Abstract
The focused field and its intensity distribution achieved by the 4π-spherical focusing scheme are investigated within the framework of diffraction optics. Generalized mathematical formulas describing the spatial distributions of the focused electric and magnetic fields are derived for the transverse magnetic and transverse electric mode electromagnetic waves with and without the orbital angular momentum attribute. The mathematical formula obtained shows no singularity in the field in the focal region and satisfies the finite field strength and electromagnetic energy conditions. The 4π-spherical focusing of the transverse magnetic mode electromagnetic wave provides the highest field strength at the focus and the peak intensity reaches 1026 W/cm2 for the laser power of 100 PW at 800 nm wavelength. As an example of using the mathematical formula, the electron-positron pair production via the Schwinger mechanism is analyzed and compared with previous results.
Highlights
Physical phenomenon, such as light-light scattering [1,2] and electron-positron pair (e+-e− pair) production [1,3], associated with the quantum electrodynamics of strong fields [4] is of great interest as the available laser intensities approach ∼1024 W/cm2 and beyond [5,6]
As an example of using the mathematical formulas, the e+-e− pair production rate is investigated with the formulas and the minimum laser power required for the pair production is estimated from the derived formulas and compared to previous results
The 4π-spherical focusing scheme has been investigated with the transverse magnetic (TM) and transverse electric (TE) mode EM waves through the diffraction optics approach
Summary
Physical phenomenon, such as light-light scattering [1,2] and electron-positron pair (e+-e− pair) production [1,3], associated with the quantum electrodynamics of strong fields [4] is of great interest as the available laser intensities approach ∼1024 W/cm and beyond [5,6]. The field distribution projected on that virtual surface can be used to calculate the field distribution near the focus through diffraction theory This approach is only valid when the wavelength of the EM wave is much smaller than the focal length of the parabolic mirror. The diffraction approach using a radially- (or azimuthally) polarized EM wave provides a mathematical formula describing the 4π-spherically focused field distribution for a TM (or TE) mode EM wave in the focal region. Through the diffraction optic theory, generalized mathematical expressions describing E- and B-field distributions under the 4π-spherical focusing condition were derived for the TM and TE mode EM waves with and without the OAM attribute. As an example of using the mathematical formulas, the e+-e− pair production rate is investigated with the formulas and the minimum laser power required for the pair production is estimated from the derived formulas and compared to previous results
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