# Cross-Medium Photoacoustic Communications: Challenges, and State of the Art
## 2 Photoacoustic Signal Generation
### Plasma Size and Shape  
The plasma formation is associated with breakdown shockwave, cavitation bubble expansion and collapse, thus creating acoustic signal. The generated acoustic signal depends on the plasma, and the size and shape of the plasma need to be controlled to control the acoustic signal. The plasma length (\(z_{max}\)) reached at maximum irradiance for a laser pulse with Gaussian shape and beam profile is [45],  
\[z_{max}=\frac{\pi\omega_{0}^{2}}{\lambda}\sqrt{\beta-1} \tag{5}\]  
where, the normalized laser pulse energy, \(\beta=\frac{E}{E_{th}}=\frac{J}{I_{th}}\) and \(\frac{\pi\omega_{0}^{2}}{\lambda}\) is the Rayleigh range. The dependency of maximum plasma length (\(z_{max}\)) on the focusing angle (\(\theta\)) is given in [55] as,  
\[z_{max}=\frac{\lambda}{\pi\tan^{2}\frac{\theta}{2}}\ \sqrt{\beta-1} \tag{6}\]  
The dependence of \(z_{max}\) on the laser wavelength, pulse energy, focusing spot size and angle is clearly visible in Equations (5) and (6); however, the dependence of \(z_{max}\) on laser pulse duration is implicit. Since the breakdown threshold varies with pulse duration, as shown in Table 1, determining the normalized laser pulse energy requires knowledge of the breakdown threshold at the pulse duration of interest, which in essence affects \(z_{max}\). In Figure 2, experimentally measured plasma lengths generated by 6 ns and 30 ps laser [55] are compared with the calculated values from Equation (6). For picosecond pulses, we can observe that the calculated plasma length is nearly identical to the experimentally measured values but is not as close for nanosecond pulses. At equal normalized laser pulse energy \(\beta\), the nanosecond plasma is longer than the picosecond plasma. This is in contrast with [PERSON]'s [45] moving breakdown model where the plasma length is predicted to be independent of pulse duration. One reason for the relative deviation of nanosecond plasma can be the breakdown threshold which is influenced by UV radiation emitted by the plasma. The breakdown threshold decreases due to plasma radiation for nanosecond pulses. However, the picosecond breakdown process is less influenced by plasma radiation and remains approximately constant during breakdown. As a result, the plasma length generated by nanosecond laser pulse grows further than predicted using Equations (5) and (6), which assume a constant threshold. Optical aberration and diffraction-limited calculations are another cause for getting longer plasma length from experiments. The dependence of plasma size and shape on laser pulse energy and the focusing geometry is investigated in [44; 55; 58; 59; 60; 61; 62]. In [55], the authors showed that the increase of plasma length with growth in laser pulse energy is more evident for picosecond pulses than for nanosecond pulses. For the same laser pulse energy, plasma generated by a picosecond laser is always longer than the nanosecond laser because of the lower breakdown threshold (see Table 1). However, nanosecond laser generated plasma lengths are shorter than picosecond laser generated plasma at equal normalized laser pulse energy (Figure 1). The focusing angle (\(\theta\)) and focal spot radius (\(\omega_{0}\)) are inversely related and the plasma length is strongly dependent on the focusing angle and spot size. Increasing the focusing angle decreases the plasma length for a fixed laser pulse energy. A shorter plasma length implies a more spherical shape; the shape becomes more cylindrical as the plasma length elongates. Unlike the case of continuous plasma on solid targets, multiple plasmas can be formed at positions along the focal volume in water. [PERSON] et al. [59] have summarized the reasons for multiple plasma formation and deduced that it is related to the focusing geometry of the laser beam. They demonstrated that the discrete and irregular plasma created in numerous locations could be transformed into continuous and stable plasma with a single core fixed at the laser focal point by increasing the laser focusing angle.