Purcell enhancement near arbitrary anisotropic multilayers: from plasmonic layers to twisted hyperbolic stacks

We present a general and numerically robust framework to calculate the decay rate of an electric dipole located at an arbitrary distance from a multilayer stack of anisotropic planar materials, directly enabling the evaluation of Purcell enhancement. The method combines a Sommerfeld integral formulation of the dyadic Green’s function with Fresnel reflection coefficients obtained via a transfer-matrix approach for stratified anisotropic media. The Fresnel coefficients are computed reliably using adaptive grid refinement around their poles, allowing precise treatment of low-loss bound modes. Numerical stability is ensured through a suitable separation of the integration domain of the Sommerfeld integrals, enabling accurate evaluation of both propagating and high- k evanescent modes. As an example, we analyze spontaneous emission above twisted multilayers of the hyperbolic van der Waals crystal MoOCl 2 , demonstrating the impact of in-plane anisotropy and interlayer rotation on the local density of optical states and the resulting Purcell enhancement. A comparison between hyperbolic and plasmonic media clarifies the role of unbounded high- k states in governing emission enhancement. We also investigate the case of a dipole placed above a twisted MoOCl 2 bilayer, where plasmon canalization occurs. The formalism provides a versatile tool for studying spontaneous emission and Purcell enhancement in complex anisotropic layered systems.