The radiation of twisted photons by charged particles traversing a cholesteric plate is studied in the framework of quantum electrodynamics in an anisotropic inhomogeneous dispersive medium. The complete set of solutions to the Maxwell equations in the cholesteric plate is constructed in the paraxial and small anisotropy approximations. The explicit expressions for the average numbers of plane-wave and twisted photons created by a charged point particle crossing the cholesteric plate are derived. The selection rules for the twisted photons radiated at the harmonic n ∈ ℤ are established. In the paraxial regime, the projection of the orbital angular momentum of a radiated twisted photon obeys the selection rule l = ± (2n + 1). In the approximation of a small anisotropy of the permittivity tensor, the selection rule becomes m = ± 2n, where m is the projection of the total angular momentum of a radiated twisted photon. The sign “±” in these selection rules is related to the choice of the forward or reflected waves in the cholesteric and is realized at the different energies of radiated photons. As the examples, the radiation of optical twisted photons by electrons with the Lorentz factors γ = 235 and γ = 500 and by uranium nuclei with γ = 2 are considered. It is shown that charged particles traversing normally a cholesteric plate can be used as a pure source of twisted photons. These results can be employed for elaboration of compact flexible sources of twisted photons, new particle detectors, and for diagnostics of the structure of liquid crystals.

在各向异性的非均匀分散介质中，在量子电动力学的框架内研究了带电粒子穿过胆甾醇板对扭曲光子的辐射。胆甾醇板中麦克斯韦方程组的完整解以近轴和小的各向异性近似构造。推导了由带电点粒子穿过胆甾醇板形成的平面波和扭曲光子平均数的明确表达式。用于在谐波辐射的扭曲的光子的选择规则Ñ  ∈ℤ成立。在近轴状态下，辐射的扭曲光子的轨道角动量的投影遵循选择规则l  =±（2 n +1）。在介电常数张量的各向异性很小的情况下，选择规则变为m  =±2 n，其中m是辐射扭曲光子的总角动量的投影。这些选择规则中的符号“±”与胆甾型中正向或反射波的选择有关，并在辐射光子的不同能量下实现。例如，洛伦兹因数γ  = 235和γ  = 500的电子以及铀核的γ核对光扭曲光子的辐射 = 2被考虑。结果表明，通常穿越胆甾醇板的带电粒子可以用作扭曲光子的纯来源。这些结果可用于阐述扭曲的光子的紧凑柔性源，新的粒子检测器以及液晶结构的诊断。