Interaction in 1-D Gold Nanogratings

Although 2-D gold nanodisks on top of GaN nanorod would be the ultimate choice for our hypersonic detector, we still begin our discussion from the 1-D gold nanogratings on GaN plain substrate, which is first described in chapter 2. Here we choose the nanogratings with 590 nm periodicity while the height and width of the slit are both 70 nm. Fig. 4.1(a) shows the transmission spectrum of the sample, which suggests that EOT occurred around 700 nm. Theoretically hypersonic pulse would modify the refractive index of the sample and shift the transmission spectrum. By choosing the probe wavelength closed to the maximum of the slope of the spectrum, such shift would induce the maximum of the transmission change (better detection sensitivity). Therefore the absolute value of the wavelength derivative of the measured transmission spectrum shown in Fig. 4.1(a) can roughly provide a guideline to estimate

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the wavelength dependent transmission modulation strength induced by the refractive index change. From Fig. 4.1(a), 670 nm and 720 nm are two most sensitive wavelengths for EOT modulation. In order to study the field intensity distribution at these two wavelengths, we performed a FDTD [1] simulation to understand the field intensity distribution at 670 nm and 720 nm respectively. The refractive index values of gold and GaN were taken from [2] and [3], respectively. Plane waves are incident from the substrate side with TM polarization (x-direction in Fig. 4.1(b)). From the FDTD simulations shown in Fig. 4.1(b), we can observe that the SPP field exists mainly at gold/GaN interfaces for the 720 nm case. However, the SPP field exists only at gold/air interface for the 670 nm case. Since there is no field below the gold grating for the 670 nm case, the SPP field is only sensitive to the environment change above the gold. In order to acoustically modulate the refractive index of GaN and to maximize the EOT modulation through the opto-acoustic effect [4], we chose the operating probe wavelength as 720 nm.

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Figure 4.1 (a) Experimental normalized transmission spectrum and the absolute value of its derivative of the studied sample. (b) Simulated results showing the energy field

distribution at 720 nm and 670 nm wavelength respectively.

A femtosecond time resolved spectroscopy [5–7] was used to generate both hypersonic pules and EOT in gold nanogratings. The light source of our spectroscopy is a 720 nm mode-locked Ti:sapphire laser (Coherent Mira 900) with a 100 fs pulse width and a 76 MHz repetition rate. As we mentioned in chapter 1, there are two laser beams in the system. One of them is pump beam, which is used to excite the hypersonic pulse in GaN. Another one is probe beam, which detects the pump-induced optical change.

There are many mechanisms responsible for the optical excitation of hypersonic pulse,

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including thermal expansion [8–10], deformation potential coupling [11,12], and piezoelectric coupling [13–15]. For a GaN single crystal, deformation potential coupling is the dominant mechanism for hypersonic pulse generation [16,17]. Once the above-bandgap pump light was absorbed, free carriers were excited and caused a mechanic strain/stress in the semiconductor [18]. Since our GaN crystal is grew on c-plane sapphire substrate, the optically induced mechanic strain/stress could launch hypersonic pulse from the GaN/sapphire interface. The pulse width of the hypersonic pulse is thus equal to the twice of the penetration depth of pump beam in the GaN single crystal, which was 150 nm.

In order to generate hypersonic pulse in GaN, the pump beam is set to be above the bandgap energy of GaN. As shown in Fig. 4.2, the mode-locked laser beam is thus first passed through the beta barium borate (BBO) crystal in order to generate frequency-doubled pump beam (360 nm) for generating hypersonic pulse in GaN. The unconverted laser beam is chose as probe beam (720 nm), which is used to generate EOT and detect the pump-induced optical change in the sample. These two laser beams are separated by the dichromatic mirror. The optical path between pump beam and probe beam can be modified by the delay stage. Probe beam is then passed through the telescope in order to make sure that both pump beam and probe beam will be focused at the sample. Since pump beam is modulated by an AO modulator, the optical change detected by probe beam would also be modulated by the same frequency. Therefore the transmitted probe beam collected by the detector is sent to the lock-in amplifier for demodulation. The diameters of pump and probe beams at focus were 10 µm and 25 µm, respectively. With a nanostructure area covering 300 µm×300 µm, the focused laser spot sizes were much smaller than the nanostructure size and we made sure that all the

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measured signals were through the nanostructure. The pump and probe average powers at the sample surface were 50 mW and 10 mW, respectively.

Figure 4.2 Schematic showing of optical transmission type of femtosecond time resolved spectroscopy (inset: pump beam and probe beam are incident from the bottom

of the sample).

With the femtosecond time resolved spectroscopy, excited free carriers generated stress with a mechanic strain on the order of 10⁻⁴, which is calculated based on Eq. (18) in [16]. Fig. 4.3(a) shows the transient transmissions change with TE polarized probe beam and with TM polarized probe beam measured in different experiments. The transient transmission change at zero time delay is due to carrier excitation by the pump beam and the exponentially-decaying background is caused by carrier relaxation. The transient transmission difference in the TM case (x-direction in Fig. 4.1(b)) is higher than the TE case (y-direction in Fig. 4.1(b)), which suggests that EOT is induced by TM polarized incident light. At the same time, a bipolar shaped signal between 400 ps and 500 ps appears in the TM case for all experimental traces. Fig. 4.3(b) shows the carrier-dynamics background-removed bipolar shaped signal from Fig. 4.3(a). Based on

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the delay time in Fig. 4.3(b), we are able to calculate the position of the hypersonic pulse in GaN. Fig. 4.3(c) shows the calculated result, which indicates that the corresponding delay time of this bipolar shaped signal agrees well with the acoustic traveling time from the GaN/sapphire interface to enter and leave the SPPs field below the gold respectively [19]. Based on the measurement, we observed that the transmission was first decreased and then increased by the hypersonic pulse. The transmission change induced by hypersonic pulse was close to zero at ~465 ps due to the fact that the center of the hypersonic pulse was near gold/air interface. The hypersonic pulse was then reflected from this interface with a sign change [20], which causes the sign change of the refractive index change and thus the sign change of the transmission modulation.

Figure 4.3 (a) Experimentally measured transient transmission in TM and TE polarized incident light. (b) Background removed transient transmission change between 300 ps

to 600 ps. (c) Schematic showing the locations of hypersonic pulse at different time delays.

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