We consider a nonlinear, passive optical system contained in an appropriate cavity, and driven by a coherent, plane-wave, stationary beam. Under suitable conditions, diff'raction gives rise to an instability which leads to the emergence of a stationary spatial dissipative structure in the transverse profile of the transmitted beam.A large variety of unstable phenomena have been reported in optics which lead to the appearance of organized behavior in time or both in time and in space. For example, it is well known that some optical systems, when subjected to stationary control parameters, may exhibit a pulsed, an oscillatory, or a chaotic output; it has been found also in optical bistability that spatial patterns of transverse and longitudinal type may occur in the switching process from the lower to the upper branch of the hysteresis curve. To our knowledge, however, the possibility of soft-mode symmetry-breaking instabilities leading to the spontaneous formation of stationary spatial patterns (dissipative structures) in an initially uniform system has never been pointed out in the field of optics. Such instabilities have drawn considerable interest in chemistry and in developmental biologỹ here they are commonly known as Turing instabilities.In these fields they arise generally from the coupling between nonlinear chemical reactions and diAusion. We show here on a simple optical model that analogous phenomena may arise from the coupling between light dispersion and diAraction in an appropriate optical cavity.We call z the longitudinal coordinate and x, y the transverse coordinates. We consider a cavity formed by four mirrors, two orthogonal to the axis z with a distance L and transmission coeScient T «1, and two orthogonal to the axis x with a distance b and 100% reflectivity.The cavity is filled with a medium with a nonlinear refractive index. A coherent, stationary, plane-wave field EI is longitudinally injected into the cavity. We assume that both the input and the internal cavity field are linearly polarized in the y direction; hence, because of the transversality condition, the internal field is independent of y. We assume that it has the structure E (x )cos(K, z )exp( -i toot ) +c.c. , where coo is the frequency of the input field Et and K, =trn, /L, with n, being a positive integer. The field transmitted by the system is proportional to the normalized envelope function E(x), which obeys the evolution equation BE . 2 . BE = -E+Et+iriE(~E~-0)+la .(1)The variable E* obeys the complex-conjugate equation.EI is taken real and positive for definiteness. The in-The parameter a is defined as a =1/2trT9, where 7 '=b /XL is the Fresnel number and k is the wavelength. The quantity g is defined as +1 or -1 in the case of self-focusing or self-defocusing nonlinearity, respectively, and gO is the detuning parameter. This model can be derived from the Maxwell-Bloch equations for a two-level system by introduction of the mean-field limit T«1, which reduces the dynamics to the single longitudinal mode n" the purely dispersi...

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]. ...

Cavity solitons are localized intensity peaks that can form in a homogeneous background of radiation. They are generated by shining laser pulses into optical cavities that contain a nonlinear medium driven by a coherent field (holding beam). The ability to switch cavity solitons on and off and to control their location and motion by applying laser pulses makes them interesting as potential 'pixels' for reconfigurable arrays or all-optical processing units. Theoretical work on cavity solitons has stimulated a variety of experiments in macroscopic cavities and in systems with optical feedback. But for practical devices, it is desirable to generate cavity solitons in semiconductor structures, which would allow fast response and miniaturization. The existence of cavity solitons in semiconductor microcavities has been predicted theoretically, and precursors of cavity solitons have been observed, but clear experimental realization has been hindered by boundary-dependence of the resulting optical patterns-cavity solitons should be self-confined. Here we demonstrate the generation of cavity solitons in vertical cavity semiconductor microresonators that are electrically pumped above transparency but slightly below lasing threshold. We show that the generated optical spots can be written, erased and manipulated as objects independent of each other and of the boundary. Numerical simulations allow for a clearer interpretation of experimental results.

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 present a new technique, differential ghost imaging (DGI), which dramatically enhances the signal-to-noise ratio (SNR) of imaging methods based on spatially correlated beams. DGI can measure the transmission function of an object in absolute units, with a SNR that can be orders of magnitude higher than the one achievable with the conventional ghost imaging (GI) analysis. This feature allows for the first time, to our knowledge, the imaging of weakly absorbing objects, which represents a breakthrough for GI applications. Theoretical analysis and experimental and numerical data assessing the performances of the technique are presented.

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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.