Metamaterial-based wireless power transfer (MM-WPT) analysis has attracted substantial attention due to its great application potential. However, traditional MM-WPT analysis is constrained by frequency domain approaches which are suitable only for infinitely extended periodic signals or fixed-frequency sine waves but not suitable for complex waveforms of various energy sources. This paper presents an innovative time-domain system analysis method for MM-WPT systems tailored to evaluate energy sources with arbitrary waveforms. The foundation of the method is to use the unit impulse response. By convolving this impulse response with any type of excitation source, a temporal waveform of the voltage across the system’s load can be obtained. It has demonstrated a high degree of correlation and agreement between theoretical calculations and experimental results for various input waveforms, affirming its validity, precision, and universality. Based on the framework, it is shown that triboelectric nanogenerators can efficiently self-powered transfer wireless energy through MM-WPT systems. Experiments reveal that the energy received is up to 59.6 times higher compared with that of WPT systems without metamaterials. When this system is applied in an implant, it demonstrates a remarkable energy transfer efficiency of 51% through biological tissues. These findings represent a significant breakthrough in optimizing WPT systems for compact and efficient self-powered energy applications.