# Reversal of Photoinduced Bending of Crystals Due to Internal Refraction of Light
## 4 Model of the Interaction of Light with a Crystal
### Simulation Results
#### 4.3.1 Round Cross Section
The results are obtained for \(\lambda\) = 400 and crystals of various thicknesses, from 12 nm to 5 \(\upmu\)m, in order to show the dependence of the effect of bend direction reversal on the diffraction parameter \(h/\lambda\). Positive values of \(\Omega_{r}\) correspond to the normal direction of crystal bend, which follows from the BBL law, while negative values correspond to the reversal of the bend direction associated with the refraction of light in the crystal. As can be seen, for all thicknesses of the crystal, a general qualitative dependence is observed--the direction of the bend is reversed when the absorption parameter \(\mu h\) decreases below a certain value, which increases with increasing influence of diffraction (with a decrease in \(h/\lambda\)). In the region of the normal direction of the crystal bend, the dependences \(\Omega_{r}(\mu h)\) behave systematically at different \(h/\lambda\): after passing through a maximum at \(\mu h>4\), \(\Omega_{r}\) asymptotically tends to 0 at strong absorption, when the transformation occurs only in a thin near-surface layer with a thickness of \(\
eg\mu^{-1}\). Increasing the diffraction effects increases the minimum required absorption for the normal bend direction, i.e., diffraction enhances the role of refraction in the area of balance conditions between various factors that determine the resulting bend direction. At the same time, in the range of negative values of \(\Omega_{r}\), quantitative dependence of the effect on diffraction parameter \(h/\lambda\) has a complex character. When approaching the diffraction limit \(h/\lambda\)-1 the slope of \(\Omega_{r}(\mu h)\) oscillates with \(h/\lambda\), which means that the effect of reversal of intensity distribution periodically increases and weakens with \(h/\lambda\). Figure 8: Relative power of radiation incident on vertical sections of a crystal at different depths. Figure 9: Dependences of the reduced moment of intensity \(\Omega_{r}\) (Equation (19)) on the parameter of light absorption in a crystal \(\mu h\) for crystals of different thicknesses (\(\lambda\) = 400 nm). This effect is associated with the successive localization of the interference maximum or minimum near the rear surface of the crystal. To demonstrate this effect, Figure 10 shows an example of the dependence of \(\Omega_{r}\) on the crystal thickness (in units of the diffraction parameter inside the crystal \(\mathrm{Re}(m)h/\lambda\)) at a constant absorption coefficient corresponding to an absorption depth of 10 \(\upmu\)m and \(\lambda=400\) nm in vacuum. Noticeable oscillations of \(\Omega_{r}(h)\) begin at \(\mathrm{Re}(m)h/\lambda<10\) (\(h<2.5\)\(\upmu\)m in the example under consideration) and are characterized by a period approximately equal to half the wavelength in the crystal \(\Delta h=\lambda/(2\mathrm{Re}(m))\). At \(h\mathrm{Re}(m)/\lambda<1/2\) the crystal becomes so thin that the field can be considered almost uniform over the entire thickness of the crystal, which leads to a zero moment of intensity distribution, \(\Omega_{r}=0\). That is, in the limit of \(h/\lambda<<1\) and \(\mu h<<1\) diffraction completely suppresses all effects that cause crystal bending; nanosized crystals should transform without bending, if the substance is not characterized by too much absorption.