## 3 Numerical Results and Discussion
### Incident Angle  
Because the incidence angle may effectively adjust the thermal radiation spectrum, the developed structure could be used as a selective thermal emitter in the THz regime [51]. As it is significant for a range of applications, and adjusting the incidence angle contributes by enabling directional emission, tuning emission spectra, and providing dynamic control over the thermal radiation. These capabilities enhance the versatility and effectiveness of THz technology in various fields. The examination of the structure's angular thermal radiation is consequently important in this case. According to the Fresnel Law, the angle of the incident can change the resultant thermal radiation. So, the direction of the incident beam which will be separated into two TE and TM modes can significantly affect the consequent radiation. Moreover, as thermal radiation is spatially incoherent, employing such periodic structures enables us to control the amount of thermal radiation in specific frequency ranges, i.e., increase, decrease, or completely stop it. The achieved power spectrum (radiance) curves in Figure 3 demonstrate some PBGs, as well as a well-behaved frequency region as maximum radiance, for the TE polarized wave under different incident angles. According to Figure 3, the maximum thermal radiation occurs at any angle of the incident beam. As shown, the maximum radiation range, of which the radiance value reaches 1, is considered from 3.63 THz to 4.73 THz \(\theta=0\), with the width \(\Delta f=1.1\) THz. As the \(\theta\) increases, the width of maximum thermal radiation becomes wide and wider, insofar as the width reaches \(\Delta f=\)1.45 THz at \(\theta=85^{\circ}\). Furthermore, the maximum range moves towards upper frequencies as \(\theta\) increases. It is obvious in the figure that the frequencies of the upper band-edges moves faster than the frequencies of the lower band-edges when \(\theta\) increases. As demonstrated in Figure 3, two PBGs emerged in the radiance spectrum as Gaps I and II, which are also tuned by the incidence angle changes. For example, Gap I is placed at 3.4 THz for \(\theta=0\), while it is placed at 3.63 THz for \(\theta=85^{\circ}\). On the other hand, the radiance minimum value of Gap II reaches zero by increasing the incidence angle so that the gap becomes a complete PBG at \(\theta=85^{\circ}\). The most remarkable property in Figure 3 relates to the dashed rectangular area on the  
Figure 2: The transmittance spectrum of the 1D MQP PC, consisting of layers \(A=\) InSb, \(B=\) Teflon, \(C=\) ENG and \(D=\) ZrO\({}_{2}\) (with FB and ML arrangements), is plotted as a function of frequency. The thicknesses of the layers are \(d_{A}=28\) μm, \(d_{B}=12\) μm, \(d_{C}=3\) μm, and \(d_{D}=12\) μm, and the number of periods is \(M=4\) under the normally incident beam at different temperatures T = (**a**) 150 K, (**b**) 200 K and (**c**) 250 K.  
maximum thermal radiation ranges. Here, the radiation spectrum remains invariant in the frequency range \(f_{a}=3.97\) THz to \(f_{b}=4.51\) THz (\(\Delta f=\)0.57 THz), with an increase in the incident angle from \(0^{\circ}\) to \(85^{\circ}\), such type of the spectra is called the omnidirectional spectrum. As shown in Figure 4, the thermal radiation spectrum of both incident TM polarized waves is plotted in terms of frequency at angles \(\theta=0^{\circ},30^{\circ},50^{\circ},85^{\circ}\). It is clear in that only the upper-frequency limits of the band-gaps are significantly sensitive to increasing the angles of incident, while for the lower frequency limits these changes are very small. Figure 4 shows a TM polarization plot of the light under identical conditions as shown in Figure 3. The relevant analysis is described as follows. Similar to Figure 3, by increasing the angle of incidence frequency limits of the PBGs move to the higher frequencies. For example, we can see the lower band-edge is occurred at 3.64 THz for \(\theta=0^{\circ}\) as the TE mode.