So far, dissipative temporal solitons in a laser with a saturable absorber have been studied mainly in the context either of Haus's master equation or of the cubic-quintic complex Ginzburg-Landau equation.
We present here a study based on an equation which includes saturation of the amplifier via a cubic approximation and saturation of the absorber at all orders. The equation describes well a system where both gain and absorption are fast, the laser is close to threshold, the unsaturated absorption is small, and the saturation intensity of the amplifier is much larger than that of the absorber. The model is appropriate for fast semiconductor lasers, such as quantum cascade lasers, since it encompasses the relevant phase-amplitude coupling via the linewidth enhancement factors of the gain and absorption media. Our study shows the crucial role played by these factors in the transition from cw emission to various types of pulsed emission, including dissipative temporal solitons.
Active resonators based on semiconductor gain media encompass a large optical nonlinearity that arises from gain saturation and enables bright soliton generation. The ability to operate these resonators below the lasing threshold as tunable passive devices –– filters, modulators, phase shifters –– opens up an untapped potential of seamlessly integrated reconfigurable devices for both generation of multimode mid-infrared (4 – 12 μm) light and its manipulation.
We use a prototypical model based on the Complex Ginzburg Landau Equation to study the dynamics of a multimode ring quantum cascade laser. We predict the existence and stability of different classes of localized structures in the system. In presence of coherent injection, we report the formation dissipative Temporal Solitons (TSs) which manifest multi-stability and coexistence with a stable CW solution. We show how these features allow for external manipulation of the spectral content of the optical frequency combs associated with TSs with a big impact on applications in the field of e.g. high precision spectroscopy and wireless communications.
Monolithic ring Quantum Cascade Lasers (QCLs) have recently emerged as a new platform for frequency comb generation in the mid-infrared with immediate applications in molecular gas spectroscopy and photonic generation of stable coherent sub-THz tones. In this talk I will show that depending on the way they are driven, ring QCLs can act as carrier generators, integrated intensity modulators, tunable filters, and on-chip optical amplifiers. The natural predisposition of these components to photonic integration opens a route to compact mid-infrared WDM transceivers for free space optical links and miniaturized 2D IR spectrometers.
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.
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 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.
CSs have been theoretically predicted and recently experimentally
demonstrated in broad area, vertical cavity, driven semiconductor
lasers (VCSELs) slightly below the lasing threshold. Above
threshold, the simple adiabatic elimination of the polarization
variable is not correct, leading to oscillatory instabilities with
a spuriously high critical wave-number. To achieve real insight on
the complete dynamical problem, we study here the complete system
of equations and find regimes where a Hopf instability, typical of
lasers above threshold, affects the lower intensity branch of the
homogeneous steady state, while the higher intensity branch is
unstable due to a Turing instability. Numerical results obtained
by direct integration of the dynamical equations show that
writable/erasable CSs are possible in this regime, sitting on
unstable background.
Cavity solitons are stationary self-organized bright intensity peaks which form over a homogeneous background in the section of broad area radiation beams. They are generated by shining a writing/erasing laser pulse into a nonlinear optical cavity, driven by a holding beam. The ability to control their location and their motion by introducing phase or amplitude gradients in the holding beam makes them interesting as mobile pixels for all-optical processing units. We show the generation of a number of cavity solitons in broad area vertical cavity semiconductor microresonators electrically pumped above transparency but slightly below threshold. The observed spots can be written, erased and manipulated as independent objects. We analyze experimentally the cavity solitons domain of existence in the parameter space and how their characteristics are affected by inhomogeneities and impurities of the vertical cavity devices. A theoretical model, keeping into account the devices characteristics, reproduces numerically the experimental observations with good agreement.
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.
The dead-space carrier multiplication theory properly predicts the reduction in the excess noise factor in a number of APDs. The theory is applied to measurements, obtained from J. C. Campbell and collaborators at the University of Texas, for InP, InAlAs, GaAs, and AlGaAs APDs with multiplication-region widths ranging from 80 nm to 1600 nm. A refined model for the ionization coefficients is reported that is independent of the width of the device multiplication region of each device. In addition, in comparison to predictions from the conventional multiplication theory, the dead-space multiplication theory predicts a reduction in the mean bandwidth as well as a reduction in the power spectral density of the impulse response. In particular, it is shown that the avalanching noise at high-frequencies is reduced as a result of the reduction of the multiplication region width.
Cavity solitons appear as bright spots in the transverse intensity profile. They are similar to spatial solitons, but arise in dissipative systems. Here we consider a broad area vertical cavity resonator, driven by an external coherent field, at room temperature. The active material is constituted either by bulk GaAs, or by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). A general model valid for both configurations is presented and a set of nonlinear dynamical equations is derived. The linear stability analysis of the homogeneous steady states is performed in a general form, holding for the two cases. Then, the nonlinear susceptibilities are specified: in the bulk case, we basically work in the free-carrier approximation, with some phenomenological corrections, such as the Urbach tail and the band-gap renormalization. For the bulk case, some numerical results concerning spatial pattern formation and cavity solitons are given. In the MQW case, on the contrary, we derive a full many-body theory, with the Coulomb enhancement treated in the Pade approximation.
We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently by Kolobov and Lugiato [Phys. Rev. A 52, 4930 (1995)] for a cavity-based geometry, such a scheme can amplify images, without deteriorating their sign-to-noise ratio, thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We investigate in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. The spatial resolution power, which guarantees noiseless amplification is estimated. We demonstrate how the optimum phase matching of a phase-sensitive wavefront of the image can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the effect of improvement of the signal-to-noise ratio in the case of observation of both the input and the amplified image, with an ideal photodetector of small area (i.e., much less than the coherence area of the amplifier). This improvement is due to the fact that the signal-to-noise ratio in the input is deteriorated by the observation with the photodetector of small area.
We consider a degenerate optical parametric oscillator consisting of a crystal in a ring resonator. The occurrence of spatial instabilities in such system due to diffraction are studied and it is shown that they may lead to the formation of stationary or dynamical spatial patterns. The thresholds for such instabilities are derived when either the pumped and the generated modes are detuned with respect to the cavity reference frequency; the patterns that emerge from the instability are calculated analytically by bifurcation analysis. Numerical simulations substantially confirm the onset of such phenomena giving evidence of the formation of rolls, zig-zag patterns, dislocations, filamentation and optical chaos.
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.
We show that to analyze the spatial structure of a squeezed state it is necessary to use a local field oscillator with arbitrary spatial configuration.
The static and dynamical structures that emerge in lasers that operate with several transverse modes are discussed. Optical vortices form crystalline arrays and give rise to processes of creation and annihilation in pairs.
A model is presented for the dynamical evolution of optical bistable devices based on Multiple Quantum Well structures, in which the
electric field is near resonance with an excitonic line, and the
parameters which appear in the equations are discussed. For room ternperature
operation, examples of steady state response curves are presented.
In conditions of adiabatic elimination of the exciton density
and within the assumption of small carrier density, it is shown that
the set of equations is equivalent to the well known model for optical
bistability in two level systems.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.