  The capability of focus control has been central to optical technologies that
require both high temporal and spatial resolutions. However, existing varifocal
lens schemes are commonly limited to the response time on the microsecond
timescale and share the fundamental trade-off between the response time and the
tuning power. Here, we propose an ultrafast holographic focusing method enabled
by translating the speed of a fast 1D beam scanner into the speed of the
complex wavefront modulation of a relatively slow 2D spatial light modulator.
Using a pair of a digital micromirror device and a resonant scanner, we
demonstrate an unprecedented refresh rate of focus control of 31 MHz, which is
more than 1,000 times faster than the switching rate of a digital micromirror
device. We also show that multiple micrometer sized focal spots can be
independently addressed in a range of over 1 MHz within a large volume of 5 mm
x 5 mm x 5.5 mm, validating the superior spatiotemporal characteristics of the
proposed technique - high temporal and spatial precision, high tuning power,
and random accessibility in a three-dimensional space. The demonstrated scheme
offers a new route towards three-dimensional light manipulation in the 100 MHz
regime.
