Tesla-Scale Terahertz Magnetic Impulses

Measuring the magnetic response of matter relies acutely on the degree to which a magnetic field source’s amplitude, spatial, and temporal character can be tailored. Magnetic fields are inseparable from light-matter interaction, yet due to the dominance of electric-field-induced effects in many systems, laser pulses have heretofore provided comparatively limited insight into the high-frequency magnetic response of matter. Conductors or superconductors arranged in a solenoidal configuration embody the state-of-the-art apparatus for generating spatially isolated magnetic fields, but the reliance on electrical circuitry limits the field amplitude, pulse brevity, and absolute timing of the generated fields. We transfer the concept of solenoidal currents commonly leveraged in electromagnets to photo-ionized electrons driven by moderately intense vector laser beams, in a scheme that does not require the laser mode to carry orbital angular momentum. We predict that this all-optical approach will enable magnetic fields exceeding 8 Tesla to be turned on within 50 femtoseconds using moderate laser intensities, an unprecedented combination of parameters that will open the possibility for ultrafast metrological techniques to be combined with intense, spatially isolated, magnetic fields.

Popular Summary

Magnetic fields play a fundamental role in our understanding of many areas of physics, yet the tools for generating magnetic fields, namely electromagnets, have changed very little since they were first invented. Over the last few decades, efforts to improve magnetic field sources have been incremental, and reliance upon electrical circuitry has prevented synchronization with sensitive ultrafast optical detection methods. This severely limits our ability to measure ultrafast magnetic-field-induced dynamics in matter. We numerically propose a new approach for generating intense magnetic fields using vector laser beams.

In contrast to conventional laser beams, vector beams have a nonuniform polarization across the beam profile and can take the shape of a “donut.” In particular, we consider azimuthal vector beams, where the polarization at each point in the beam is aligned along the azimuthal unit vector. We demonstrate that when two azimuthal vector beams (one being the second harmonic of the other) are used to ionize atoms with a large ionization potential, strong azimuthal photocurrents are excited. Through simulations, we demonstrate that the spatial distribution of this current resembles that of a solenoid current and produces a longitudinal magnetic field. We predict magnetic-field strengths of 8.4 T that can be turned on within 50 fs.

We anticipate that readily available laser systems could be used with our proposed scheme and that the dynamic azimuthal current will radiate a terahertz bandwidth magnetic impulse. Using terahertz techniques to collect and refocus this impulse would then enable it to be combined with ultrafast optical techniques for the measurement of ultrafast magnetic-field-induced dynamics in atomic, molecular, and condensed-matter systems using an unprecedented combination of field strength and pulse duration.

Figure 1

Numerical simulations of strong field coherent control in atomic hydrogen using azimuthal vector beams. (a) A snapshot of the electric field from an azimuthal vector beam propagating through a Gaussian focusing geometry with beam waist, $w_0=6\mu \mathrm{m}$. (b) A transverse slice of the azimuthal electric field mode at the beam waist. (c) A transverse slice of the azimuthal current density at the beam waist. (d) A transverse slice of the longitudinal magnetic field produced by the current density at the beam waist.

Figure 2

Temporal dynamics relating the electric field excitation, gas ionization, current generation, and magnetic field induction. (a) An exemplary $\omega /2\omega$ electric field waveform at the beam waist. (b) Growth of the ionized population density when this field is incident on a hydrogen gas target with a density $n={10}^{17}{\mathrm{cm}}^{-3}$. (c) The current density dynamics that occurs as the excited population interacts with the remainder of the laser pulse. (d) The magnetic field produced by this current density.

Figure 3

Coherent control of magnetic fields. Simulation results for a beam waist $w_0=6\mu \mathrm{m}$, fundamental wavelength $\lambda =4\mu \mathrm{m}$, medium thickness $L=300\mu \mathrm{m}$, equal $\omega /2\omega$ pulse durations ${\tau }_p=40\mathrm{fs}$, and gas density $n_i={10}^{17}{\mathrm{cm}}^{-3}$. (a) Adjusting the phase offset between the $\omega$ and $2\omega$ beams enables precise control of the direction and amplitude of the generated magnetic field. In addition, the relative phase influences the spatial distribution of the magnetic fields. Longitudinal slices of the magnetic fields generated in the focusing geometry are shown for (b) $\mathrm{\Delta }\phi =\pi /8$, (c) $\mathrm{\Delta }\phi =5\pi /8$, (d) $\mathrm{\Delta }\phi =9\pi /8$, and (e) $\mathrm{\Delta }\phi =13\pi /8$.

Figure 4

The influence of back-EMF on magnetic field scaling. Simulation results for atomic hydrogen and helium, for a beam waist $w_0=100\mu \mathrm{m}$, fundamental wavelength $\lambda =4\mu \mathrm{m}$, medium thickness $L=150\mu \mathrm{m}$, equal $\omega /2\omega$ pulse durations ${\tau }_p=40\mathrm{fs}$, and variable gas density. For each gas density, one simulation is performed without back-EMF included, and another including back-EMF is performed. (a) Magnetic fields calculated for atomic hydrogen [fundamental peak electric field $E_{\omega }=2.9\mathrm{V}/\AA$ ($I_{\omega }=1.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$), second harmonic peak electric field $E_{2\omega }=1.2\mathrm{V}/\AA$ ($I_{2\omega }=0.19\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$)] reach a maximum amplitude of $B=3.6\mathrm{T}$ and are significantly suppressed by back-EMF. (b) Because of a higher ionization potential, stronger electric fields [fundamental peak electric field $E_{\theta ,\omega }=7.4\mathrm{V}/\AA$ ($I_{\omega }=7.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) and second harmonic peak electric field $E_{\theta ,2\omega }=2.3\mathrm{V}/\AA$ ($I_{2\omega }=0.70\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$)] can be applied to atomic helium while maintaining the same ionization dynamics. This method counteracts back-EMF and enables the generation of magnetic fields up to $B=8.4\mathrm{T}$.