  As we read this text, our eyes dynamically adjust the focal length to keep
the line image in focus on the retina. Similarly, in many optics applications
the focal length must be dynamically tunable. In the quest for compactness and
tunability, flat lenses based on metasurfaces were introduced. However, their
dynamic tunability is still limited because their functionality mostly relies
upon fixed geometry. In contrast, we put forward an original concept of a
tunable Optical Magnetic Lens (OML) that focuses photon beams using a
subwavelength-thin layer of a magneto-optical material in a non-uniform
magnetic field. We applied the OML concept to a wide range of materials and
found out that the effect of OML is present in a broad frequency range from
microwaves to visible light. For terahertz light, OML can allow 50% relative
tunability of the focal length on the picosecond time scale, which is of
practical interest for ultrafast shaping of electron beams in microscopy. The
OML based on magneto-optical natural bulk and 2D materials may find broad use
in technologies such as 3D optical microscopy and acceleration of charged
particle beams by THz beams.
