L. A. Lugiato

Ghost Imaging with Thermal Light: Comparing Entanglement and Classical Correlation

We consider a scheme for coherent imaging that exploits the classical correlation of two beams obtained by splitting incoherent thermal radiation. This case is analyzed in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a precise formal analogy is pointed out. This analogy opens the possibility of using classical beams from thermal radiation for ghost imaging schemes in the same way as entangled beams.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 quasi-thermal 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 new scenario for the discussion of what role the entanglement plays in correlated imaging.

High-resolution ghost image and ghost diffraction experiments with thermal light.

High-resolution ghost image and ghost diffraction experiments are performed by using a single source of thermal-like 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 untouched the object arm. The product of spatial resolutions of the ghost image and ghost diffraction experiments is shown to overcome a limit which was formerly thought to be achievable only with entangled photons.

Cavity solitons as pixels in semiconductor microcavities

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.

Coherent imaging with pseudo-thermal incoherent light

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.

Pattern formation in a passive Kerr cavity

Analytic and numerical investigations of a cavity containing a Kerr medium are reported. The mean field equation with plane-wave excitation and diffraction is assumed. Stable hexagons are dominant close to threshold for a self-focusing medium. Bistable switching frustrates pattern formation for a self-defocusing medium. Under appropriate parametric conditions that we identify, there is coexistence of a homogeneous stationary solution, of a hexagonal pattern solution and of a large (in principle infinite) number of localized structure solutions which connect the homogeneous and hexagonal state. Further above threshold, the hexagons show defects, and then break up with apparent turbulence. For Gaussian beam excitation, the different symmetry leads to polygon formation for narrow beams, but quasihexagonal structures appear for broader beams.

Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm.

We formulate a theory for entangled imaging, which includes also the case of a large number of photons in the two entangled beams. We show that the results for imaging and for the wave-particle duality features, which have been demonstrated in the microscopic case, persist in the macroscopic domain. We show that the quantum character of the imaging phenomena is guaranteed by the simultaneous spatial entanglement in the near and in the far field.

Optical Pattern Formation

Publisher Summary This chapter focuses on the concept of optical pattern formation. The field of optical pattern formation (OPF) studies the spatial and spatiotemporal phenomena that arise in the structure of electromagnetic field in the planes orthogonal with respect to the direction of propagation. Most theoretical treatments of the interaction between matter and radiation introduce the plane wave approximation—that is, they assume that the electric field is uniform in each transverse plane. However, the field of OPF studies mainly the interaction with nonlinear media, where the phenomena emerge spontaneously as a consequence of an instability; another name that is commonly used to designate OPF is “transverse nonlinear optics.” Historically, the broad interest in OPF emerged as a natural evolution of the previous development of the field of optical instabilities and chaos, when the main attention shifted gradually from purely temporal effects to spatio-temporal phenomena. For both the fields of optical instabilities and OPF, continuous inspiration arose from the formulation of general disciplines as Hakens synergetics or Prigogines theory of dissipative structures

Cooperative frequency locking and stationary spatial structures in lasers

We investigate the spontaneous emergence of transverse patterns in lasers by using both the standard two-level model and the so-called cubic approximation, which is generally valid in the threshold regions. The stationary intensity configurations fall into two distinct classes. The first includes solutions of the single-mode type with the frequency and spatial structure of one of the transverse resonances. The solutions of the second group involve the simultaneous oscillation of several cavity modes, operating in such a way as to produce a stationary intensity profile. The stationary character of these multimode configurations emerges from the fact that the transverse modes of the resonator lock onto a common frequency during the nonlinear transient. We call this phenomenon cooperative frequency locking.

Instabilities and spatial complexity in a laser

We discuss the emergence of spatial structures in a ring laser model with transverse effects. The emphasis of this study is on the development of a description that can capture the essential features of transverse dynamics without the need for large-scale numerical efforts. We introduce an extension of the uniform field limit and derive a set of modal equations that we solve with conventional numerical methods. Our solutions show evidence of transverse mode competition in the laser dynamics, leading to both time-dependent and multimode stationary (cooperative frequency-locking) behaviors. In the time-dependent regime we analyze the resulting spatial structures and suggest a scheme for the investigation and characterization of spatial complexity.

Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion

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.