Subtracting accidental coincidences is a common practice in quantum optics experiments. For zero mean Gaussian states, such as a squeezed vacuum, we show that if one removes accidental coincidences, the measurement results are quantitatively the same for both photon coincidences at very low flux and intensity covariances. Consequently, pure quantum effects at the photon level, like interference of photon wave functions or photon bunching, are reproduced in the correlation of fluctuations of macroscopic beams issued from spontaneous down-conversion. This is true both in experiment if the detection resolution is smaller than the coherence cell (size of the mode) and in stochastic simulations based on sampling the Wigner function. We also discuss the limitations of this correspondence, such as Bell inequalities (for which one cannot subtract accidental coincidences), highly multimode situations such as quantum imaging, and higher-order correlations.

Experimental demonstrations of entangled quantum images produced through parametric downconversion have so far been confined to studying two photon correlations. Here we show that multiphoton correlations between quantum images are accessible experimentally and exhibit many new features including being sensitive to the phase of the bi-photon wavefunction. As a concrete example, we consider a modification of existing quantum imaging experiments in which the CCD cameras are moved out of focus, provide detailed analytical predictions for the resulting 4 photon intereferences, and support these by numerical simulations. The proposed experiment can also be interpreted as entanglement swapping: Bob's photons are initially unentangled, but the joint detection of Alice's photons projects Bob's photons onto an entangled state. The general approach proposed here can be extended to other quantum optics experiments involving high dimensional entanglement.

We report experimental results where a momentum entangled biphoton state with a giant dimensionality of 8000 is retrieved and manipulated when only one photon of the pair is transmitted through a thin scattering medium. For this purpose, the transmission matrix of the complex medium is first measured with a phase-shifting interferometry measurement method using a spatial light modulator (SLM) illuminated with a laser source. From this matrix, different phase masks are calculated and addressed on the SLM to spatially control the focusing of the laser through the complex medium. These same masks are used to manipulate the phase of the biphoton wave function transmitted by the thin diffuser in order to restore and control in the same way the momentum correlations between the far-field images of twin beams issued from strongly spatial-multi-mode spontaneous parametric down conversion.

We report experimentally and numerically quantum correlations imaging through thick random media. We demonstrated that spatial correlations between twin photon are still detected but no in form of two-photon speckle-like patterns.

At first sight, the use of an everywhere positive Wigner function as a probability density to perform stochastic simulations in quantum optics seems equivalent to the introduction of local hidden variables, thus preventing any violation of Bell inequalities. However, because of the difference between symmetrically and normally ordered operators, some trajectories in stochastic simulations can imply negative intensities, despite a positive mean. Hence, Bell inequalities do not apply. Here, we retrieve for a weakly squeezed Gaussian state the maximum violation on polarization states allowed by quantum mechanics, for the Clauser-Horn-Shimony-Holt (CHSH), as well as for the Clauser-Horn Bell inequalities. For the case of the Clauser-Horn Bell inequality, the influence of the quantum efficiency of the detectors is studied, and for both inequalities, the influence of the degree of squeezing is assessed, as well as the uncertainty range versus the number of trajectories used in the simulations.

We first extend our recent experiments of spatial quantum correlations imaging through thin scattering media to the case where two phase scattering plates placed respectively in the image and the Fourier planes of the biphoton source, mimics a thick scattering medium. Spatial correlations between twin photons are still detected at the quantum level but no more in the form of two-photon speckle-like patterns. However, we show that spatial entanglement of very-high dimensionality can be retrieved through thick scattering media with moderate losses and without any fair sampling assumption in the space and time domains. Second, a numerical simulation of the biphoton wave function is developed and applied to our experimental situation, with a good agreement.

We present the experimental demonstration of a self-trapped optical beam bending in a photorefractive Fe-doped lithium niobate (LN:Fe) crystal controlled by the pyroelectric effect. Formation of self-trapped beams with typical [Formula: see text]50[Formula: see text][Formula: see text]m diameter and large bending of [Formula: see text]140[Formula: see text][Formula: see text]m are depicted in a 1[Formula: see text]cm length LN:Fe crystal for a laser beam at 632.8[Formula: see text]nm wavelength and 0.5[Formula: see text]mW power with a 30 ∘ C crystal temperature change. The self-trapped beam bending is opposite to the crystal [Formula: see text]-axis. The underlying physics is elaborated and numerical simulations are performed. The long-living waveguiding channels with controlled curvilinear trajectories are promising for optical information routing.

Among the whole experiments using entangled pairs of photons, the famous experiment of two-photon interference known now as Hong-Ou-Mandel (HOM) interference, is probably one of the most fascinating. This ground-breaking experiment paved the way for a multitude of experiments showing the richness of the quantum properties of Spontaneous Parametric Down conversion (SPDC) and their applications to original communication protocols. Most of them use the coherence time property of a bi-photon state and measurement are mainly performed with bucket detectors and coincidence counters. While some studies report the spatial coherence of two-photon state, measurements are always performed in the temporal domain.

We report 2D micrometric scale regular optical patterns formation induced by a laser beam propagating through a Fe doped lithium niobate (LN:Fe) crystal. A single mode CW laser radiation at 632.8 nm wavelength and beam powers from 0.5 to 10 mW and LN:Fe samples with 0.03 wt% Fe concentration and thicknesses of 4 mm and 10 mm were used in the experiments. The observed phenomenon of optical patterns formation in photorefractive crystal is explained with the light-induced complex refractive index variation with a central minimum (negative lens) and symmetric maxima (positive lenses) on each side due to photovoltaic effect in the crystal. Light-induced complex lenses produce beam defocusing from the beam center and focusing on the periphery. Mutual interference of the beams leads to a regular optical pattern formation. Regular optical pattern, in its turn, leads to the formation of quasi-crystalline photonic structure in LN:Fe crystal. Experimental results are supported by numerical simulations.

We report the experimental observation of a spatiotemporal Hong-Ou-Mandel (HOM) interference of biphoton states of extremely high Schmidt number. Two-photon interference of 1500 spatial modes and a total of more than 3 x 10(6) spatiotemporal modes is evidenced by measuring momentum spatial coincidences, without any prior selection of the photons in time and space coincidence, between the pixels of the far-field images of two strongly multimode spontaneous parametric down-conversion (SPDC) beams propagating through a HOM interferometer. The outgoing SPDC beams are recorded on two separate detector arrays operating in the photon-counting regime. The properties of HOM interference are investigated both in the time and space domains. We show that the two-photon interference exhibits temporal and two-dimensional spatial HOM dips with visibilities of 60% and widths in good agreement with the spatiotemporal coherence properties of the biphoton state. Moreover, we demonstrate that maxima of momentum spatial coincidences are evidenced within each image, in correspondence with these dips.

We first extend our recent experiments of correlation imaging through scattering media to the case of a thick medium, composed of two phase scatterers placed respectively in the image and the Fourier planes of the crystal. The spatial correlations between twin photons are still detected but no more in the form of a speckle. Second, a numerical simulation of the biphoton wave function is developed and applied to our experimental situation, with a good agreement.

Lithium niobate crystal is widely used for the design and fabrication of integrated electro-optic modulators. As a ferroelectric material, one sees its spontaneous polarization change with temperature variations. This phenomenon, known as the pyroelectric effect, induces strong waveguide transmission variations for waveguides realized on Z -cut wafers. Waveguides made by titanium in-diffusion either on the Z + or Z − side of the crystal show a significant difference in temperature behavior. Experimental data, enlightened by numerical simulations, help to show why Z − waveguides are more immune to temperature changes than Z + ones.

The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghost imaging techniques, and the development of parallel processing methodologies for photonic artificial intelligence.

We report results of two-photon quantum holography where spatial information stored in phase holograms is retrieved by measuring quantum spatial correlations between two images formed by spatially entangled twin photons with a dimensionality of 1790 in the two-dimensional transverse space. In our experiments, the entire flux of spontaneous down converted photons illuminates the phase holograms and the photons of pairs signal-idler transmitted by the holograms are detected separately in far field on two electron-multiplying charge coupled device cameras.

We image with cameras entangled photon light transmitted through a random medium. Near-field and far-field spatial quantum correlations show that entangled photon pairs (bi-photons) generated by spontaneous optical parametric down-conversion exhibit speckle pattern. In contrast, no information from the random medium can be extracted using incoherent light issued from one photon of the pair. Although these measurements require several hours to record thousands of image pairs, our method is instantaneous for the recording of one pair of twin images and involve all the photons of the images.

We develop a fully spatiotemporal numerical model, based on stochastic simulations, simulating the generation of spatiotemporal multimode spontaneous parametric down-conversion, the propagation of the signal and idler beams through a Hong-Ou-Mandel (HOM) interferometer, and the detection of the outgoing beams with two separate detectors arrays. Spatial and temporal properties of the two-photon interference are investigated by measuring the spatial distribution of the momentum correlations between the time-integrated outgoing far-field images and a full spatiotemporal HOM dip is exhibited. Numerical results also demonstrate that the spatiotemporal coherence properties of biphoton wave packets can be fully characterized by detectors arrays with no temporal resolution.

We report results of quantum holography where spatial information stored in phase hologram is retrieved by measuring spatial coincidences between two images formed by spatially entangled twin photons of high-dimensionality transmitted by the hologram.

We report ghost imaging of a single non-reproducible temporal signal with kHz resolution by using pseudo-thermal speckle light patterns and a single detector array with a million of pixels working without any temporal resolution. A set of speckle patterns is generated deterministically at a sampling rate of tens kHz, multiplied by the temporal signal and time integrated in a single shot by the camera. The temporal information is retrieved by computing the spatial intensity correlations between this time integrated image and each speckle pattern of the set.

We use twin photons generated by spontaneous parametric down conversion to perform temporal ghost imaging of a single time signal. The retrieval of a binary signal containing eight bits is performed with an error rate below 1%.

Exploitation of the statistical properties of classical or non-classical light sources is the cause of fascinating new applications. For the two last decades, ghost imaging has emerged as a way to form images of an object with a Single Point Detector (SPD) that does not have spatial resolution [1-5]. By taking into account space-time duality in optics, the extension of the results of spatial ghost imaging to the time domain was investigated [6]. However, the proposed solution used an SPD and many realizations (several thousands) of the same temporal signal, limiting the current applications to the detection of synchronized and reproducible signals. This is in contrast with the original concept of spatial ghost imaging, where the object is unique, but multiplied in the time domain by a random modulation, different from one pixel to another, leading to multiplexing in this time domain.