Dipole pulse theory: Maximizing the field amplitude from $4\pi$ focused laser pulses

We present a class of exact nonstationary solutions of Maxwell equations in vacuum from dipole pulse theory: electric and magnetic dipole pulses. These solutions can provide for a very efficient focusing of electromagnetic field and can be generated by $4\pi$ focusing systems, such as parabolic mirrors, by using radially polarized laser pulses with a suitable amplitude profile. The particular cases of a monochromatic dipole wave and a short dipole pulse with either quasi-Gaussian or Gaussian envelopes in the far-field region are analyzed and compared in detail. As a result, we propose how to increase the maximum field amplitude in the focus by properly shaping the temporal profile of the input laser pulses with given main wavelength and peak power.

Figure 1

The principal scheme for dipole pulse generation by using a parabolic mirror. Here $f$ is a focusing parameter of the mirror (focal length), $L$ is the distance from the focus (approximate length of the mirror), and $I_l\left(r\right)$ is the radial intensity distribution of the input laser radiation.

Figure 2

Electromagnetic energy density distribution of the monochromatic $e$-dipole wave. The energy density ($\omega t=0$) (a) as a function of transverse coordinates and (b) as a function of the transverse coordinate and the longitudinal one.

Figure 3

Electromagnetic energy density distribution of an $e$-dipole pulse with a quasi-Gaussian envelope ($a/\omega =0.2$). The energy density ($\omega t=0$) (a) as a function of transverse coordinates and (b) as a function of the transverse coordinate and the longitudinal one.

Figure 4

Field distribution of the dipole pulse with a sharp front at some fixed moment of time (green line); $l_i$ is a characteristic pulse buildup length.

Figure 5

Comparison of the normalized field amplitudes as functions of time (left) in the far-field region and (right) in the focus for a monochromatic $e$-dipole wave (yellow lines) and $e$-dipole pulses with sharp fronts (blue and red lines).