FOCUS
WAVEFRONT control
maintain the ultrashort pulse durations needed for resonant wakefield excitation.
This motivates an achromatic flying focus( see Insert 1), which realises the same principle through geometry rather than dispersion, preserving the full bandwidth of a short pulse. The radius-to-position mapping is provided by an axiparabola [ 3 ], a reflective optic necessary for ultra-high intensity pulses, that produces a quasi-Bessel beam by focusing each
ACHROMATIC FLYING FOCUS radius r of the beam at a different longitudinal position z( r). The velocity is then set by a radial group delay imposed across the beam.
DEPHASINGLESS LASER- WAKEFIELD ACCELERATION These flying focus pulses can then be used to drive a laser-wakefield accelerator, with the RGD tuned so that the peak intensity propagates through the plasma at exactly c. The wake it excites travels at this
Figure 2. Principle of achromatic flying focus with a lens doublet to introduce the radial delay.
An achromatic flying focus requires two ingredients: an optic that stretches the focus into a line, and a controlled delay that times the arrival of light along it. The axiparabola sets where each ray focuses. A standard parabola brings every radius to a single point; an axiparabola is a reflective optic whose surface departs from this shape by a controlled amount, so that each annular zone is focused at a different longitudinal position: for instance, inner radii near the optic, outer radii further away. This produces a continuous focal line of length L far beyond the Rayleigh range of an equivalent Gaussian focus, with the curvature designed to keep the on-axis intensity nearly uniform along the line. The arrival time of each ray is controlled by introducing a radial group delay( RGD) with both quadratic and higher-order quartic terms, τ( r) = ar 2 + br 4. This non-quadratic pulse front causes outer and inner regions of the beam to reach focus at different times. Because the axiparabola maps beam radius to longitudinal position, this RGD dictates when each point along the focal line reaches peak intensity, controlling the focus velocity. This RGD can be imposed with an aspheric refractive doublet made of two glasses of different dispersion, with equal and opposite power, leaving the beam collimated at the central wavelength while their difference in dispersion imprints a radius-dependent group delay. Together, the axiparabola fixes the geometry of the focal line and the radial group delay controls its timing, yielding a superluminal intensity peak. same luminal velocity, so the electrons, quickly accelerated to relativistic speeds, no longer outrun it: they remain in the accelerating phase along the whole focal line, thus overcoming the dephasing limit [ 4 ].
Flying focus also addresses the other two limitations. Along the focal line the wake is driven not by a single packet of light that propagates along the axis, but by fresh rays reflected from different radii of the axiparabola and reaching the axis each at their own position z = f( r). As new light continuously takes over while the focus advances, the on-axis available energy is not depleted during propagation, so diffraction and pump depletion are removed together. All three limitations are thus overcome at once, and the acceleration length is then set only by the total available laser energy, which limits the maximum focal-line length over which a sufficiently high intensity can be maintained.
Using numerical Particle-in-Cell simulations, we showed that a flying focus with a pulse energy of 1 J could achieve an electron energy gain of 1.4 GeV, while conventional LWFA could only achieve a gain of 0.65 GeV with the same pulse energy. Scaled to multi-petawatt lasers, electron energies of tens of GeV, up to 100 GeV, could become accessible using flying focus, compared to a present record of 10 GeV achieved with the standard scheme by working at low plasma density to limit dephasing and using a plasma waveguide to overcome diffraction [ 5 ]. Figure 3 shows a wakefield driven by a flying focus, where the on-axis peak intensity creates a plasma bubble that accelerates electrons. Around it, the outer rings of the quasi-Bessel beam, not yet in focus at this position along the line, drive weaker sub-wakes on either side of the axis.
Transitioning from numerical simulations to experimental realization poses major challenges in physical understanding, beam shaping, and diagnostics. Significant milestones have already been achieved with the experimental demonstration
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