Direct laser acceleration leveraging transverse fields promises unparalleled gradients exceeding $1\mathrm{TeV}/\mathrm{m}$ yet is fundamentally constrained by phase slippage, which limits interaction length and final energy gain. Here, we overcome this dephasing limitation by employing a pulse-front-tilted laser interacting with a plasma grating. This configuration ensures sustained phase matching, facilitating extended acceleration and stable near-field confinement. Uniquely, this structure functions as a phase-selective sieve that generates dense electron bunches with durations of hundreds of attoseconds. Particle-in-cell simulations demonstrate that a 61 J laser pulse yields an 11 pC beam with energies surpassing 10 GeV at gradients of approximately $2\mathrm{TeV}/\mathrm{m}$. Derived for an idealized dephasingless regime, linear scaling laws predict that 1 kJ pulses can drive beams to 200 GeV. These findings present a promising pathway toward on-chip TeV-scale accelerators and attosecond sources, with potential applications for high-energy colliders, ultrafast electron imaging, and advanced light sources.

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• Electron beams & optics
• High intensity laser-plasma interactions
• Integrated optics
• Laser driven electron acceleration
• Ultrafast phenomena
• Electron sources
• Periodic gratings
• Particle-in-cell methods