Finite-Difference Time-Domain Methods: From Fields and Potentials to Gauge-Invariant Field-Impulses With Universal Current-Impulse Source

This article presents the finite-difference time-domain (FDTD) method for gauge-invariant field-impulses, which constitute the fundamental physical quantities of electromagnetics (EM) in lieu of fields and potentials. The field-impulses not only provide satisfactory resolution to various shortcomings of fields/potentials, but also facilitate simple and versatile numerical computations. They overcome the inadequacy of fields and the issues of gauge-dependent potentials in classical and quantum EM. The significance and advantages of field-impulses are discussed and compared against those of fields and potentials, in physical, mathematical, and computational aspects. The single electric field-impulse is sufficient to aptly describe all EM, including electrostatics, magnetostatics, and electrodynamics. For the excitation of field-impulses, we resort to a universal current-impulse source in lieu of traditional charges and currents. Such current-impulse can encapsulate simultaneously all static charges, direct current and time-varying dynamic sources. Moreover, it is inherently complying with charge conservation and current continuity condition. There is no need to explicitly impose such condition as required for traditional charges and currents. The FDTD update equations for field-impulses with current-impulse source are much simpler with significantly fewer terms and arithmetic operations compared to those for potentials. Numerical experiments demonstrate the full versatility of the field-impulse FDTD method for computing all electrostatics, magnetostatics, and electrodynamics, which would be useful for classical and quantum EM.