The basic effects of wave propagation in a PC structure can be described by looking at the direction of power propagation in the PC structure (Notomi, 2000). The main difference between wave propagation in a conventional homogeneous mass medium and propagation in a PC is therefore caused by the unique variation in the direction of the group velocity for PC modes at different wavelengths and directions. Figure 11 shows the operating range of some of the spatial dispersion properties of a PC disk on its 2D band structure in the plane. The PC in Figure 11 consists of a 45° rotating square grid of air holes in the Si on an OSI wafer, and the isofrequency contours for the first TE-type mode of this PC are shown. Electromagnetic waves are generated by the radiated power of the current-carrying conductor. In conductors, some of the energy generated escapes and propagates in free space in the form of an electromagnetic wave, which has an electric field, a magnetic field and a direction of propagation varying orthogonally with respect to each other. Phase velocity is the rate at which a constant phase point of the wave moves for a discrete frequency. The angular frequency ω cannot be chosen independently of the wavenumber k, but the two are related by the dispersion relation: this wave propagation can be classified as where i = −1 as a function of the frequencies. This equation is then used to define the signature of the wave nucleus (see section 4.3) and the Hamilton/Schrödinger operator (see section 5.10). EM waves transfer energy by absorbing and returning wave energy through atoms in the medium. The atoms absorb the energy of the waves, are subjected to oscillations and transmit the energy by re-emitting EM of the same frequency.

The optical density of the medium influences the propagation of EM waves. When the ground wave moves away from the transmitting antenna, it is dampened. In order to minimize this loss, the transmission path must pass over the ground with high conductivity. In terms of this condition, seawater should be the best conductor, but it has been observed that large water reservoirs in ponds, sandy or rocky bottoms have maximum losses. A bump moves along the surface of the earth. These waves are vertically polarized. Therefore, vertical antennas are useful for these waves. When a horizontally polarized wave propagates as a ground wave due to the conductivity of the Earth, the electric field of the wave is short-circuited.

Suppose the receiving antenna receives all the power generated by the radio waves without loss. Let be the maximum power received by the receiving antenna under adjusted load conditions. If the effective aperture is the receiving antenna, we can write as, Closely related to the wave equation, the Schrödinger equation in equation (14) prescribes the evolution of a quantum particle via the u(x,t):L2(M)×R+→C, so that |u(x, t)|2 is interpreted as the probability density function of the particle (p.d.f.) at position x and time t: where βB=π/Λ is the Bragg wavenumber for a first-order lattice. It refers to the Bragg wavelength through the Bragg condition λB = 2n ̄Λ and can be used to define the Bragg frequency as ωB = πc / (n ̄Λ). The cross-sectional variations for the two opposite waves are controlled by the same modal distribution F(x,y) in a singlemode fiber. The maximum propagation range of ground waves depends not only on the frequency, but also on the power of the transmitter. When ground waves pass through the Earth`s surface, they are also called surface waves. The propagation of the waves is determined by the wave equation in which u(x, t) measures the amplitude of the displacement at x at time t: the inelastic nature of the liquid layer also leads to a weakening of AW, whose size depends on frequency, density and viscosity. In high-frequency SAW devices, this attenuation is much more severe than in shear mode devices: Rayleigh waves have a normal essential surface component that creates compression waves in a contact liquid and dissipates most of the SAW energy (the attenuation range is about 4 dB/cm-MHz). Therefore, liquid phase measurement with SAW devices is limited to frequencies below approximately 10 MHz [23,62].