Abstract
Quantum optics has advanced our understanding of the nature of light and enabled applications far beyond what is possible with classical light. The unique capabilities of quantum light have inspired the migration of some conceptual ideas to the realm of classical optics, focusing on replicating and exploiting non-trivial quantum states of discrete-variable systems. Here, we further develop this paradigm by building the analogy of quantum squeezed states using classical structured light. We have found that the mechanism of squeezing, responsible for beating the standard quantum limit in quantum optics, allows for overcoming the "standard spatial limit" in classical optics: the light beam can be "squeezed" along one of the transverse directions in real space (at the expense of its enlargement along the orthogonal direction), where its width becomes smaller than that of the corresponding fundamental Gaussian mode. We show that classical squeezing enables nearly sub-diffraction and superoscillatory light focusing, which is also accompanied by the nanoscale phase gradient of the size in the order of λ/100 (λ/1000), demonstrated in the experiment (simulations). Crucially, the squeezing mechanism allows for continuous tuning of both features by varying the squeezing parameter, thus providing distinctive flexibility for optical microscopy and metrology beyond the diffraction limit and suggesting further exploration of classical analogies of quantum effects.