Asymmetry of the angular distribution of radiation of channeled relativistic electrons in optically transparent crystals

It has been shown that optical and ultraviolet radiation from relativistic electrons at planar channeling in optically transparent crystals is characterized by an unusual dependence on the polar and azimuth angles. A fraction of radiation with the frequency $\omega$ near which the derivative of the refractive index is nonzero, $n'(\omega) = dn(\omega)/d\omega \neq 0$, should be observed at an angle close to $\pi/2$ with respect to the electron beam. For normal dispersion ($n'(\omega)>0$), this angle is smaller than $\pi/2$, whereas for anomalous dispersion ($n'(\omega)<0$), it is larger than $\pi/2$ (“backward” radiation). A pronounced dependence of the radiation intensity on the azimuth angle $\varphi$, i.e., azimuthal asymmetry, appears beyond the region of normal and anomalous dispersion at a fixed polar angle $\theta$. In particular, the ratio of radiation intensities at angles $\varphi = 0$ and $\pi/2$ at $\theta = \pi/2$ reaches a maximum value of about the square of the refractive index.