The time reversal method has been shown to be capable of reconstructing electromagnetic sources. However, in the past, most sources reconstructed are point sources that may not be often seen in practical situations. This paper presents preliminary studies on the time-reversal reconstruction of the sources with arbitrary geometrical shapes and with finite frequency bandwidths. Our results show that the time-reversal method, incorporating the Kurtosis, can effectively find the locations, excitation, and band-limited arbitrarily shaped sources. In addition, in an ergodic cavity, a single sensor is adequate to reconstruct the sources with reduced operational cost and complexity.This paper lays the groundwork for further development of the TR method for its uses in realistic scenarios of source reconstructions.

Electromagnetic time-reversal (TR) has been proven to be an effective and efficient method for solving source reconstruction problems. Different algorithms are proposed to deal with difficulties in real-world scenarios. In our previous work, we proposed the electromagnetic kurtosis methods and discussed the resolution in band-limited TR. However, traditional kurtosis methods may not work effectively with narrow bandwidth. This work further extends the idea of arbitrary-order kurtosis and demonstrates its capabilities of achieving super-resolution in real applications. Compared to other super-resolution techniques, the proposed methods are algorithmic simple and do not incorporate subwavelength structures. Numerical experiments show the field concentration beyond the diffraction limit which can increase the accuracy of source reconstruction with band-limited TR. Quantitative analysis is also presented to illustrate the characteristics of arbitrary-order kurtosis and its applications in multiple sources reconstruction or future complex environments.

Time-reversal (TR) is an effective method of solving inverse problems. However, the theory about the TR is still not clear. This work starts by examining fundamental laws in wave physics and electromagnetics and presents a revisit of the electromagnetic TR method. Then a cavity is employed, and the hardware experiments are performed to validate the TR as a robust and straightforward method for source reconstruction. Since the testing equipment has a limited working bandwidth, special algorithms are developed to transform the band-limited testing data into causal time-domain signals for the TR operations. The results verify the effectiveness of the TR method in real-world situations. The work presented in this paper paves the way for extensions and applications of the TR method toward solving complex, realistic problems.

The time-reversal method has been applied to the source location due to its spatiotemporal focusing properties. Much work on the topic is to locate the impulse or wideband sources. However, most sources in practical situations are narrowband. Therefore, it is desirable to develop a single-frequency time-reversal method to reconstruct narrowband-source locations. Unlike the conventional time-reversal method, the single-frequency time-reversal method we propose in this paper extracts the field signals at a single frequency at the time-reversal-mirror locations and reinjects them into the solution domain for the backward simulations. The preliminary experimental results with an ergodic cavity demonstrate the effectiveness of our proposed method and move one crucial step forward for the practical uses of the time-reversal method. They lay the foundations for further extensions of time-reversal theory and applications.