Abstract
The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss’s theorem. Experimental results show an excellent agreement with theoretical predictions.
Highlights
The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task
In the present paper we propose a method to estimate the longitudinal components in the focal region of a highly focused beam based on the information contained on complex amplitudes of the corresponding transverse part
To recover the longitudinal component of an electromagnetic field by means of Eq (12), it is necessary to determine the complex amplitudes of the transverse components
Summary
The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. The most intriguing property of focused beams is the longitudinal component that, under certain conditions, can gather more energy than the transverse one. Several techniques for direct measuring of the longitudinal component have been described, but they typically are complex or specific for the field of application where they have been d esigned[37,38,39]. Since the transverse components are accessible, an alternative can be found by estimating the longitudinal component using the Gauss’ theorem, provided the complex amplitude and polarization of the transverse field are k nown[36,47]. In the present paper we propose a method to estimate the longitudinal components in the focal region of a highly focused beam based on the information contained on complex amplitudes of the corresponding transverse part. The estimation of the longitudinal component can be found in "Results and discussion" and our conclusions are summarized in the "Concluding remarks" section
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