# Towards the Feasibility of Long Range Wireless Power Transfer over an Ocean Surface
## 2 Methodology and Materials
### Choice of Materials for Medium 2  
According to our experimental results, polar substances with a high loss tangent can be used as medium 2 to support propagation of surface waves if and only if medium 2 has a conductive pathway to a higher altitude, where the atmospheric electrostatic potential is always higher. This conductive pathway can be easily realized with a vertically mounted monopole antenna.  
On the other hand, a high-voltage plasma has an ability to unlock the ions in a liquid in a way to increase the surface conductivity [31; 32; 33; 34; 35]. As revealed in one of our experiments, a slightly salted tap water has been successfully used as medium 2 to realize a wireless power transfer.  
The polarity of medium 2 is the key to the feasibility of wireless power transfer. In order to form a surface electromagnetic wave on the surface of a liquid, medium 2 must be either an ionic solution or a polar substance having a finite conductivity. In the sections which follows, we will explore all the optional materials for medium 2 that may potentially lead to fulfillment of Equation (9).  
Option 1: Both media 1 and 2 are non-polar.  
If medium 1 and medium 2 are both non-polar, their conductivities are unlikely high. In this case, the first term on the lefthand side of (9) is definitely a positive number. Under this condition, it is impossible to fulfill the dispersion conditions as dictated by Equation (9).  
Option 2: Medium 1 is non-polar. Medium 2 is polar.  
If medium 1 is non-polar and medium 2 is polar, then inequality of (12) can be rewritten as  
\[Re\left(\frac{\varepsilon_{\infty,1}-j\frac{\delta_{1}}{\omega}}{\varepsilon_{ \infty,2}-\frac{\omega^{2}\omega_{p}z^{2}}{\omega^{4}+j\omega^{2}T_{2}}-j\left( \frac{\delta_{2}}{\omega}+\frac{\omega\Gamma_{2}}{\omega^{4}+j\omega^{2}T_{2} }\right)}\right)<0 \tag{14}\]  
By expanding Equation (14), the following expression is obtained:  
\[\varepsilon_{\infty,1}\left(\varepsilon_{\infty,2}-\frac{\omega_{p}}{\omega^{ 2}+\Gamma_{2}^{2}}\right)+\frac{\delta_{1}}{\omega}\left(\frac{\delta_{2}}{ \omega}+\left(\frac{\Gamma_{2}}{\omega}\right)\frac{{\omega_{p}}^{2}}{\omega^ {2}+\Gamma_{2}{}^{2}}\right)<0 \tag{15}\]  
The implication of (15) is very easy to interpret if we apply some approximation. One of the approximations that we can use is to truncate \(\delta_{1}\). Since medium 1 is non-polar, its ion density will be very low, and there is no reason to factor in \(\delta_{1}\) if medium 1 is just air or an insulator with a negligible loss tangent. Then, the second bracketed term on the left of (15) will be zero. What we have left is for the first bracketed term on the left of (15) to be negative, or equivalently,  
\[\varepsilon_{\infty,2}\ll\frac{\omega_{p}}{\omega^{2}+\Gamma_{2}{}^{2}} \tag{16}\]  
Inequality (16) suggests that the higher ratio \(\omega_{p}/\omega\) tends to support propagation of surface electromagnetic waves along the interface. By surface electromagnetic waves, it means an evanescent wave with the maximum electric field at the propagation interface [36].