# Thermal Effect of the Back Radiation from Disk to Head after Laser Heating in HAMR
## 3 Results and Discussion
### Spectral Heat Flux of the Back Radiation in HAMR  
In Figure 2, assume that the thickness of film 1 is 15 nm, the flying height, i.e., the thickness of air film 2 between head and disk is 2 nm, the radiative heat flux from film 1 to bulk 3 is calculated at full frequency after ignoring the frequencies where the heat flux is several orders of magnitude below the maximum value. The frequency-flux graph at an effective frequency band, from \(\omega=1\times 10^{11}\) rad/s to \(\omega=1\times 10^{15}\) rad/s, is plotted shown in Figure 4. Overall, the contribution of the near-field radiative heat flux (the red line) is several orders of magnitude larger than that of the far-field radiative heat flux (the blue line), related to the frequency band; thus, the contribution of far-field for radiative heat flux can be ignored here. Moreover, the near-field heat transfer is enhanced at the resonant frequency, which is related to the properties of the material. Notice the near-field part, there is a remarkable fluctuation of the heat flux during the frequencies from \(\omega_{1}=1.10\times 10^{13}\) rad/s to \(\omega_{2}=2.04\times 10^{13}\) rad/s, which is because of the electromagnetic properties of the materials. The abrupt change in the heat flux at frequencies \(\omega_{1}=1.10\times 10^{13}\) rad/s (Figure 5a) and \(\omega_{2}=2.04\times 10^{13}\) rad/s (Figure 5b) is because the sign of the imaginary part of the electrical permittivity changes at these two frequencies, i.e., when \(\omega<\omega_{1}=1.10\times 10^{13}\) rad/s, the imaginary part of the electrical permittivity is negative, and it changes to positive when \(\omega_{1}=1.10\times 10^{13}\) rad/s \(<\omega<\omega_{2}=2.04\times 10^{13}\) rad/s, and changes again to negative when \(\omega>\omega_{2}=2.04\times 10^{13}\)rad/s, as shown in Figure 5. Noticed that there is a deviation between the peaks of the heat flux and the peaks of the electrical permittivity of Al\({}_{2}\)O\({}_{3}\) during the frequency band from \(\omega_{1}=1.10\times 10^{13}\) rad/s to \(\omega_{2}=2.04\times 10^{13}\) rad/s, which is because of the influence of the imaginary part of the electrical permittivity of Fe, as shown in Figure 6. Generally, the electromagnetic properties of the materials, particularly the electrical permittivity of the materials, have great influence on the spectral heat flux. In addition, the surface phonon-polariton resonance is visible during the frequencies \(\omega_{2}=2.04\times 10^{13}\) rad/s to \(\omega_{4}=4.40\times 10^{13}\) rad/s, and the large value of the near-field heat flux is at the frequency \(\omega_{3}=3.42\times 10^{13}\) rad/s.  
Figure 4: Spectral heat flux for a flying height of 2 nm.  
Figure 5: The sign of the imaginary part of the electrical permittivity changes at the frequency.  
Figure 6: The imaginary part of electrical permittivity for Al\({}_{2}\)O\({}_{3}\)(red line) and Fe (blue line).  
The spectral heat flux at an effective frequency band under varying flying heights from 1 nm to 10 nm is plotted in Figure 7 to discuss the influence of the flying height on the spectral heat flux. As shown in Figure 7, the surface phonon-polariton resonance frequency band of the heat flux in the extreme near-field distance, i.e., \(d=1\) nm and 2 nm, is narrower than that in the far-field band, i.e., \(d=5\) nm and 10 nm. In addition, there is a remarkable end of the resonance frequency for the extreme near-field radiative heat transfer.