# Cross-Medium Photoacoustic Communications: Challenges, and State of the Art
## 2 Photoacoustic Signal Generation
### Laser-Induced Breakdown  
The laser-induced breakdown in transparent liquid (e.g., water) is a nonlinear process where a combination of photoionization, inverse Bremsstrahlung absorption, and cascade (avalanche) ionization produces free electrons in larger amounts and, together with the positive ions, form a plasma [41; 42; 43]. High-intensity laser pulses can create underwater plasma by focusing into a small spot so that the laser irradiance (\(I\)) surpasses the breakdown threshold irradiance. The laser irradiance can be calculated from the peak power of the laser divided by the focal spot area. The peak power of the laser is measured by the ratio of laser pulse energy (\(E\)) and pulse duration (\(\tau_{L}\)). Thus, the laser irradiance is [44],  
\[I=\frac{E/\tau_{L}}{A_{f}} \tag{1}\]  
Here, the focal spot area, \(A_{f}=\pi\omega_{0}^{2}\) where spot radius (\(\omega_{0}\)) can be calculated by,  
\[\omega_{0}=\frac{\lambda fM^{2}}{\pi\left(D/2\right)} \tag{2}\]  
In Equation (2), \(f\) is the focal length of the lens, \(D\) is the diameter of the laser beam, \(\lambda\) is the wavelength of the laser beam, and \(M^{2}\) is the beam propagation ratio. \(M^{2}\) signifies how close a laser is to a single-mode TEM00 beam and defines how small a beam waist can be focused. When such beam propagation ratio, \(M^{2}\), equals 1, it indicates the perfect Gaussian condition where the focused spot is diffraction limited. Thus, the diffraction-limited focus spot radius is,  
\[\omega_{0}=\frac{2\,\lambda}{\pi}.\frac{f}{D} \tag{3}\]  
Based on Equation (3), in order to decrease the focal spot radius, a lens with a shorter focal length needs to be used or the laser beam diameter needs to be increased. Here, the ratio of focal length to beam diameter is known as \(f\)-number (\(f/\#=f/D\)). \(f\)-number can be calculated by the focusing angle (\(\theta\)),  
\[f/\#=\frac{1}{2\times\tan{\theta/2}} \tag{4}\]  
From Equations (3) and (4), we can observe that the \(f\)-number and the focus spot radius will increase if the focusing angle decreases. Similarly, the \(f\)-number and the focus spot radius will decrease if the focusing angle increases. The laser irradiance can be boosted to exceed the breakdown threshold by increasing the pulse energy or decreasing the \(f\)-number. The breakdown threshold is related to the laser parameters and the dependence of wavelength, pulse duration, and focusing geometry on breakdown threshold for plasma formation is investigated theoretically and experimentally in [41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56]. Table 1 shows the experimental breakdown thresholds for water for different pulse durations, wavelengths, and focusing angles with measured spot diameter. From Table 1, we can observe that the irradiance threshold values are in the order of \(10^{11}\) W/cm\({}^{2}\) for a few nanosecond pulse durations and rise up to \(10^{13}\) W/cm\({}^{2}\) for 100 femtosecond pulse duration. The energy threshold for breakdown decreases by reducing the pulse duration, and the irradiance threshold increases. The irradiance required for optical breakdown for 30 ps laser pulses is on average 5.9 times higher than 6 ns laser pulses [55]. The optical breakdown threshold is slightly higher at 1064 nm than 532 nm. The breakdown threshold at 532 nm for 6-ns pulses is 0.57 times lower than the corresponding value at 1064 nm, while it is 0.83 times lower for 30-ps pulses [55]. [PERSON] et al. [57] also observed similar results. All the spot sizes in Table 1 are measured in the experiment. The measured and diffraction limited spot size is nearly identical for small focusing angles. However, the measured spot size deviates from diffraction-limited spot size calculation for large focusing angles. [PERSON] et al. [55] did not observe any systematic dependence between breakdown threshold and spot size, which is in contrast to the work of [PERSON] [48] and [PERSON] et al. [46].