Impulse electromagnetic wave propagation in Kerr medium
Abstract
Background: Propagating ultrashort impulse fields concentrate energy in a small time interval in a limited space that can cause nonlinear phenomena. The study of the influence of nonlinear phenomena on the shape of pulses during propagation will help to avoid the difficulties in the signal identifying by their shape, such as the Kalman filter method.
Objectives: The aim of the work is to study the effect of Kerr nonlinearity on the step response of the antenna with a circular aperture and uniform current distribution. Given that the shape of the pulse depends on the coordinates of the 9observation point, to simplify the problem, consider the case when the observation point is on the longitudinal axis of the radiator.
Materials and methods: The object of the study is an electric field radiated from the antenna with the circular aperture and propagating in a Kerr nonlinear medium. The solution of the direct electromagnetic problem of electrodynamics, namely, the generation of a field by transient electric current, is carried out by the method of evolutionary equations. The nonlinear radiation problem is solved using the perturbation theory. Numerical integration of improper integrals to obtain the nonlinear correction for the electric field is carried out by quadrature methods, taking into account the unbounded integration interval. A cubic model of nonlinearity is considered as an example of a nonlinear medium.
Results: The initial source of the field is a flat disk with a uniform distribution of transient current. The method of evolutionary equations is applied to solve the problem of radiation of such a source. The approach that consists of the analyzing of the linear part of the solution to effectively limit the calculation domain, which significantly affects on the formation of the resulting field was verified. The influence of weak nonlinearity of the Kerr medium on the shape of the radiated transient pulse is estimated.
Conclusion: the ultrawideband signal propagating through the Kerr medium shows significant self-influence changing its shape. The additional components form a delay in the arrival time and have a shape resembling the first derivative of the exciting current.
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References
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