# Cross-Medium Photoacoustic Communications: Challenges, and State of the Art
## 4 Properties of Nonlinear Photoacoustic
### Acoustic Pulse Duration and Dominant Frequency  
The generated acoustic pulse duration is dependent on plasma volume where the higher laser pulse energy and larger plasma volume produce longer acoustic pulses. However, the acoustic pulse length is not necessarily the same in all acoustic propagation directions. A laser pulse can produce a disc-shaped ionized volume from only GVD-induced longitudinal compression to generate breakdown [70]. This can produce longer acoustic pulse lengths in directions parallel to the plane of the disc. Alternatively, for applications that require short underwater propagation distances, optical pulses with little or no frequency chirp can be created that rely solely on NSF effects to achieve laser-induced breakdown intensities [70]. [PERSON] et al. [73] numerically and experimentally showed that the nonlinear energy deposition and plasma density distribution depend on the input pulse chirp and focusing conditions. First, they demonstrated that the lowest optical transmission corresponds to negatively pre-chirped pulses that form a plasma with the maximum possible energy. Then further negative pre-chirping of the laser pulse results in a plasma volume with maximized length where the electron density is still relatively high. Finally, plasma densities are maximized at the expense of plasma channel length for even greater negative values of the input chirp.  
The propagation of acoustic pulses is dependent on the overall distribution of their component frequencies, specifically on the frequency with the greatest power within that distribution, represented by \(f_{peak}\). A smaller \(f_{peak}\) corresponds to a longer range because the attenuation of a propagating acoustic pulse is proportional to the square of \(f_{peak}\). A way to reduce \(f_{peak}\) by more than an order of magnitude (from 200 kHz to 15 kHz) is developed by NRL [74]. The key to low-frequency acoustic generation is shaping the underwater plasma volume, where more elongated volumes produce longer-duration acoustic pulses containing more energy at low frequencies. [PERSON] et al. proposed a technique to generate meter-scale elongated plasma utilizing two laser pulses with energy spectral density (ESD) centered near 1 kHz [75]. In this technique, a first laser pulse is fired into the water to form an underwater optical filament coinciding with a low energy plasma. The second laser pulse is used to heat the filament plasma, causing the formation of an extended superheated plasma volume. The two laser pulses can be delivered simultaneously or sequentially, with the second pulse following up to the filament plasma lifetime after the first. The two-laser pulse technique enables the generation of much longer energetic plasmas, of order 1 m in length or longer, than the plasmas generated with a single pulse, which have a length up to order 5 cm [75].  
The acoustic pulse duration (\(\tau_{ac}\)) in any direction of acoustic propagation is dependent on the plasma dimension (\(d\)) in that direction and the initial shock propagation speed (\(\overset{\rightarrow}{V}_{shock}\)) [75],  
\[\tau_{ac}\approx\begin{array}{c}d\\ \overset{\rightarrow}{V}_{shock}\end{array} \tag{21}\]  
Therefore, spherical plasma can generate isotropic acoustic pulse duration, and only increasing laser pulse energy is an inefficient means to increase the pulse duration because \(\tau_{ac}\sim E^{1/3}\). On the other hand, elongated plasmas produce anisotropic pulse duration even though \(\overset{\rightarrow}{V}_{shock}\) is similar in all directions. This is because the elongated plasma has a shorter dimension \(d_{\perp}\) in a direction normal to the laser beam axis than the dimension \(d_{\parallel}\) in a direction parallel to the beam. Thus, for elongated plasma \(\tau_{\parallel}>\tau_{\perp}\).