# Cross-Medium Photoacoustic Communications: Challenges, and State of the Art
## 4 Properties of Nonlinear Photoacoustic
### Broadband Signal  
Underwater acoustic signals can be generated from a remote, aerial location by using a high-energy pulsed laser. The nonlinear PA signal generation is more efficient, i.e., greater source level but less controlled approach for producing underwater acoustic signals than the linear mechanism. We have experimentally investigated the nonlinear PA signal by a 1064 nm, 6 ns pulse duration Q-switch Nd:YAG laser. Underwater acoustic signal is generated by the laser focusing with a 7.5 cm lens in water and plasma is created approximately 2 cm below from the water surface. A hydrophone with frequency range 15 Hz to 480 kHz is placed at \(0^{\circ}\) angle relative to the norm at the incident point of the laser  
Figure 8: General geometry for linear optoacoustic communication from air to underwater for a wavy water surface. Figure 9: Optimum position of laser beam incident angle and receiver observation angle for flat water surface, (**a,b**) and wavy water surface (**c**). The figure has been redrawn from [67]. beam to monitor the generated acoustic signal. Figure 10a illustrates the acoustic signal generated from a single laser pulse. After laser pulsing, little flashes of white light were noticed in the water, which is connected with the plasma generated during each optical breakdown event. The frequency spectrum of the generated acoustic signal is shown in Figure 10b. We can observe that a single laser pulse produces a broadband acoustic signal with considerable acoustic energy. The frequency components of bubble oscillation, particularly the delay between the breakdown and bubble shock waves, resulting in a variation of the frequency content, complicating the acoustic spectrum. The generated acoustic signal and its associated spectral character depend on the laser parameters, and thus can be controlled by the proper choice of the laser modulation parameters, i.e., laser wavelength, pulse energy, repetition rate, and laser beam focusing. [PERSON] et al. (2018) investigated and demonstrated a means of deterministically controlling the spectrum of the underwater acoustic signal by varying the laser pulse repetition rate. The following equation gives the general time domain expression for the pressure waveform as a function of range and vertical observation angle,  
\[ \begin{array}{ll}p(r,\theta_{v},\ t)=&P_{m}(r,\theta_{v})\sum\limits_{n=0}^{N -1}\exp\left[-\frac{(t-nT_{B})}{\tau(r)}\right]u(t-nT_{R})\\ &+\sum\limits_{j}P_{Bj}(r,\theta_{v})\sum\limits_{n=0}^{N-1}\exp\left[-\frac{(t -T_{Bj}-nT_{R})}{\tau_{Bj}(r)}\right]\times u\big{(}t-T_{Bj}-nT_{R}\big{)}\end{array}  \tag{16}\]  
where,  
\(N=\) number of laser pulses,  
\(T_{R}=\) laser pulse repetition period,  
\(T_{Bj}=\) time delay between peak of plasma generated transient and peak of _jth_ cavitation generated transient,  
\(P_{m}(r,\theta_{v})=\) peak pressure of plasma generated acoustic transient as a function of range,  
\(P_{Bj}(r,\theta_{v})=\) peak pressure of the _jth_ cavitation generated acoustic transient as a function of range,  
\(\tau(r)=\) time constant of plasma-generated acoustic transient as a function of range,  
Figure 10: (**a**) Acoustic signal generated from a single laser pulse and (**b**) frequency spectrum of that acoustic signal. \(\tau_{Bj}(r)=\text{time constant}\) of the _jth_ cavitation generated acoustic transient as a function of range. In Equation (16), the pressure waveform contains an optical breakdown pressure term followed by a summation of time-delayed, cavitation bubble generated pressure terms; each pressure term is a scaled exponential acoustic transient.