is around 50 nm.
Fig. 8. (a) The operating region and the sensitivity of the proposed DPMG transducer. It can be seen that the best operating region is located around 40 nm finger height. The background thickness is not of importance as long as it is thick enough to allow reflection. The detection grating period is set to 300 nm while the launcher grating was 1500 nm in this case. (b) The grating periods that can achieve a k-vector within (1 ± 0.1)kp.
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A. Arca / Ultrasonics 57 (2015) 50–56
contrary, Fig. 6b there is no field confinement and no visible signs of plasmons. This is also a demonstration of the device operation principle. Figs. 8a and 7b show the parameter spaces of merged transducers, where the primary grating period is 300 nm and secondary grating period is 1500 nm and 500 nm respectively. In Fig. 8a, the maximum sensitivity occurs when the detection grating finger height is around 40 nm and the background of the transducer is 40 nm thick. The figure shows the operation region when the primary grating finger height is at 90 nm. It can be seen that the change in reflectivity is in the range of 0.22. This is remarkable signal amplitude considering the ka -matched transducers for ka < ko , which barely reached a modulation level of 0.09. In Fig. 7b it is clear that the optimum grating height is around 80 nm and the optimum background thickness is above 30 nm. It is also noted that the finger heights do change the amount of signal received, however, they do not deteriorate the signal for ±25% change. For 800 nm incident wavelength, the grating combinations that yield k-vectors within (1 ± 0.1)kp were chosen. However, depending on the combination, the grating heights must be carefully chosen to optimize the transducer. The grating period to achieve a k-vector that is within (1 ± 0.1)kp is shown in Fig. 8b. It should be noted that the same calculations can be applied and the designs can be optimized for different optical wavelengths in accordance with Eq. (2). Consequently, the gratings will be designed for a single plasmon k-vector, which corresponds to a single optical wavelength. Hence, the type of source (pulsed or CW) used does not affect the operation of the sensor, although different optical set-ups for detection would be necessary. 5. Conclusion The paper describes the operating principle of a plasmonic transducer which is capable of detecting sub-optical-wavelength ultrasonic surface acoustic waves. It was found that the proposed transducer, which utilizes the modulation of the surface plasmon coupling efficiency by SAWs, can be used to circumvent the diffraction limit and detect perturbations smaller than half the optical wavelength. This is achieved by matching the plasmon k-vector
to that of the sum of two grating k-vectors. One of these gratings is needed for the detection of SAWs, whereas the other grating is necessary to complement the primary grating k-vector to that of plasmons. Three design suggestions were made, to achieve and demonstrate the operation principle. Furthermore, the design yields signal levels that are more than 5 times those previously reported for such SAW wavelengths. Fabrication methods have been proposed and realistic measures were given so as to maintain sensitivity through possible fabrication tolerance limits and errors. These transducers can be used to detect small surface breaking cracks or defects, in hard to reach places, by the transfer of light through fibre optics. Application areas include turbines in renewable energy and aerospace industries. References [1] Tribikram Kundu, Ultrasonic and Electromagnetic NDE for Structure and Material Characterization: Engineering and Biomedical Applications Hardback, CRC Press, 2012. [2] C.B. Scruby, L. Drain, Laser Ultrasonics: Techniques and Applications, Adam Hilger, 1990. [3] G.A. Antonelli, H.J. Maris, S.G. Malhorta, J.M.E. Harper, Picosecond ultrasonics study of the vibrational modes of a nanostructure, J. Appl. Phys. 91 (1) (2002) 3261–3267. [4] W.S. Capinski, H.J. Maris, Improved apparatus for picosecond pump-and-probe optical measurements, Rev. Sci. Instruments 67 (8) (1996) 2720–2726. [5] J.P. Monchalin, Optical Detection of Ultrasound, IEEE Transactions on ultrasonics, ferroelectrics and frequency control, vol. UFFC-33, no. 5, 1986. [6] T. Stratoudaki, J.A. Hernandez, M. Clark, M.G. Somekh, Cheap optical transducers (CHOTs) for narrowband ultrasonic applications, Mater. Sci. Technol. 18 (2007) 843–851. [7] B. Bonello, A. Ajinou, V. Richard, P. Djemia, S.M. Cherif, Surface acoustic waves in the GHz range generated by periodically patterned metallic stripes illuminated by an ultrashort laser pulse, J. Acoustic. Soc. Am. 110 (4) (2001) 1943–1949. [8] K.L. Telshchow, D.H. Hurley, Picosecond surface acoustic waves using a suboptical wavelength absorption grating, Phys. Rev. B 66 (15) (2002). [9] P. Ahn, Z. Zhang, C. Sun, O. Balogun, Ultrasonic near-field optical microscopy using a plasmonic nanofocusing, J. Appl. Phys. 113 (2013). [10] A. Arca, T. Stratoudaki, R. Smith, M. Clark, M. Somekh, Evanescent CHOTs for the optical generation and detection of ultrahigh frequency SAWs, in: Ultrasonics Symposium (IUS), IEEE International, Rome, 2009. [11] G.W.C. Laby, T.H. Kaye, Tables of Physical and Chemical Constants, Longman Group Limited, 1973. [12] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, vol. 111, Springer Tracts in Modern Physics, 1988.
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
A plasmonic SAW transducer Ahmet Arca ⇑ Department of Electrical and Electronic Engineering, Faculty of Engineering, European University of Lefke, Gemikonagi, Mersin 10, Turkey
a r t i c l e
i n f o
Article history: Received 3 April 2014 Received in revised form 11 August 2014 Accepted 21 October 2014 Available online 13 November 2014 Keywords: Optical transducers SAW transducer GHz frequency SAW Plasmonic SAW transducer Optical detection of ultrahigh frequency SAW
a b s t r a c t In this work, an acoustic–optical transducer that is based on the utilization of plasmons is proposed to optically detect SAW of wavelength ( ko then diffraction based methods are viable such as knife-edge detection [2]. Another
⇑ Tel.: +90 3926602000. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ultras.2014.10.021 0041-624X/Ó 2014 Elsevier B.V. All rights reserved.
approach to the detection of SAWs involves using a transducer to maximise the change in the optical signal during the interaction of the acoustic signal with the transducer. Transducer based detection can be achieved through a grating structure whose period is equal to the SAW wavelength and whose finger height is carefully chosen to optimize the signal levels [6–8]. In the work of Stratoudaki et al. [6], the finger heights were chosen to be 1/8 of the optical wavelength, to obtain an in situ interferometer (CHOTs). The geometry of the devices looks like that in Fig. 1a. Transducer based techniques described in the literature rely on the diffraction of the optical waves due to the periodic disturbance caused by the SAW or the transducer. This requires that the disturbance wavelength i.e. SAW wavelength is in the vicinity of the optical wavelength used. As the SAW wavelength gets shorter than this value, the light no longer diffracts yielding no detection. This makes the utilization of ultrahigh frequency (GHz) SAWs very difficult. When ka < ko diffraction based techniques cannot be used, therefore interferometric methods and measurements of reflectivity due to acousto-optic effects can be used. The detection sub-optical-wavelength ultrasound, is mostly dominated by the interferometric techniques such as those demonstrated in [3] and scanning techniques such as [9]. These methods are difficult to use in the field and require sample removal and isolation. Transducer based detection techniques in the region where ka < ko , were investigated in [10]. As the wavelength of the SAW was decreased, approached and went below the optical wavelength, it was observed numerically that the reflected orders of the CHOT in [6] became evanescent and the energy trade was abolished. In this case, the transducers were optimized and
A. Arca / Ultrasonics 57 (2015) 50–56
another energy transfer mechanism was suggested, which relied on the modulation of the resistive heating taking place in a thin film placed underneath the grating [10]. Even though this device has the best possible signal for a grating of such structure, it still yielded low signal levels as compared with the original CHOTs. In this article, a new method for the optical detection of suboptical-wavelength SAWs is described. The operating principle depends on matching the total grating k-vector to that of the plasmon, whose coupling to the transducer is then modulated via the interaction with the SAW, thereby changing the overall reflectivity of the transducer. Three different designs are proposed that can utilize this operating principle. These are the Double Period Merged Gratings with Uniform Height (DPMG-UH), Double Period Superimposed Gratings (DPSG), and Double Period Merged Grating (DPMG). They are shown in Fig. 1b–d respectively. Samples are designed to be built on glass substrate (for modelling purposes), although substrate medium can be varied considering the SAW travel speed. They are Aluminium gratings, which can be fabricated using standard lithography/metallization techniques (see section 2.2). Transducers are all designed for 800 nm optical and 300 nm acoustic wavelengths (different wavelengths would require changes in the grating periodicity and parameter space). DPSG and DPMG use secondary grating periods (500 nm) multiplied by 3, in order to obtain a period which is greater than the optical wavelength, for easy fabrication using methods such as photolithography. Therefore the -3-order of the secondary grating is utilized to complete the k-vector to that of the plasmon (see Section 3.2). DPSG uses a direct superposition of two gratings, while DPMG merges the gratings by muting the primary grating fingers when it is to superimpose on the fingers of the secondary grating. The muting is done by making the primary grating finger
51
height equal to zero at the corresponding areas. The DPMG-UH combines two gratings whose periods are smaller than the optical wavelength (300 nm vs 500 nm). While the method of superposition is the same as in DPMG, all the grating heights are kept constant facilitating a single stage, e-beam lithography-metallization fabrication procedure. The -1-order of the secondary grating is used to complement the primary (detection) grating. 2. Methods 2.1. Description of the numerical model The numerical model has been developed using commercial software employing Finite Element Method (FEM) to simulate p-polarized 800 nm electromagnetic plane waves incident on a transducer from air. The incident side is on the right where a refractive index of 1 has been used to model air. The middle layer, i.e. the grating structure is modelled as Aluminium with a complex refractive index of, n = 2.8 j8.449. The transmission layer is set to be glass (n = 1.512), which is the leftmost medium in Fig. 1. Since the transmission medium is of no significance (metal layer is too thick), it is set to be glass for easier extraction of far field data. On the transmission and reflection sides, PMLs have been used to eliminate back reflections into the model. After the model is run, a separate script collects the transmitted and reflected far field from the transmitted side (glass) and reflected side (air). The numerical model is manipulated using scripts and multiple gratings can thus be introduced. Any two arbitrary grating can be simulated by finding their least common multiple and letting the simulation domain width be equal to this number so as to maintain periodicity. The acoustic wave propagation is modelled by a phase changing sinusoid which is superimposed onto the grating. The
Fig. 1. (a) The geometry for a grating based transducer whose period is ka-matched. The incident side is right hand side. The grating can be deposited on a glass or metal substrate. Rightmost medium is considered to be air. (b) The geometry for the DPMG design. (c) The geometry of the DPSG design. (d) The geometry of the DPMG-UH design.
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transducer is, thus, deformed by the sinusoid, i.e. the acoustic wave, so as to model the displacement caused by the acoustic wave. Reflections of the SAW from the grating walls are ignored, since the grating walls are small compared to half the acoustic wavelength. The photo-acoustic effect (refractive index change due to the SAW) was ignored, since the change in reflectivity due to this effect is negligible compared to the signal amplitude. The periodicity of this effect is also ignored, since the SAW wavelength is below the optical wavelength used for detection. The SAW amplitude was taken to be 10 nm for all simulations, although for lower values, the obtained signal amplitudes scaled linearly. For every phase of the SAW considered, a time harmonic optical simulation is run and the far field data are collected. Since the speed of the acoustic wave (2906 m/s) [11] is too small compared to the speed of light, the simulations associated with each SAW phase can be modelled as separate time-harmonic electromagnetic model. 2.2. Fabrication methods The transducer can be fabricated using a top to bottom approach. The first two designs (DPMG and DPSG) where the grating heights are not the same (see Fig. 1b and c) can be fabricated using a combination of photolithography-metallization and e-beam lithography-metallization techniques. In both of these designs, two approaches can be taken. If two sub-optical-wavelength-period gratings are to be produced successively, two stages of e-beam lithography may be necessary. This may be difficult since the first fabrication area may be too small to locate easily. However, the secondary grating period can be multiplied by an integer, and the grating heights readjusted, so as to make its fabrication possible using photolithography (see Fig. 1c). Since much bigger areas are possible using photolithography, the primary grating can then be fabricated on this template. The third design (DPMG-UH) can be fabricated with only one stage of e-beam lithography-metallization (see Fig. 1d). The difficulty in the fabrication of the structures that require two-stage lithography-metallization comes about when the alignment of the two gratings is considered. The alignment of the two gratings was found to affect the sensitivity of the transducer, for large misalignments. When the grating periods are small compared to the wavelength, such as 300 nm vs 500 nm, the alignment mistakes do reduce the sensitivity, but they do not deteriorate the signal. When the difference in grating periods is increased, the alignment does effect and deteriorate the sensitivity.
r: radius vector of the surface S (not a unit vector). Ep: calculated field at point p. The farfield is extracted from both sides of the model. For the DPMG-UH, the farfield pattern looks like those in Fig. 2a. Fig. 2b shows the farfield patterns obtained for the transducer with the grating that is ka-matched when the ka > ko . This corresponds to the CHOTs in [6]. Afterwards, the spectrum is sampled at appropriate locations to extract the desired reflected orders. The fields are normalized with the incident field and squared to give the reflectivity at desired far field angles. The difference between the maximum and the minimum reflectivity in the 0, +1, 1 orders or the sum of all orders (depending on the grating structure) yields a measure of signal amplitude of the sensor as SAW interacts with the transducer (details discussed in Sections 4.1, 4.2, 4.3). 3.2. Excitation of plasmons using grating k-vector matching Grating coupling of plasmons is well known [12]. The k-vector of plasmons travelling at an interface between semi-infinite media is given along with the grating equation in Eq. (2). 1
kp ¼ k0 ðee11þee22 Þ2 ð2Þ
kp ¼ kin sin h þ kg kg ¼ mkg1 þ nkg2
m; n 2 Z
where kp: k-vector of plasmons. k0: k-vector in free space of the excitation. e1: dielectric constant of the first medium. e2: dielectric constant of the first medium. h: angle of incidence (measured from surface normal). kin: k-vector of the incident radiation in medium 1. kg: grating k-vector. Presence of plasmons is ensured by using TM waves and complementing the detection grating k-vector to that of plasmon k-vector. The matching is shown in Eq. (2). Here the parallel component of the incoming k-vector is complemented by the k-vector due to the grating, kg. This k-vector can be obtained due to linear combination of various gratings. The detection (primary) grating is chosen so as to match the SAW wavelength. The secondary grating is there to complement the resulting k-vector to that of plasmons, kp.
3. Theory and calculations
4. Results and discussion
3.1. Farfield extraction
Using the model described in Section 0, three different scenarios involving the optical detection of SAWs have been modelled. In the first case, the acoustic wavelength is bigger than the optical wavelength, where a grating is used which is wavelength-matched to the acoustic wave (see Fig. 1a. In Fig. 1a the deformation due to the SAW is also demonstrated. This corresponds to the transducer described in [6]. The second case is when the acoustic wavelength is smaller than the optical wavelength. This corresponds to the transducer described in [10]. For the second scenario, the proposed idea of complementary gratings can be used. The proposed idea uses two gratings to modulate the excitation of surface plasmons on the transducer surface. Depending on the fabrication capabilities, 3 different designs are suggested and demonstrated. The three transducer designs are shown in Fig. 1b–d. These are ‘‘Double Period Superimposed Gratings (DPSG)’’ design, the ‘‘Double Period Merged Gratings (DPMG)’’ design, and the ‘‘Double Period Merged Gratings-Uniform Height (DPMG-UH)’’ design, where all the grating heights are kept at one level to facilitate easy fabrication.
The far field extraction uses the Stratton-Chu formulation, modified from its original form to incorporate media with refractive indices other than 1. Also the field is apodised to get rid of any possible cancellation effects inherent in plane waves passing through the extraction source unchanged. The Formulation is given in Eq. (1).
Ep ¼
jkn ro 4p
Z
½n Eap gn ro ðn H ap Þ expðjkn r r o ÞdS
where Eap: electric field on the aperture (apodised). Hap: magnetic field on the aperture (apodised). ro: unit vector pointing from origin to the field at p. n: unit normal to the surface S. gn: impedance of the ambient medium. kn: wave number in the ambient medium.
ð1Þ
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Fig. 2. (a) The reflected far field spectrum of the proposed DPMG-UH plasmonic transducer. The x-axis represents the far field extraction angle. The 0° is set to be the 0-order reflection, which corresponds to the outward surface normal measured from the transducer. (b) The farfield spectrum of the transducer whose period is wavelength-matched to the acoustic wave, when ka > ko .
4.1. ka-Matched grating transducer based surface acoustic wave detection for ka > ko When ka > ko , the grating period is larger than the optical wavelength, therefore diffraction of the incident EM wave is possible. A grating of period 1500 nm was deformed with a SAW of wavelength 1500 nm (geometry shown in Fig. 1a). The grating modelled had 0.5 duty cycle. The far field pattern for such a structure looks like Fig. 2b. In this figure it is clearly visible that the 0-order reflection is modulated as well as the ±1-orders. The signal amplitude, which is defined as the change in reflectivity, for this transducer, where ka ¼ 1500 nm; k0 ¼ 800 nm, was found to be around 0.18. Fig. 3a shows the plots of the relevant orders and demonstrates their modulation. As can be seen, the 0-order reflection undergoes significant modulation, which is facilitated by ±1-orders. 4.2. ka -matched grating transducer based surface acoustic wave detection for ka < ko As the ka approaches ko , the diffracted orders are expected to get closer toward 90° and to become evanescent when the limit is reached, where ka ¼ ko . For smaller values of ka , there is no diffraction and the signal amplitude deteriorates. A method based
on resistive heating can be used to raise signal amplitude by optimizing the grating parameters so as to facilitate transduction via resistive heating. The signal amplitude was found to be 0.084 for this grating transducer, whose period is ka-matched, when ka ¼ 300 nm; k0 ¼ 800 nm. Fig. 3b shows the extracted far field of the transducer when the ka < ko . There are no orders to plot other than the 0-order reflection. 4.3. The plasmonic transducer for ka < ko In this work, a double grating structure is proposed to successfully increase the signal levels for the optical detection of surface acoustic waves whose wavelength is smaller than the optical wavelength. In this paper, ka is assumed to be 300 nm and k0 = 800 nm. While one of the grating periods is designed so as to match the acoustic wavelength of interest (detection grating), the period of the secondary is designed to complement the former so as to match the total grating k-vector to those of plasmon as shown in Eq. (2). Three design suggestions are made utilizing the same principle with varying ease of fabrication (see Fig. 4). In the proposed mechanism, plasmons are launched on the surface and travel towards both sides of the transducer. As the acoustic waves interact with the transducer, the plasmon coupling
Fig. 3. (a) Plot for the orders of the grating based transducer for ka > ko where the grating period is k-matched to the SAW. (b) The reflected orders of the ka -matched grating when ka < ko . There is a change in the reflectivity of the 0-order reflection. As expected there are no ±1 – orders and the energy transfer is among the reflection and resistive heating. The modulation in the reflectivity, i.e. signal amplitude is 0.084.
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efficiency of the transducer changes with the perturbation, changing the overall reflectivity as measured from the 0-order reflection, +1 reflection, 1 reflection or their sum, depending on the design. Therefore, the operation mechanism of the proposed transducer differs greatly from that suggested in [6], i.e. energy transfer trade among orders, and [10] energy trade via resistive heating. 4.3.1. Double Period Superimposed Gratings (DPSG) The first design suggestion demonstrate the operating principle explicitly, where two gratings are superimposed directly (see Fig. 1c). The farfield patterns of such a grating where the secondary grating period is 500 nm is shown in Fig. 4a. This structure can be fabricated using two stage e-beam lithography-metallization. Fig. 4b shows the reflected orders where the secondary grating period is multiplied by 3 to make it 1500 nm. This structure can be built by photolithography-metallization followed by e-beam lithography-metallization. The 300 nm vs 500 nm transducer was measured to have 0.18 0-order reflection modulation. The 300 nm vs 1500 nm transducer had a similar, slightly lower, modulation of 0.16. However, the modulation was not only on the 0-order reflection, but was on the sum of all the reflected orders in the spectrum. 4.3.2. Double Period Merged Gratings (DPMG) The second design involves merging the gratings, rather than direct superposition. The geometry looks like that in Fig. 1b. The detection grating is ‘‘muted’’ when the secondary grating is on.
This structure can be fabricated in a similar fashion, two-stage lithography-metallization. The grating periods for this transducer are 300 nm vs 1500 nm. The reflected orders are shown in Fig. 5a, where the 0-order reflection modulation was around 0.22. The plasmonic nature can be seen in the farfield (see Fig. 5a and b) and in the near field of the structure (Fig. 6a and b) when the transducer was modelled in TM and TE modes (see Section 4.3.4). 4.3.3. Double Period Merged Gratings-Uniform Height (DPMG-UH) The transducer in Section 4.3.2 can be optimized to yield equal heights, which will simplify the fabrication process. If the grating heights are all equal, and the two gratings are merged, a single stage e-beam lithography-metallization could result in the final structure where 300 nm and 500 nm gratings were mixed (see Fig. 1d). The far field pattern of this design is also demonstrated in Fig. 2a). The 0-order reflection is modulated by 0.48, which is remarkable compared to the rest of the designs, even those where ka > ko . The reflected orders can be seen in Fig. 7a. 4.3.4. Parameter space for the plasmonic transducer The transducer is optimized for various grating parameters such as the height of both the grating fingers, the thickness of the background film. The models were run for TE and TM modes so as to verify the effect of plasmons in the operating principle. It was found that the device operation mechanism is based on the formation and modulation of surface plasmon waves in the transducer.
Fig. 4. (a) The reflected orders for the DPSG design. The 0-order reflection carries the signal. The difference in the reflectivity modulation is around 0.18, which is comparable to the transducers where ka > ko . (b) The reflected orders for the DPSG design where the secondary grating period is multiplied by an integer, to make it possible to fabricate using photolithography. In this case, all the light must be collected rather than a single order. The sum of all orders is modulated around 0.16.
Fig. 5. (a) The reflected orders for the DPMG plasmonic transducer when ka < ko . It can be seen that the modulation of the 0-order reflected light is much more pronounced (around 0.22) compared to the structure that is matched to the acoustic wavelength. (b) The reflected orders for the DPMG plasmonic transducer for TE modes when ka < ko . It can be seen that the reflected light is not modulated and hence there is no signal.
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Fig. 5a represents results obtained using TM waves, i.e. p-polarized incidence. When the same model was tested with s polarisation, ie TE incidence, no signal was found (see Fig. 5b). Fig. 6a shows the
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near field effects on the transducer during the interaction with the SAW when p-polarized waves are used as excitation. Here the field enhancements inherent to plasmons are visible. On the
Fig. 6. (a) The DPMG transducer when illuminated by TM polarized waves. Field enhancements are visible on the metallic surface. This demonstrates the presence of SPs on the surface. (b) The transducer when illuminated with TE polarized light. No field enhancements or confinements are visible. There is no evidence of plasmons.
Fig. 7. (a) The reflected orders obtained from the DPMG-UH plasmonic transducer. The primary grating period was chosen to be 300 nm and secondary grating period was 500 nm. The 0-order reflection is modulated by 0.48. (b) The parameter space of the DPMG-UH plasmonic transducer. The optimum grating height is 85 nm and the optimum background height is around 50 nm.
Fig. 8. (a) The operating region and the sensitivity of the proposed DPMG transducer. It can be seen that the best operating region is located around 40 nm finger height. The background thickness is not of importance as long as it is thick enough to allow reflection. The detection grating period is set to 300 nm while the launcher grating was 1500 nm in this case. (b) The grating periods that can achieve a k-vector within (1 ± 0.1)kp.
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contrary, Fig. 6b there is no field confinement and no visible signs of plasmons. This is also a demonstration of the device operation principle. Figs. 8a and 7b show the parameter spaces of merged transducers, where the primary grating period is 300 nm and secondary grating period is 1500 nm and 500 nm respectively. In Fig. 8a, the maximum sensitivity occurs when the detection grating finger height is around 40 nm and the background of the transducer is 40 nm thick. The figure shows the operation region when the primary grating finger height is at 90 nm. It can be seen that the change in reflectivity is in the range of 0.22. This is remarkable signal amplitude considering the ka -matched transducers for ka < ko , which barely reached a modulation level of 0.09. In Fig. 7b it is clear that the optimum grating height is around 80 nm and the optimum background thickness is above 30 nm. It is also noted that the finger heights do change the amount of signal received, however, they do not deteriorate the signal for ±25% change. For 800 nm incident wavelength, the grating combinations that yield k-vectors within (1 ± 0.1)kp were chosen. However, depending on the combination, the grating heights must be carefully chosen to optimize the transducer. The grating period to achieve a k-vector that is within (1 ± 0.1)kp is shown in Fig. 8b. It should be noted that the same calculations can be applied and the designs can be optimized for different optical wavelengths in accordance with Eq. (2). Consequently, the gratings will be designed for a single plasmon k-vector, which corresponds to a single optical wavelength. Hence, the type of source (pulsed or CW) used does not affect the operation of the sensor, although different optical set-ups for detection would be necessary. 5. Conclusion The paper describes the operating principle of a plasmonic transducer which is capable of detecting sub-optical-wavelength ultrasonic surface acoustic waves. It was found that the proposed transducer, which utilizes the modulation of the surface plasmon coupling efficiency by SAWs, can be used to circumvent the diffraction limit and detect perturbations smaller than half the optical wavelength. This is achieved by matching the plasmon k-vector
to that of the sum of two grating k-vectors. One of these gratings is needed for the detection of SAWs, whereas the other grating is necessary to complement the primary grating k-vector to that of plasmons. Three design suggestions were made, to achieve and demonstrate the operation principle. Furthermore, the design yields signal levels that are more than 5 times those previously reported for such SAW wavelengths. Fabrication methods have been proposed and realistic measures were given so as to maintain sensitivity through possible fabrication tolerance limits and errors. These transducers can be used to detect small surface breaking cracks or defects, in hard to reach places, by the transfer of light through fibre optics. Application areas include turbines in renewable energy and aerospace industries. References [1] Tribikram Kundu, Ultrasonic and Electromagnetic NDE for Structure and Material Characterization: Engineering and Biomedical Applications Hardback, CRC Press, 2012. [2] C.B. Scruby, L. Drain, Laser Ultrasonics: Techniques and Applications, Adam Hilger, 1990. [3] G.A. Antonelli, H.J. Maris, S.G. Malhorta, J.M.E. Harper, Picosecond ultrasonics study of the vibrational modes of a nanostructure, J. Appl. Phys. 91 (1) (2002) 3261–3267. [4] W.S. Capinski, H.J. Maris, Improved apparatus for picosecond pump-and-probe optical measurements, Rev. Sci. Instruments 67 (8) (1996) 2720–2726. [5] J.P. Monchalin, Optical Detection of Ultrasound, IEEE Transactions on ultrasonics, ferroelectrics and frequency control, vol. UFFC-33, no. 5, 1986. [6] T. Stratoudaki, J.A. Hernandez, M. Clark, M.G. Somekh, Cheap optical transducers (CHOTs) for narrowband ultrasonic applications, Mater. Sci. Technol. 18 (2007) 843–851. [7] B. Bonello, A. Ajinou, V. Richard, P. Djemia, S.M. Cherif, Surface acoustic waves in the GHz range generated by periodically patterned metallic stripes illuminated by an ultrashort laser pulse, J. Acoustic. Soc. Am. 110 (4) (2001) 1943–1949. [8] K.L. Telshchow, D.H. Hurley, Picosecond surface acoustic waves using a suboptical wavelength absorption grating, Phys. Rev. B 66 (15) (2002). [9] P. Ahn, Z. Zhang, C. Sun, O. Balogun, Ultrasonic near-field optical microscopy using a plasmonic nanofocusing, J. Appl. Phys. 113 (2013). [10] A. Arca, T. Stratoudaki, R. Smith, M. Clark, M. Somekh, Evanescent CHOTs for the optical generation and detection of ultrahigh frequency SAWs, in: Ultrasonics Symposium (IUS), IEEE International, Rome, 2009. [11] G.W.C. Laby, T.H. Kaye, Tables of Physical and Chemical Constants, Longman Group Limited, 1973. [12] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, vol. 111, Springer Tracts in Modern Physics, 1988.
