We generalized the well-known Lugiato-Lefever Equation to unify the description of combs and localized structures formation in nonlinear optical systems such as Kerr micro-resonators (passive systems) and Quantum Cascade Lasers (QCL) (active systems). In particular this model was applied to the study of pattern formation in a unidirectional ring QCL driven by a coherent injected field. We showed the existence of Dissipative Solitons (DS) and Turing rolls associated to standard and harmonic Optical Frequency Combs (OFC) in the system. We also provided a proof of principle demonstration of the possibility to deterministically control the spectral properties of these OFC by switching-on one or more DS with suitable addressing pulses.
These results considerably increase the theoretical insight in chip-scale combs sources in the mid-infrared region of the electromagnetic spectrum for timely applications in the field of e.g. high resolution and/or time resolved molecular spectroscopy, long range and high bit rate wireless communications.
We propose a generalization of the well-known Lugiato-Lefever Equation to unify the description of combs- and structures- forming nonlinear optical systems. This approach rigorously connects for the first time passive systems such as Kerr micro-resonators and active systems such as Quantum Cascade Lasers (QCLs) which were so far treated separately. The model effectively describes a unidirectional ring QCL driven by a coherent signal where we show the existence of temporal solitons and Turing rolls, previously identified only in Kerr micro-resonators, considerably increasing the theoretical insight and the technological potential of chip-scale comb sources.
It is well known that optical twin-beam states (TWB) generated by spontaneous parametric down-conversion (PDC) exhibit spatial and spectral correlations, which can appear in single-shot images obtained by using an imaging spectrometer to resolve emission angles and wavelengths simultaneously. By analyzing series of single-shot images recorded by an EMCCD camera at different powers of the pump beam, we studied the evolution of several quantities characterizing the generated TWB. In particular, we demonstrated that correlation widths in spectrum and space increase monotonically at low pump powers and then start decreasing at higher powers due to the onset of pump depletion. In a complementary way, the Fedorov ratio decreases and then increases again. At the same time, the number of modes evaluated from photon statistics follows a complementary behavior to correlation widths that can be interpreted in terms of the evolution of the number of Schmidt modes in the field.
In this paper we report about the experimental investigation of the non factorable spatio-temporal correlation of
twin beams generated in parametric down conversion (PDC) at the crystal output. We present the correlation
features to be reconstructed by means of the inverse process of PDC, that is sum frequency generation, in a
scheme based on achromatic imaging. In particular we show the ultra-narrow temporal localization (6fs) observed
thanks to the huge spectral bandwidth detected in the near field of the crystal. We illustrate the deteriorating
effects of imperfect imaging conditions or spatial modes selection on the temporal correlation, giving evidence of
the interdependence of spatial and temporal degrees of freedom in PDC as claimed by the theory. Throughout
the paper we shall discuss about the characteristics of the experimental set-up being used for the investigation
of the twin beam correlation in both the temporal and spatial domain, highlighting the important features for
the success of the experiment and the demonstration of the X-shaped structure of the space-time correlation,
already emerging from preliminary results.
We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function
of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-
matching taking into consideration a major part of the broad spectral and angular bandwidth of the down-
converted light. We derive an analytical expression for the Schmidt number as a function of the filter bandwidth
in the limit of spectrally narrow pump.
We investigate the spatio-temporal structure of the biphoton entanglement in Parametric Down Conversion
(PDC). In particular we study the biphoton amplitude at the output face of the nonlinear crystal (near-field)
and we demonstrate its X-shaped geometry in the space-time dimensions, i.e. the non-factorability of the state
with respect to spatial and temporal variables. Our analysis provides a precise and quantitative characterization
of this structure in various regimes and types of phase matching of PDC. The key elements of novelty emerging
from our analysis are the non-factorability of the state with respect to spatial and temporal variables, and the
extreme relative localization of the entangled photons, both in space (few microns) and time (few femtoseconds).
This extreme localization is connected to our ability to resolve the photon positions in the source near-field. The
non factorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of
freedom of twin photons.
We review and compare the results of quantum spatial correlation measurements in parametric down-conversion
in the high-gain pulsed regime, with preliminary measurements performed in the low-gain cw-pumped regime.
The diagnostics is based on a high quantum efficiency CCD camera, and in the second case the radiation pattern
is recorded after temporal integration of the "single-photon" spatial distribution. The effect of the detected
number of temporal modes on the accessibility of the sub-shot noise regime is discussed, together with the
identification of suitable regimes for weak image detection.
We propose an imaging scheme based on the quantum spatial correlation of twin beams generated by PDC,
and we show that it provides a substantial enhancement of the signal-to-noise ratio with respect to classical
schemes.
We propose an imaging scheme based on the quantum spatial correlation of twin beams generated by PDC,
and we show that it provides a substantial enhancement of the signal-to-noise ratio with respect to classical
schemes.
High-resolution ghost image and ghost diffraction are performed by using a single source of pseudo-thermal speckle light divided by a beam splitter. By only operating on the optical setup of the light in the reference arm, that never interacted with the object, we are able to pass from the image to the diffraction pattern. 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. A complementarity between the spatial coherence of the beams and their mutual correlation is demonstrated by showing a complementarity between ghost diffraction and ordinary diffraction patterns.
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.
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 the wave-particle duality features, which have been demonstrated in the microscopic case, persist in the macroscopic domain. Although the visibility of the information retrieved via correlation measurements in the regime of high photon number is lower than in the coincidence counting regime, we show that efficient reconstruction of both the image and the diffraction pattern of an object is possible.
KEYWORDS: Optical parametric oscillators, Chaos, Signal generators, Diffraction, Near field optics, Paraxial approximations, Nonlinear optics, Modulation, Analytical research, Near field
We demonstrate that the optical parametric oscillator is an ideal system for studying spatial pattern formation and quantum effects in spatial structures. In the first part of the article we analyze a semiclassical model which includes diffraction in the paraxial approximation, and we show the formation of rolls, zig-zag patterns, dislocations, filamentation, and optical chaos. In the second part of the paper we describe the spatial structure of the squeezed vacuum state emitted by the optical parametric oscillator below the threshold for signal generation.
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