We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. The case of such two classically correlated beams is treated in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a basic analogy is pointed out. The results are compared in a specific numerical example.The topic of entangled imaging has attracted noteworthy attention in recent years [1,2,3,4,5,6,7,8]. This tecnique exploits the quantum entaglement of the state generated by parametric down-conversion (PDC), in order to retrieve information about an unknown object. In the regime of single photon pair production of PDC, the photons of a pair are spatially separated and propagate through two distinct imaging systems. In the path of one of the photons an object is located. Information about the spatial distribution of the object is not obtained by detection of this photon, but rather by registering the coincidence counts as a function of the other photon position [1,2,3,4,5]. In the regime of a large number of photon pairs, this procedure is generalized to the measurement of the signal-idler spatial correlation function of intensity fluctuations [6]. Such a two-arm configuration provides more flexibility in comparison with standard imaging procedures, as e.g. the possibility of illuminating the object with one light frequency and performing a spatially resolved detection in the other arm with a different light frequency, or of processing the information from the object by only operating on the imaging system of arm 2 [5,6]. In addition, it opens the possibility of performing coherent imaging by using, in a sense, spatially incoherent light, since each of the two down-converted beams taken separately is described by a thermal-like mixture and only the two-beam state is pure(see e.g. [5] and [6]).In this paper we show that it is possible to implement such a scheme using a truly incoherent light, as the radiation produced by a thermal (or quasi-thermal) source. A comparison between thermal and biphoton emission is performed in [9], where an underlying duality accompanies the mathematical similarity between the two cases. Here, we considerCorrelated imaging with incoherent thermal light. The thermal beam a is splitted into two beams which travel through two distinct imaging systems, described by their impulse response functions h1 and h2. Arm 1 includes an object. Detector D1 is either a point-like detector or a bucket detector. Beam 2 is detected by an array of pixel detectors. v is a vacuum field. a different scheme (Fig.1), appropriate for correlated imaging, in which a thermal beam is divided by a beam-splitter (BS) and the two outgoing beams are handled in the same way as the PDC beams in entangled imaging. A basic analogy between the PDC and the thermal case emerges from our analysis. Currently there is a debate whether quantum entanglement is necessary to perform correlated imaging [5,6,7,8]. ...

High-resolution ghost image and ghost diffraction experiments are performed by using a single classical source of pseudothermal speckle light divided by a beam splitter. Passing from the image to the diffraction result solely relies on changing the optical setup in the reference arm, while leaving the object arm untouched. The product of spatial resolutions of the ghost image and ghost diffraction experiments is shown to overcome a limit which seemed to be achievable only with entangled photons.

We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. A formal analogy is demonstrated between two such classically correlated beams and two entangled beams produced by parametric down-conversion. Because of this analogy, the classical beams can mimic qualitatively all the imaging properties of the entangled beams, even in ways which up to now were not believed possible. A key feature is that these classical beams are spatially correlated both in the near field and in the far field. Using realistic numerical simulations the performances of a quasithermal and a parametric down-conversion source are shown to be closely similar, both for what concerns the resolution and statistical properties. The results of this paper provide a scenario for the discussion of what role the entanglement plays in correlated imaging

Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.

We investigate experimentally fundamental properties of coherent ghost imaging using spatially incoherent beams generated from a pseudo-thermal source. A complementarity between the coherence of the beams and the correlation between them is demonstrated by showing a complementarity between ghost diffraction and ordinary diffraction patterns. In order for the ghost imaging scheme to work it is therefore crucial to have incoherent beams. The visibility of the information is shown for the ghost image to become better as the object size relative to the speckle size is decreased, and therefore a remarkable tradeoff between resolution and visibility exists. The experimental conclusions are backed up by both theory and numerical simulations.

We study the spatial correlations of quantum fluctuations that can be observed in multi-mode spontaneous parametric down-conversion in the regime of high gain. A stochastic model has been solved numerically to obtain quantitative results beyond the stationary plane-wave pump approximation. The pulsed shape of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account. Their effect on the spatial quantum correlations predicted by the plane-wave pump theory is investigated, both for near field and far field measurements, in a type I and in a type II phase-matching configuration.

We study soliton pulse compression in materials with cascaded quadratic nonlinearities and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible. c 2018 Optical Society of America OCIS codes: 320.5520, 320.7110, 190.5530, 190.2620, 190.4400 Efficient soliton pulse compression is possible using second-harmonic generation (SHG) in the limit of large phase mismatch, because a Kerr-like nonlinear phase shift is induced on the fundamental wave (FW). Large negative phase shifts can be created, since the phase mismatch determines the sign and magnitude of the effective cubic nonlinearity. This induced self-defocusing nonlinearity thus creates a negative linear chirp through an effective self-phase modulation (SPM) term, and the pulse can therefore be compressed with normal dispersion. Beam filamentation and other problems normally encountered due to self-focusing in cubic media are therefore avoided. This self-defocusing soliton compressor can create high-energy few-cycle fs pulses in bulk materials with no power limit [1][2][3][4]. However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH) limits the pulse quality and compression ratio. Especially very short input pulses (< 100 fs) give asymmetric compressed pulses and pulse splitting occurs [4,5]. In this case, the system is in the nonstationary regime, and conversely when GVM effects can be neglected it is in the stationary regime [3][4][5]. Until now, the stationary regime was argued to be when the characteristic GVM length is 4 times longer than the SHG coherence length [1], while a more accurate perturbative description showed that the FW has a GVM-induced Raman-like term [4,5], which must be small for the system to be in the stationary regime [4]. However, no precise definition of the transition between the regimes exists.On the other hand, the concept of nonlocality provides accurate predictions of quadratic spatial solitons [6,7], and many other physical systems (see [8] for a review). Here we introduce the concept of nonlocality to the temporal regime and soliton pulse compression in quadratic nonlinear materials. As we shall show, GVM, the phase mismatch, and the SH group-velocity dispersion (GVD) all play a key role in defining the nonlocal behavior of the system. Two different nonlocal response functions appear naturally, one with a localized amplitude -representing the stationary regime -and one with a purely oscillatory amplitude -representing the nonstationary regime. In the presence of GVM they are asymmetric and thus give rise to a Raman effect on the compressed pulse.In the theoretical analysis we may neglect diffraction, higher-order dispersion, cubic Raman terms, and selfsteepening to get the SHG propagation equations for the FW (ω 1 ) and SH (ω 2 = 2ω 1 ) fields E 1,2 (z, t) [3, 9]:wher...

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (i.e., the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -related to the difference between the SHG and the Kerr soliton numbers -and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, which control the behaviour of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a β-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.