Flying-focus techniques produce laser pulses whose focal points travel at arbitrary, controllable velocities. While this flexibility can enhance a broad range of laser-based applications, existing techniques constrain the motion of the focal point to the propagation direction of the pulse. Here, we introduce a flying-focus configuration that decouples the motion of the focus from the propagation direction. A chirped laser pulse focused and diffracted by a diffractive lens and grating creates a focal point that can move both along and transverse to the propagation direction. The focal length of the lens, grating period, and chirp can be tuned to control the direction and velocity of the focus. Simulations demonstrate this control for a holographic configuration suited to high-power pulses, in which two off-axis pump beams with different focal lengths encode the equivalent phase of a chromatic lens and grating in a gas or plasma. For low-power pulses, conventional solid-state or adaptive optics can be used instead. Multidimensional control over the focal trajectory enables new configurations for applications, including laser wakefield acceleration of ions, nonlinear Thomson scattering, and surface-plasmon emission of terahertz radiation.

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• Classical optics
• Laser applications
• Plasma optics
• Structured light
• Lenses
• Holography
• Laser techniques
• Particle-in-cell methods