WAVEFRONT CONTROL FOCUS of optical modes across all degrees of freedom( spatial, polarization, and spectral), which, combined with the inherently low photon flux of non-classical sources, makes measurements extremely challenging. Consequently, only a few initial heroic experiments successfully detected these residual quantum effects, notably the first observation of two-photon speckle generated by propagating an entangled state through a thin scattering layer [ 1 ].
In parallel with this research, wavefront shaping- the ability to control the incident wavefront over a large number of degrees of freedom- was beginning its revolution in the field of complex media optics. It would soon also change the game for quantum optics.
WAVEFRONT SHAPING: A NEW TOOL TO MANIPULATE NON-CLASSICAL LIGHT The first revolution brought by wavefront shaping was conceptual: by determining the transmission matrix of a complex medium, the scattering process was no longer seen as an unknown transformation, but rather as a deterministic and— crucially— a known one. Operationally, this also made a big
Figure 1. Turning a complex medium into a beam splitter.( a) Conceptual schematic showing non-classical light propagating through a complex medium after being shaped by a spatial light modulator( SLM). At the output, single-photon detectors and a coincidence counter detect the quantum properties of light across a large number of output modes.( b) Through wavefront shaping, the initially complex highly-multimode transformation is reconfigured into a perfectly controlled, lower-dimensional optical transformation- in this case, a 2 × 2 matrix acting as a programmable lossy beam splitter.( c) Intensity distribution measured by a camera at the output of the medium when the SLM programs the beam splitter, showing two high-intensity spots corresponding to the two targeted output ports.( d) When a single-photon state( obtained via a heralding scheme) is sent into the medium( here, a slab of Ti0₂ powder on a microscope slide), the scattering medium acts as a beam splitter within an interferometer, enabling single-photon interference with a tunable relative phase.( e) When two indistinguishable photons propagate through the system( here, a multimode optical fiber), Hong-Ou-Mandel two-photon interference is achieved, yielding either a coincidence dip or antibunching depending on how the beam splitter is programmed. The green, blue, and red curves were obtained by setting the phase α to 0, π / 2, and π in the beam splitter matrix shown in( b), respectively. More details can be found in Refs.[ 2,3 ], as well as in similar experiments conducted in parallel at this period [ 4,5 ].
difference. Instead of spreading a state over many spatial modes in an unpredictable way, wavefront shaping( whether via optimization or transmission matrix measurement) made it possible to concentrate energy with high efficiency into one or a few diffraction-limited spots, with deterministic amplitude and phase. On the one hand, this drastically reduced acquisition times and the number of modes to be detected, making experiments practically feasible. On the other hand, it enabled the design of arbitrary ad hoc transformations, effectively turning a highly multimode, disordered system into a programmable optical system of controlled dimensionality.
As shown in Figures1( a, b), a key demonstration of this was the construction of a synthetic beam splitter [ 2-5 ]. By splitting two input modes evenly and focusing them onto two positions through a complex medium( Fig. 1( c)), researchers could emulate an arbitrary beam splitter at any location. This allowed them to
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