Interact with Confined Acoustic Modes in Gold Nanodisk

Chapter 4 Interaction between Plasmons and Hypersonic Pulse

4.3 Interaction in 2-D Gold Nanodisks Arrays

4.3.1 Interact with Confined Acoustic Modes in Gold Nanodisk

We chose the nanodisk arrays with a period of 250 nm, but with a different lengths since closer-packed arrays maximize the signal-to-noise ratio. Based on the discussion of section 2.3, rod length longer than 120 nm could excite LSPs in the nanorod array.

We thus compare the extinction spectra between different rod length cases (Fig. 4.4(a)).

We observed that more light is absorbed by gold nanodisks on rods because of the excitation of LSPs. To enhance the detection of acoustic vibrations, the wavelength of the probe beam was chosen to be 720 nm, which was near the maximum of the derivative of the extinction spectrum.

Figure 4.4 (a) Experimental extinction spectra and (b) the derivative of spectra of gold nanodisk on plain substrate and 120 nm nanorod substrate.

As shown in the inset of Fig. 4.5, both pump beam and probe beam were incident from the side of the gold nanodisks to directly generate and detect the CAMs of gold nanodisk. In order to avoid the absorption of GaN nanorod, the wavelength of the pump beam was also 720 nm. Therefore the BBO crystal was removed from the experimental setup. Furthermore the telescope, which was used to compensate the dichromatic aberration due to different wavelengths between pump and probe beam, was also

removed. The reflected probe beam from the gold nanodisk was collected by the detector. The diameters of the pump and probe beams at focus were respectively 20 m and 30 m, which are also much smaller than the area covered with nanostructures (300 µm×300 µm). The average power of the pump and probe at the sample surface were 40 mW and 4 mW, respectively.

Figure 4.5 Schematic showing of optical reflection type of femtosecond time resolved spectroscopy (inset: pump beam and probe beam are incident from the top of the

sample).

Fig. 4.6(a) shows the transient reflection changes of the gold nanodisk arrays with 250 nm periodicity on GaN nanorod arrays with two different rod lengths after removing the background, while the inset shows the original transient reflection changes. From Fig. 4.4(a), the extra pump light absorbed by the LSPs at 720 nm was calibrated, and subsequently, stronger optical reflection oscillations were observed for the gold nanodisks on the nanorod substrate. Combined with our above discussion, we attribute this difference to the different probe sensitivities because a stronger field

intensity of LSPs is excited in the samples on top of nanorod arrays. This strong LSP field enhanced the detection sensitivity of the probe beam compared to those on top of a plain substrate. The time-frequency analysis was adopted to analyze the frequency of the measured change in transient reflection as a function of time. In Fig. 4.6(b), oscillation signals at 11, 18, and 22 GHz were clearly observed for the 120 nm rod length substrate. However, only oscillations at 11 GHz were obvious in the plain substrate. Comparing to the acoustic dispersion curve of a single gold nanodisk with a 150 nm diameter, which was calculated based on the Pochammer Chree Theory [22, 23]

(Fig. 3.2(a)), theoretically expected frequencies of the CAMs of the gold nanodisk are 11 GHz, 17 GHz, and 21 GHz. Our experimental observation and the calculation are in good agreement with these values. We thus attribute the frequencies observed in the experiment to the CAMs of the gold nanodisk. Furthermore it can be seen that, weak, higher-order vibrations of the gold nanodisk become observable because of the stronger LSP field intensity in the nanorod. This result verifies that the well-confined LSP field in the nanorod indeed increases the sensitivity of hypersonic detection.

Figure 4.6 (a) Transient reflection changes of gold nanodisk arrays with 250 nm periodicity and different rod length. (b) Time-frequency analysis of transient reflection

change in Fig. 4.6(a). Higher-order vibrational modes of gold nanodisk are observable for 120 nm rod length substrate.

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Chapter 5 Hypersonic Pulse Transmission between Bulk Substrate and Nanorod Arrays

5.1 Introduction

In the previous chapters, we have successfully excited LSPs in the gold nanodisk array on top of GaN nanorod in order to make each gold nanodisk as an independent opto-acoustic sensor (Chapter 2). Then the interaction between LSPs and CAMs of gold nanodisk was experimentally investigated, which confirmed that the intense LSPs field indeed increased the hypersonic detection sensitivity (Chapter 4). For phased array imaging application, it is critical to apply this structure to passively detect the hypersonic waves and to study the effect of the array periodicity. Fig. 5.1 presents the scheme showing the detection of the propagated hypersonic waves by one gold nanodisk on top of a GaN nanorod, which was connected to a GaN substrate. The propagated hypersonic waves were assumed to be coupled either from a liquid sample or a solid sample through a matching layer into the GaN substrate, then propagated toward the GaN nanorod. After scattered at the interface between the nanorod and the substrate, part of the hypersonic waves would be coupled into the nanorod, and then propagated as the AGM in the nanorod [1, 2]. The hypersonic signal would finally be detected by the gold nanodisk through coupling to its vibrational modes [3, 4]. The vibration of the gold nanodisk will modify the LSP effect and will be eventually detected by an optical probe.

Figure 5.1 Schematic showing the detection of propagated hypersonic waves by one gold nanodisk on top of a GaN nanorod.

5.2 Slowness Curve of GaN

Since hypersonic pulse propagates in the GaN single crystal, we first calculated all possible acoustic modes in wurtzite GaN. Fig. 5.2(a), (c) are the schematic showings of the direction of the propagated acoustic modes and Fig. 5.2(b), (d) show the slowness curves (the reciprocal of sound velocity) for wurtzite GaN as a function of propagation vector for out-of-c-plane and in-c-plane acoustic waves. P (primary) wave is the longitudinal acoustic mode, which has the fast sound velocity. SV (shear vertical) and SH (shear horizontal) waves are the transverse acoustic mode, whose sound velocities are slower than the longitudinal mode. Since GaN is an anisotropic crystal, the sound velocity is dependent of the angle of propagated direction for out-of-c-plane acoustic mode. On the other hand, one can observe that the sound velocities of all acoustic modes propagate on the c-plane are not angle dependent due to the fact that the crystal structure is symmetric on the c-plane. From the slowness curves, the sound velocities of the fast and slowest acoustic mode are 8020 m/s and 4130 m/s, respectively. Based on the discussion in section 3.3, the two lowest detectable frequencies by the 150 nm gold nanodisk are 11 GHz, and 21 GHz. Meanwhile the design of our hypersonic array is

intended to detect the 11 GHz hypersonic waves due to the smaller acoustic impedance mismatch between nanorod and substrate. Therefore the shortest wavelength for the 11 GHz hypersonic waves in GaN is 375 nm. Since grating lobes are not significant until spatial sampling is more than one wavelength [5], therefore the periodicity of our gold nanodisk array is chosen to be slightly shorter than 375 nm in order to accommodate all different modes. Fig. 5.2(e) further compares the dispersion curves of surface acoustic wave (SAW) mode as well as SV, SH, P modes. This result indicates that the scattered hypersonic waves in Fig. 5.1 may propagate with 3932 m/s on the wurtzite GaN surface.

In this study, we only focus on the longitudinal mode propagating along the c-axis. In order to study the effect of array periodicity, the periodicities of our arrays are chose as 250 nm, 300 nm, 350 nm and 400 nm. The length of nanorod is set as 120 nm and 220 nm for LSPs excitation [6].

Figure 5.2 Schematic showings of the propagated direction of (a) out-of-c-plane and (c) in-c-plane acoustic mode. Calculated slowness curves in wurtzite GaN for (b) out-of-c-plane and (d) in-c-plane acoustic wave propagation. (e) Dispersion curves of

SAW, SV, SH, P acoustic mode in wurtzite GaN.

5.3 Simulated Hypersonic Pulse Transmission at Nanorod/Substrate Interface

In the simulation, we launched a hypersonic pulse from the substrate to gold nanodisks on top of GaN nanorod with different periodicities. We set the sound velocity in gold and GaN as 3240 m/s and 8020 m/s. Fig. 5.3(a) shows the boundary condition in our simulation, the yellow surface is the free surface (no constraints and no loads acting on the boundary) and hypersonic pulse with 150 nm pulse width [7] is launched from the blue surface below our structure. Pink surface at the bottom of the structure is set as low-reflection boundary condition to simulate the infinite space and transparent surfaces is set as periodic boundary condition so that we can only calculate the unit cell of the array structure. Theoretically the longitudinal pulse will first transfer to the fundamental AGM in the GaN nanorod, and then couple to the CAMs of gold nanodisk. The signal detected by gold nanodisk is obtained by calculating the volume change of gold nanodisk in the lateral direction. Fig. 5.3(b) is the signal detected by single gold nanodisk on top of 120 nm GaN nanorod array with a 250 nm periodicity (simulated by the finite element method, COMSOL Multiphysics, COMSOL, Inc.). Oscillation with 91 ps (11 GHz), which corresponds to the fundamental CAM of 150 nm-diameter gold nanodisk, can clearly be observed. Fig. 5.3(c) is the Fourier Transform of Fig. 5.3(b), which is the frequency spectrum of our detected signal. We can not only observe the fundamental mode (11 GHz), but also the high-order vibrational mode (22 GHz) of 150 nm gold nanodisk. It is noted that we are not able to observe the 18 GHz vibrational mode due to the poor coupling efficiency between fundamental GAM of GaN nanorod and 18 GHz vibrational mode of gold nanodisk, as we discussed in chapter 3.2.

Figure 5.3 (a) The schematic showing the boundary condition in the simulation (yellow:

free surface, blue: source surface, pink: low reflecting boundary condition, transparent:

periodic boundary condition). (b) The simulated signal detected by gold nanodisk on top of GaN nanorod arrays, with 150 nm rod diameter, 120 nm rod length and with 250 nm

periodicity. (c) Frequency spectrum of the detected signal in Fig. 5.3(b).

In order to study the effect of the array periodicity, we further calculated the transmission coefficient for hypersonic waves with 11 GHz and 22 GHz at the interface between bulk substrate and nanorod array with different periodicities (Fig. 5.4(a)). Note that the transmission coefficient is obtained by comparing the pressure in the nanorod and the initial source pressure. One can first observe that the transmission efficiency for 22 GHz hypersonic waves is lower than 11 GHz case due to the larger acoustic impedance mismatch between nanorod and substrate for 22 GHz hypersonic waves, as we discussed in chapter 3.3. Furthermore the transmission is higher for nanorod arrays with 187 nm and 350 nm periodicities for 22 GHz hypersonic waves. Based on the dispersion curves in Fig. 5.2(e), the sound velocity of SAW mode at the surface of wurtzite GaN is 3932 m/s and the hypersonic wavelength is 179 nm for 22 GHz. This result indicates that although we initially only launch the longitudinal hypersonic pulse, this longitudinal pulse may be scattered into the other surface modes at the interface between the nanorod array and substrate due to the acoustic impedance mismatch. The scattered surface modes could induce resonant transmission when the array periodicity is the integer multiple of their wavelength and lead to enhancement on the detected signal. However such resonant enhancement is not observed when the periodicity of the array is close to the wavelength of 11 GHz hypersonic waves (358 nm). This result may be attributed to the much reduced acoustic impedance mismatch between bulk substrate and nanorod for 11 GHz hypersonic waves. The magnitude of the scattered surface mode is thus not as strong as the 22 GHz case. Meanwhile, one can also observe that the transmission of 11 GHz hypersonic waves reaches its maximum for the array with a 187 nm periodicity. To understand this phenomenon, in Fig. 5.4(b) we simulated the displacement field distribution for 11 GHz hypersonic waves in the GaN nanorod array

with a 187 nm periodicity and a 120 nm rod length. As Fig. 5.4(b) shows, the displacement field is mainly located in the nanorod rather than being scattered at the rod/substrate interface. Furthermore this displacement field is very similar to the field of the extensional mode of nanorod [8-10], which suggests that the extensional-vibration-like mode of GaN nanorod may couple to each other for array with a very short periodicity. The frequency of the coupled mode would shift with periodicity. For example, the frequency of the coupled mode shifts from 11.5 GHz to 10.6 GHz by increasing the periodicity of 120 nm GaN nanorod array from 170 nm to 200 nm, as shown in Fig. 5.4(b). When the coupled mode frequency matches the frequency of the incoming hypersonic waves, an enhanced transmission was thus observed. To suppress this coupling effect, which would lead to cross-talk between neighboring pixels in the imaging array application, the most straightforward solution is to change the rod length so as to shift the extensional mode frequency away from the desired detection frequency. By increasing the rod length to 220 nm, our simulation indicated that a similar mode would be excited by 6 GHz hypersonic waves (Fig. 5.4(b)).

It also suggested that the detected signal of the fundamental vibrational mode of gold nanodisk on top of the 220 nm-length GaN nanorod is not altered by the array periodicity within our studied range.

Figure 5.4 (a) Transmission coefficient sat the interface between bulk substrate and GaN nanorod array with different periodicities for hypersonic waves with different frequencies.

(b) Displacement field distribution excited by 11.5 GHz,11 GHz, 10.6 GHz and 6 GHz hypersonic waves for the GaN nanorod arrays with 120 nm rod length and 170 nm, 187

nm, 200 nm periodicities as well as 220 nm rod length and 187 nm periodicity.

5.4 Hypersonic Pulse Transmission at Nanorod/Substrate Interface

To study the signal detected by gold nanodisk in our studied sample experimentally and verify our simulated result, we launched hypersonic pulses from the interface between GaN and sapphire substrates by 360 nm femtosecond pump pulses and

detected the gold nanodisk vibration by 720 nm femtosecond probe pulses. The light source of such a transmission-type pump-probe system [11, 12] is a mode-locked Ti:sapphire laser (Coherent Mira 900) with a 100 fs pulse width and a 76 MHz repetition rate with an output wavelength of 720 nm. The output pulses were frequency-doubled to 360 nm by a BBO crystal to serve as our pump pulses, which were used to generate the hypersonic pulses from the GaN substrate through deformation potential coupling [13-15]. With an absorption depth of 75 nm in GaN, the pulse width of the generated longitudinal acoustic pulse was approximately twice the absorption depth of the pump beam, which was 150 nm [7]. The 720 nm probe beam was responsible for the excitation of LSPs and acousto-optical detection. The upper part of Fig. 5.5 compares the measured extinction spectra of gold nanodisk on top of 120 nm GaN nanorod with different periodicities. The maximum of the extinction spectra indicates the resonant wavelength of the excited LSPs, which is independent of the array periodicity. To enhance the detection sensitivity, the wavelength of the probe beam was chosen to be 720 nm, which was near the maximum of the frequency derivative of the extinction spectrum.

Figure 5.5 Normalized Experimental extinction spectra and the derivative of spectra of the gold nanodisks on 120 nm-length nanorods with different periodicities.

Both pump beam and probe beam were incident from the bottom side of the GaN substrate, as shown in Fig. 5.6(a). The diameters of the pump and probe beams at focus were respectively 20 μm and 30 μm, which are much smaller than the area covered with nanostructures (300 μm

×

300 μm). The average power of the pump and probe at the sample surface were 40 mW and 4 mW, respectively. Fig. 5.6(b) is the background removed transient transmission changes of probe beam in our studied sample, while original trace is shown in the inset of Fig. 5.6(b). By observing the background removed transient transmission change, one can see that the transmission change start to increase at

370 ps (time delay 1) and oscillation is observed after 421 ps (time delay 2). This result can be explained by the interaction of plasmons and the hypersonic pulse [16, 17], as we discussed in chapter 4.2. After hypersonic pulse transforms into the AGM in the nanorod and enters the plasmonic field in the nanorod (time delay 1), the transient transmission starts to be modulated due to the fact that the AGM modulates the refractive index of GaN nanorod and modifies the property of LSPs (Fig. 5.6(c)). At time delay 2, the travel distance of hypersonic waves is 3.37 m, which is very closed to the averaged substrate thickness before etching (3.4 m), the AGM thus reaches the interface between gold and GaN. Since plasmonic field is well-confined at this interface, the modulation thus reaches its maximum (Fig. 5.6(d)). After hypersonic pulse passed through gold/GaN interface, part of the hypersonic waves will be transferred into the CAMs of gold nanodisk, while the rest of the hypersonic waves will be reflected from the gold/air interface with a

-shift in the phase and generate the opposite signal compared to the first part.

Therefore we not only observe another part of the bipolar signal, but also the oscillations contributed from the CAMs of gold nanodisk.

Figure 5.6 (a) The schematic showing of the incident direction of pump beam and probe beam. (b) Background removed transient transmission change for gold nanodisk on top

of GaN nanorod array with different periodicities after normalizing the gold nanodisk number for different array periodicity (Inset: the original transient transmission change).

(c), (d) Locations of the excited hypersonic pulses at time delay 1 and time delay 2 in Fig.

5.5(b), respectively.

Fig. 5.7 shows the results of time-frequency analysis of the trace in Fig. 5.6(b), which indicates that oscillation is mainly consisted by fundamental (11 GHz) and high-order (22 GHz) vibrational mode. One can also observe that the magnitude of fundamental vibrational mode (11 GHz) is increased by decreasing the periodicity of the array and the magnitude of high-order mode (22 GHz) is only enhanced in the array with

a 350 nm periodicity. The trend of the detected signals for 11 GHz and 22 GHz are in excellent agreement with our simulation (Fig. 5.4(b)). Note that the 18 GHz vibrational mode was also observed in the experiment, but its magnitude was much weaker than the 11 GHz and 22 GHz vibrational modes, as expected from our simulation result due to weak coupling between the fundamental AGM and the 18 GHz vibrational mode. We further compares the 11 GHz signal detected by the gold nanodisks with different periodicities on 120 nm-length and 220 nm-length GaN nanorods. One can see that the 11 GHz signal detected by the gold nanodisks on top of 220 nm nanorods is not dependent of the array periodicity due to the fact that the frequency of coupled extensional-like mode of GaN nanorod is far away from 11 GHz.

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