## 3 Results and Discussion
### Calculation of Optical Constants  
The measured characteristics were further used to determine the refractive index n, the extinction coefficient \(k\), the absorption coefficient \(\alpha\), and the band gap Eg [25]. The absorption coefficient was calculated by the expression: \(\alpha=\text{A}/\text{d}\), where A is absorption and d is the film thickness (d \(\approx\) 1 \(\upmu\)m). The extinction coefficient was calculated in terms of \(\alpha\) using the expression: \(k=\alpha\lambda/(4\pi)\), where \(\lambda\) is the wavelength. The ratio of reflected light from the film is expressed in terms of the Fresnel equations.  
The value of \(n\) was calculated in terms of light reflectance \(R\) from the following equation [26]:  
\[n=[(1+R)+\{(1+R)^{2}-(1-R)^{2}(1+k^{2})\}^{0.5}]/(1-\text{R})\]  
where \(R\)--the reflective index.  
This expression is applicable to the case when the film is strongly absorbing and the substrate influence can be neglected.  
The expression was derived as a solution to the quadratic equation [26]:  
\[R=[(n-1)^{2}+k^{2}/(n+1)^{2}+k^{2}\;]\]  
Figure 11 shows the calculated optical constants of the untreated film and the film after laser modification. As a result of film laser modification, a decrease in the refractive index and an increase in the absorption coefficient and extinction coefficient were observed. Since the greatest increase in absorption was observed after laser treatment in the darkening mode, the extinction and absorption coefficients, which characterize the material absorbance, have the highest values for samples after laser modification during darkening. As a result of the photothermal action on the film with a high temperature gradient, the valence boundaries and conduction bands shifted, which affected the optical characteristics modification discussed above.  
The PbSe film band gap was also determined before and after laser and heat treatment. By extrapolation of two straight sections, the following values were determined: untreated sample Eg = 1.59 eV, after laser modification on wavelength 1064 nm in the bleaching mode Eg = 1.45 eV, after heat treatment Eg = 1.33 eV, and after laser modification in the darkening mode Eg = 1.30 eV (Figure 12). In the authors' previous work [23], PbSe films, after modification by continuous radiation with a wavelength = 405 nm, had a band gap value in the darkening mode of Eg = 1.33. Since the Eg shift is fairly easy to achieve, some research groups [27; 28] shift the band gap from intrinsic 0.27 eV to 1.8 eV, which corresponds to wavelengths of 4.6 \(\upmu\)m and 690 nm, respectively. Thus, the band gap values obtained are in good agreement with the previously published results [25; 28].  
Figure 11: Optical characteristics of PbSe films for an untreated film (blue curve), a film after heat treatment (red curve), and a film after laser modification by pulsed radiation (pink and violet curves): (**a**) absorption coefficient \(\alpha\), (**b**) extinction coefficient k, (**c**) refractive index n.  
Figure 12: Determination of the optical band gap Eg before and after modification of PbSe films: untreated (light blue curve), heat treatment (red curve), bleaching mode (yellow curve), darkening mode (blue curve).  
Structural changes caused by laser action led to an increase in the defect center concentration, which increased the probability of free charge carrier transfer. As a result, a decrease in the band gap was observed after laser modification [29].  
Comparison of the advantages and disadvantages of processing with pulsed and continuous laser radiation with heat treatment is given in Table 3.