Conflict of interest

notable change in the edges of the phononic band gaps. Second, here in the plane wave case, the thermal stress is absent, so the lattice constants will increase

The reflectance R versus ωa=2π cT for P-wave (red lines) and S-waves (blue lines) at temperatures effects (a)

according to Eq. (25) and can make change in the width of the phononic band gaps

In this chapter, we used the transfer matrix method and Bloch theory to compute and study the propagation of mechanical waves through different 1D PnC structures with thermal effects. We performed numerical simulations to calculate the reflection coefficient and dispersion curves for the 1D PnC structure. We have discussed and studied the effects of many parameters on the phononic band gaps. The effects of temperature and defect mode on the properties of the PnC and on the localized modes were studied for both SH-waves and in-plane waves. The output

1. The defect layer has a different and unique effect on the number of localized modes inside the phononic band gaps for both plane and SH-waves. The effects of the incident angle, thickness ratio on the propagation, and localization of elastic waves were studied. The number of localized modes was increased with increasing the defect layer thickness. Also, the material type of the defect layer has an obvious effect on the width and number of resonant defect modes, where the localized modes were increased by using a material with low elastic constant. Inserting a defect layer inside the perfect structure facilitates the process of localized modes generation inside the PnC structure. Also, it can be utilized in many potential applications such as acoustic filter and waveguides and can be applied to produce new types of laser called phonon laser with low

2. Results revealed that temperature increment has a significant effect on the phononic band gaps and on the number of the localized modes inside the PnC structure, especially for plane wave, where the P-waves velocity and lattice constants are directly related to temperature increment. The contribution of phonons in the thermal conductivity of a solid can be limited by the existence of phononic band gaps, which could be very useful for the thermoelectric

thermal effects especially in the hypersonic PnCs regime.

as well.

24

Figure 10.

T = 35°

4. Conclusions

C and (b) T = 180°

C.

Photonic Crystals - A Glimpse of the Current Research Trends

results can be stated as follows:

The authors declare that there is no conflict of interest.
