## 1 Introduction
\[\mathbf{J}=\sigma\mathbf{E}+\hat{\varepsilon}\frac{\partial\mathbf{E}}{ \partial\mathbf{t}}, \tag{1}\]  
where \(\mathbf{J}\) (A-m\({}^{-2}\)) is current density vector, \(\sigma\) (S-m\({}^{-1}\)) is conductivity, \(\mathbf{E}\) (V-m\({}^{-1}\)) is electric field strength, and \(\hat{\varepsilon}\) (-) is complex permittivity. The interaction of the biological environment with the EMF can be described by the complex permittivity in the following form:  
\[\hat{\varepsilon}(\omega)=\varepsilon^{\prime}-j\varepsilon^{\prime\prime}= \varepsilon^{\prime}-j\frac{\sigma}{\omega\varepsilon_{0}}=\varepsilon^{ \prime}(1-j\tan\delta)=\varepsilon^{\prime}\bigg{(}1-j\frac{\varepsilon^{ \prime\prime}}{\varepsilon^{\prime}}\bigg{)}, \tag{2}\]  
where \(\omega\) (rad-s \({}^{-1}\)) is the angular velocity, \(\varepsilon_{0}\) (F-m\({}^{-1}\)) is the vacuum permittivity, \(\varepsilon^{\prime}\) is the real component of the complex permittivity (it is the relative permittivity of the dielectric \(\varepsilon_{\mathrm{r}}\), expressing the amount of energy stored in the unit volume of the dielectric during exposure to the field), and \(\varepsilon^{\prime\prime}\) is an imaginary component representing energy losses in the dielectric. By the value of the loss factor (tan \(\delta\)), which expresses the ratio of the imaginary and real components of the complex permittivity, we classify high-loss dielectric (tan \(\delta>>1\)) and low-loss dielectric (tan \(\delta<<1\)) [8; 9]. When studying EM waves in a biological environment, we are considering a linear, homogeneous, isotropic, and lossy environment. By applying the rotation vector operator to the first and second Maxwell's equations and then using the third and fourth Maxwell's equations, we can derive the Helmholtz wave equations outside the source. \[\
abla^{2}\mathbf{E}-\mu\;\sigma\frac{\partial\mathbf{E}}{\partial\mathbf{t} }-\mu\;\varepsilon\frac{\partial^{2}\mathbf{E}}{\partial t^{2}}=0, \tag{3}\]\[\
abla^{2}\mathbf{H}-\mu\ \sigma\frac{\partial\mathbf{H}}{\partial\mathbf{t}}-\mu\ \varepsilon\frac{\partial^{2}\mathbf{H}}{\partial t^{2}}=0, \tag{4}\]  
where \(\mathbf{E}\) (V\(\cdot\)m\({}^{-1}\)) is electric field strength, \(\mathbf{H}\) (A\(\cdot\)m\({}^{-1}\)) is magnetic field intensity, \(\sigma\) (S\(\cdot\)m\({}^{-1}\)) is conductivity, \(\mu\) (H\(\cdot\)m\({}^{-1}\)) is permeability, and \(\varepsilon\) (F\(\cdot\)m\({}^{-1}\)) is permittivity. When dealing with field vectors that exhibit harmonic behaviour over time, we use the complex form to represent their spatial and temporal dependencies. In this context, the quantities \(\mathbf{E}_{\mathrm{m}}\) and \(\mathbf{H}_{\mathrm{m}}\) denote the spatially dependent complex amplitudes of the complexors \(\mathbf{E}\) and \(\mathbf{H}\). Wave equations take the form of their partial derivatives with respect to time, divided by the time factor \(\mathrm{e}^{\mathrm{i}\omega t}\), after substituting the complex expression. \[\
abla^{2}\mathbf{E}_{\mathrm{m}}-j\omega\mu\sigma\ \mathbf{E}_{ \mathrm{m}}+\omega^{2}\mu\varepsilon\mathbf{E}_{\mathrm{m}}=\
abla^{2} \mathbf{E}_{\mathrm{m}}-\mathrm{j}\omega\mu(\sigma+\mathrm{j}\omega \varepsilon)\ \mathbf{E}_{\mathrm{m}}=\
abla^{2}\mathbf{E}_{\mathrm{m}}+\mathbf{k}^{2} \mathbf{E}_{\mathrm{m}}=0, \tag{5}\] \[\
abla^{2}\mathbf{H}_{\mathrm{m}}-j\omega\mu\sigma\ \mathbf{H}_{ \mathrm{m}}+\omega^{2}\mu\varepsilon\mathbf{H}_{\mathrm{m}}=\
abla^{2} \mathbf{H}_{\mathrm{m}}-\mathrm{j}\omega\mu(\sigma+\mathrm{j}\omega \varepsilon)\ \mathbf{H}_{\mathrm{m}}=\
abla^{2}\mathbf{H}_{\mathrm{m}}+\mathbf{k}^{2} \mathbf{H}_{\mathrm{m}}=0, \tag{6}\]  
where the constant \(\mathbf{k}\) is known as the wave vector and describes the propagation of a harmonic wave in a dissipative medium.