## 4 Discussion  
In this study, composite transducers with larger diameters (2 cm, 5 cm, and 8 cm) were used for the experiments, and higher peak amplitudes of the shock waves were successfully achieved. The three optoacoustic transducers exhibited a similar pattern of increased peak pressures with an increase in diameter. As the diameter of the transducer increases, the expansion of the laser energy also increases, resulting in higher peak pressures. Under the same laser energy (800 mJ/pulse), the transducer with an 8 cm diameter produced the maximum positive and negative amplitudes of 53 MPa and \(-25\) MPa, respectively. The laser-generated acoustic pressure increased with the increased input of laser energy. The higher amplitudes of shock waves obtained in this study have the potential for utilization in many applications, such as transcranial studies. The pattern of the shock waves was similar in all three transducers. Optoacoustic-generated shock waves have a very short duration of 0.1-0.4 \(\upmu\)s [2] compared to shock waves from other sources (electrohydraulic, electromagnetic, and piezoelectric) [15; 16]. The shock wave observed in this study showed a duration of 0.2 \(\upmu\)s. (Figure 2). The characteristic feature of the shock wave with a broad frequency distribution was observed in the frequency domain of the signals. In Figure 2, the frequency spectra show a similar pattern with a center frequency and \(-6\) dB bandwidth less than 10 MHz, although the composite transducer with a 2 cm diameter shows large amounts of energy at a frequency range of less than 2 MHz. In another study involving smaller transducers with diameters  
Figure 5: Scatter graph of predicted and experimental (measured) values of the CNT-PDMS composite transducer for different diameters. The dotted lines correspond to the predicted values, while the marks represent the measured values, indicating an agreement between them. This prediction was made at the energy levels of 600 mJ/pulse, 700 mJ/pulse, and 800 mJ/pulse. in millimeters, similar peak amplitudes and spectra were achieved but at a higher center frequency of around 20 MHz [4]. As shock waves constitute higher frequency components, they attenuate faster at high frequencies [8]. This explains the faster decay of the shock wave. When the relationship between laser energy and different diameters of the composite transducer was analyzed, it was observed that the measured peak pressures have a linear relationship with the laser energy, which is also confirmed in previous studies [18]. However, in negative peak pressures, the 2 cm transducer was saturated at higher laser energy levels (Figure 3) [10]. We observed another important phenomenon: at a lower laser energy, the 5 cm and 8 cm transducers show almost similar positive and negative pressures, but when the laser energy is increased, there is a difference between the peak pressures. The CNT-PDMS films could withstand higher optical fluence, and this endurance of CNT-PDMS makes it possible to increase the laser energy to the maximum available optical energy [10]. Otherwise, materials with less laser fluence can be damaged when the laser beam's energy is increased [2]. Figure 5 shows an agreement between the measured and predicted peak amplitudes of the shock waves with the different diameters of the CNT-PDMS composite transducers. The reference laser energy values used for predicting peak amplitudes are higher values over 600 mJ/pulse. In an experimental setting, higher energy values are usually employed as it is useful to make predictions at these levels. For lower energy values, there is little difference; therefore, it is not very practical to make predictions at these levels. The comparison between the shock wave signal of the CNT-PDMS composite transducer and extracorporeal shock wave therapy (ESWT) shows that the former has a narrower beam width than the latter. The shock wave generated by the CNT-PDMS composite transducer has a beam width of 2.5 mm in the axial direction and 0.70 mm in the lateral direction (Figure 4).