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We study the interaction of a laser cavity-soliton microcomb with an externally coupled, co-propagating tunable CW pump, observing parametric Kerr interactions which lead to the formation of both a cross-phase modulation and a four-wave mixing replica of the laser cavity-soliton. We compare and explain the dependence of the microcomb spectra from both the cavity-soliton and pump parameters, demonstrating the ability to adjust the microcomb externally without breaking or interfering with the soliton state. The parametric nature of the process agrees with numerical simulations. The parametric extended state maintains the typical robustness of laser-cavity solitons.

This joint issue of Optics Express and Optical Materials Express showcases 29 articles that report the latest advancements in nonlinear optics. These articles include contributions from authors who participated in the Optica Nonlinear Optics Topical Meeting, which took place in Honolulu, Hawaii, from July 10th to July 14th, 2023. The conference was organized by Optica (formerly known as OSA). As an introduction, the editors provide a summary of these articles, which cover a broad range of topics in nonlinear optics, spanning from fundamental nonlinear optical concepts to novel nonlinear effects, and from innovative nonlinear materials to topics such as ultrafast optics, machine learning empowered nonlinear optics, and unconventional applications. This diverse array of contributions reflects the dynamic and interdisciplinary nature of contemporary research in the field of nonlinear optics while showcasing some of the most recent developments.

Complex media have emerged as a powerful and robust framework to control light-matter interactions designed for task-specific optical functionalities. Studies on wavefront shaping through disordered systems have demonstrated optical wave manipulation capabilities beyond conventional optics, including aberration-free and subwavelength focusing. However, achieving arbitrary and simultaneous control over the spatial and temporal features of light remains challenging. In particular, no practical solution exists for field-level arbitrary spatiotemporal control of wave packets. A new paradigm shift has emerged in the terahertz frequency domain, offering methods for absolute time-domain measurements of the scattered electric field, enabling direct field-based wave synthesis. In this work, we report the experimental demonstration of field-level control of single-cycle terahertz pulses on arbitrary spatial points through complex disordered media., Competing Interests: The authors declare no competing financial interest., (© 2024 The Authors. Published by American Chemical Society.)

Terahertz time-domain imaging targets the reconstruction of the full electromagnetic morphology of an object. In this spectral range, the near-field propagation strongly affects the information in the space-time domain in items with microscopic features. While this often represents a challenge, as the information needs to be disentangled to obtain high image fidelity, here, we show that such a phenomenon can enable three-dimensional microscopy. Specifically, we investigate the capability of the time-resolved nonlinear ghost imaging methodology to implement field-sensitive micro-volumetry by plane decomposition. We leverage the temporally resolved, field-sensitive detection to "refocus" an image plane at an arbitrary distance from the source, which defines the near-field condition, and within a microscopic sample. Since space-time coupling rapidly evolves and diffuses within subwavelength length scales, our technique can separate and discriminate the information originating from different planes at different depths. Our approach is particularly suitable for objects with sparse micrometric details. Building upon this principle, we demonstrate complex, time-domain volumetry resolving internal object planes with subwavelength resolution, discussing the range of applicability of our technique., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Controlling the transmission of broadband optical pulses in scattering media is a critical open challenge in photonics. To date, wavefront shaping techniques at optical frequencies have been successfully applied to control the spatial properties of multiple-scattered light. However, a fundamental restriction in achieving an equivalent degree of control over the temporal properties of a broadband pulse is the limited availability of experimental techniques to detect the coherent properties (i.e., the spectral amplitude and absolute phase) of the transmitted field. Terahertz experimental frameworks, on the contrary, enable measuring the field dynamics of broadband pulses at ultrafast (sub-cycle) time scales directly. In this work, we provide a theoretical/numerical demonstration that, within this context, complex scattering can be used to achieve spatio-temporal control of instantaneous fields and manipulate the temporal properties of single-cycle pulses by solely acting on spatial degrees of freedom of the illuminating field. As direct application scenarios, we demonstrate spatio-temporal focusing, chirp compensation, and control of the carrier-envelope-phase (CEP) of a CP-stable, transform-limited THz pulse., Competing Interests: No competing interests were disclosed., (Copyright: © 2023 Cecconi V et al.)

Laser cavity-soliton microcombs are robust optical pulsed sources, usually implemented with a microresonator-filtered fibre laser. In such a configuration, a nonlinear microcavity converts the narrowband pulse resulting from bandwidth-limited amplification to a background-free broadband microcomb. Here, we theoretically and experimentally study the soliton conversion efficiency between the narrowband input pulse and the two outputs of a four-port integrated microcavity, namely the 'Drop' and 'Through' ports. We simultaneously measure on-chip, single-soliton conversion efficiencies of 45% and 25% for the two broadband comb outputs at the 'Drop' and 'Through' ports of a 48.9 GHz free-spectral range micro-ring resonator, obtaining a total conversion efficiency of 72%.

Scattering-assisted synthesis of broadband optical pulses is recognized to have a cross-disciplinary fundamental and application importance. Achieving full-waveform synthesis generally requires means for assessing the instantaneous electric field, i.e., the absolute electromagnetic phase. These are generally not accessible to established methodologies for scattering-assisted pulse envelope and phase shaping. The lack of field sensitivity also results in complex indirect approaches to evaluate the scattering space-time properties. The terahertz frequency domain potentially offers some distinctive new possibilities, thanks to the availability of methods to perform absolute measurements of the scattered electric field, as opposed to optical intensity-based diagnostics. An interesting conceptual question is whether this additional degree of freedom can lead to different types of methodologies toward wave shaping and direct field-waveform control. In this work, we theoretically investigate a deterministic scheme to achieve broadband, spatiotemporal waveform control of terahertz fields mediated by a scattering medium. Direct field access via time-domain spectroscopy enables a process in which the field and scattering matrix of the medium are assessed with minimal experimental efforts. Then, illumination conditions for an arbitrary targeted output field waveform are deterministically retrieved through numerical inversion. In addition, complete field knowledge enables reconstructing field distributions with complex phase profiles, as in the case of phase-only masks and optical vortices, a significantly challenging task for traditional implementations at optical frequencies based on intensity measurements aided with interferometric techniques., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters 1,2 . These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser 3 that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons 2 that generally need to be induced by external perturbations, as in the case of optical memories 4,5 . In the past decade, these highly localized states have enabled important advancements in microresonator-based optical frequency combs 6,7 . However, the very advantages that make cavity solitons attractive for memories-their inability to form spontaneously from noise-have created fundamental challenges. As sources, microcombs require spontaneous and reliable initiation into a desired state that is intrinsically robust 8-20 . Here we show that the slow non-linearities of a free-running microresonator-filtered fibre laser 21 can transform temporal cavity solitons into the system's dominant attractor. This phenomenon leads to reliable self-starting oscillation of microcavity solitons that are naturally robust to perturbations, recovering spontaneously even after complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space in which specific states, highly stable over long timeframes, can be achieved., (© 2022. The Author(s).)

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not require saturation of the gain, the results offer an alternative to standard techniques that provide laser mode-locking.

Background: The use of dasatinib and nilotinib in the treatment of patients with chronic myeloid leukemia represents a valid therapeutic option for patients resistant or intolerant to imatinib. In this multicentre study, adherence, persistence and efficacy in real life over two years of treatment were evaluated., Materials and Methods: Adherence to treatment was calculated as the ratio between the dose received and the prescribed dose. The dose received was calculated using pharmacy refill data. The persistence with treatment was calculated as the difference between the end and the beginning of the treatment. Efficacy was assigned as Progression-Free Survival (PFS) and Events-Free Survival (EFS) and represented through the Kaplan-Meier curve., Results: The number of patients analysed was 117, 70 treated with dasatinib and 47 with nilotinib. Adherence to treatment for dasatinib and nilotinib at two years was 0.91 and 0.82 respectively. Persistence at two years was 77% while the PFS was 92% for both drugs in the study., Conclusion: Adherence to the treatment calculated over two years showed a superiority of dasatinib over nilotinib. Nevertheless, the efficacy in terms of PFS and EFS is superimposable between the two drugs in the study.

Two-color terahertz (THz) generation is a field-matter process combining an optical pulse and its second harmonic. Its application in condensed matter is challenged by the lack of phase matching among multiple interacting fields. Here, we demonstrate phase-matching-free two-color THz conversion in condensed matter by introducing a highly resonant absorptive system. The generation is driven by a third-order nonlinear interaction localized at the surface of a narrow-band-gap semiconductor, and depends directly on the relative phase between the two colors. We show how to isolate the third-order effect among other competitive THz-emitting surface mechanisms, exposing the general features of the two-color process.

Terahertz (THz) imaging is a rapidly emerging field, thanks to many potential applications in diagnostics, manufacturing, medicine and material characterisation. However, the relatively coarse resolution stemming from the large wavelength limits the deployment of THz imaging in micro- and nano-technologies, keeping its potential benefits out-of-reach in many practical scenarios and devices. In this context, single-pixel techniques are a promising alternative to imaging arrays, in particular when targeting subwavelength resolutions. In this work, we discuss the key advantages and practical challenges in the implementation of time-resolved nonlinear ghost imaging (TIMING), an imaging technique combining nonlinear THz generation with time-resolved time-domain spectroscopy detection. We numerically demonstrate the high-resolution reconstruction of semi-transparent samples, and we show how the Walsh-Hadamard reconstruction scheme can be optimised to significantly reduce the reconstruction time. We also discuss how, in sharp contrast with traditional intensity-based ghost imaging, the field detection at the heart of TIMING enables high-fidelity image reconstruction via low numerical-aperture detection. Even more striking-and to the best of our knowledge, an issue never tackled before-the general concept of "resolution" of the imaging system as the "smallest feature discernible" appears to be not well suited to describing the fidelity limits of nonlinear ghost-imaging systems. Our results suggest that the drop in reconstruction accuracy stemming from non-ideal detection conditions is complex and not driven by the attenuation of high-frequency spatial components (i.e., blurring) as in standard imaging. On the technological side, we further show how achieving efficient optical-to-terahertz conversion in extremely short propagation lengths is crucial regarding imaging performance, and we propose low-bandgap semiconductors as a practical framework to obtain THz emission from quasi-2D structures, i.e., structure in which the interaction occurs on a deeply subwavelength scale. Our results establish a comprehensive theoretical and experimental framework for the development of a new generation of terahertz hyperspectral imaging devices., Competing Interests: The authors declare no conflict of interest.

Nanohybrid materials based on nanoparticles of the intrinsically microporous polymer PIM-1 and graphene oxide (GO) are prepared from aqueous dispersions with a reprecipitation method, resulting in the surface of the GO sheets being decorated with nanoparticles of PIM-1. The significant blueshift in fluorescence signals for the GO/PIM-1 nanohybrids indicates modification of the optoelectronic properties of the PIM-1 in the presence of the GO due to their strong interactions. The stiffening in the Raman G peak of GO (by nearly 6 cm -1 ) further indicates p-doping of the GO in the presence of PIM. Kelvin probe force microscopy (KPFM) and electrochemical reduction measurements of the nanohybrids provide direct evidence for charge transfer between the PIM-1 nanoparticles and the GO nanosheets. These observations will be of importance for future applications of GO-PIM-1 nanohybrids as substrates and promoters in catalysis and sensing.

We report on 'slow' pulsing dynamics in a silica resonator-based laser system: by nesting a high-Q rod-resonator inside an amplifying fiber cavity, we demonstrate that trains of microsecond pulses can be generated with repetition rates in the hundreds of kilohertz. We show that such pulses are produced with a period equivalent to several hundreds of laser cavity roundtrips via the interaction between the gain dynamics in the fiber cavity and the thermo-optical effects in the high-Q resonator. Experiments reveal that the pulsing properties can be controlled by adjusting the amplifying fiber cavity parameters. Our results, confirmed by numerical simulations, provide useful insights on the dynamical onset of complex self-organization phenomena in resonator-based laser systems where thermo-optical effects play an active role. In addition, we show how the thermal state of the resonator can be probed and even modified by an external, counter-propagating optical field, thus hinting towards novel approaches for all-optical control and sensing applications.

Modern optical systems increasingly rely on complex physical processes that require accessible control to meet target performance characteristics. In particular, advanced light sources, sought for, for example, imaging and metrology, are based on nonlinear optical dynamics whose output properties must often finely match application requirements. However, in these systems, the availability of control parameters (e.g., the optical field shape, as well as propagation medium properties) and the means to adjust them in a versatile manner are usually limited. Moreover, numerically finding the optimal parameter set for such complex dynamics is typically computationally intractable. Here, we use an actively controlled photonic chip to prepare and manipulate patterns of femtosecond optical pulses that give access to an enhanced parameter space in the framework of supercontinuum generation. Taking advantage of machine learning concepts, we exploit this tunable access and experimentally demonstrate the customization of nonlinear interactions for tailoring supercontinuum properties.

We propose a scheme for bifurcation control in micro-cavities based on the interplay between the ultrafast Kerr effect and a slow nonlinearity, such as thermo-optical, free-carriers-induced, or opto-mechanical one. We demonstrate that Hopf bifurcations can be efficiently controlled with a low energy signal via four-wave mixing. Our results show that new strategies are possible for designing efficient micro-cavity-based oscillators and sensors. Moreover, they provide new understanding of the effect of coherent wave mixing in the thermal stability regions of optical micro-cavities, fundamental for micro-resonator-based applications in communications, sensing, and metrology, including optical micro-combs.

We introduce a method for diagnosing the electric surface potential of a semiconductor based on THz surface generation. In our scheme, that we name Optical Pump Rectification Emission, a THz field is generated directly on the surface via surface optical rectification of an ultrashort pulse after which the DC surface potential is screened with a second optical pump pulse. As the THz generation directly relates to the surface potential arising from the surface states, we can then observe the temporal dynamics of the static surface field induced by the screening effect of the photo-carriers. Such an approach is potentially insensitive to bulk carrier dynamics and does not require special illumination geometries.

In this paper, we demonstrate a novel dual-pump approach to generate robust optical frequency comb with varying free spectral range (FSR) spacing in a CMOS-compatible high-Q micro-ring resonator (MRR). The frequency spacing of the comb can be tuned by an integer number FSR of the MRR freely in our dual-pump scheme. The dual pumps are self-oscillated in the laser cavity loop and their wavelengths can be tuned flexibly by programming the tunable filter embedded in the cavity. By tuning the pump wavelength, broadband OFC with the bandwidth of >180 nm and the frequency-spacing varying from 6 to 46-fold FSRs is realized at a low pump power. This approach could find potential and practical applications in many areas, such as optical metrology, optical communication, and signal processing systems, for its excellent flexibility and robustness.

Nonlinear optical processes are one of the most important tools in modern optics with a broad spectrum of applications in, for example, frequency conversion, spectroscopy, signal processing and quantum optics. For practical and ultimately widespread implementation, on-chip devices compatible with electronic integrated circuit technology offer great advantages in terms of low cost, small footprint, high performance and low energy consumption. While many on-chip key components have been realized, to date polarization has not been fully exploited as a degree of freedom for integrated nonlinear devices. In particular, frequency conversion based on orthogonally polarized beams has not yet been demonstrated on chip. Here we show frequency mixing between orthogonal polarization modes in a compact integrated microring resonator and demonstrate a bi-chromatically pumped optical parametric oscillator. Operating the device above and below threshold, we directly generate orthogonally polarized beams, as well as photon pairs, respectively, that can find applications, for example, in optical communication and quantum optics.

Terahertz technologies recently emerged as outstanding candidates for a variety of applications in such sectors as security, biomedical, pharmaceutical, aero spatial, etc. Imaging the terahertz field, however, still remains a challenge, particularly when sub-wavelength resolutions are involved. Here we demonstrate an all-optical technique for the terahertz near-field imaging directly at the source plane. A thin layer (<100 nm-thickness) of photo carriers is induced on the surface of the terahertz generation crystal, which acts as an all-optical, virtual blade for terahertz near-field imaging via a knife-edge technique. Remarkably, and in spite of the fact that the proposed approach does not require any mechanical probe, such as tips or apertures, we are able to demonstrate the imaging of a terahertz source with deeply sub-wavelength features (<30 μm) directly in its emission plane.

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

We demonstrate, theoretically and experimentally, that a four-wave mixing parametric interaction is able to arrest the collapse of a two-dimensional multicolor beam in an instantaneous Kerr medium. We consider two weak idlers interacting via a third order nonlinearity with two pump beams and we show that a class of collapse-free quasisolitary solutions can be experimentally observed in a normal dispersion Kerr glass. This observation is sustained by rigorous theoretical analysis demonstrating the stability of the observed self-trapped beams.

We report an integrated all-optical radio frequency spectrum analyzer based on a ~4 cm long doped silica glass waveguide, with a bandwidth greater than 2.5 THz. We use this device to characterize the intensity power spectrum of ultrahigh repetition rate mode-locked lasers at repetition rates up to 400 GHz, and observe dynamic noise related behavior not observable with other techniques.

We report an integrated photon pair source based on a CMOS-compatible microring resonator that generates multiple, simultaneous, and independent photon pairs at different wavelengths in a frequency comb compatible with fiber communication wavelength division multiplexing channels (200 GHz channel separation) and with a linewidth that is compatible with quantum memories (110 MHz). It operates in a self-locked pump configuration, avoiding the need for active stabilization, making it extremely robust even at very low power levels.

We report a novel geometry for OPOs based on nonlinear microcavity resonators. This approach relies on a self-locked scheme that enables OPO emission without the need for thermal locking of the pump laser to the microcavity resonance. By exploiting a CMOS-compatible microring resonator, we achieve oscillation featured by a complete absence of "shutting down", i.e. the self-terminating behavior that is a very common and detrimental occurrence in externally pumped OPOs. Further, our scheme consistently produces very wide bandwidth (>300nm, limited by our experimental set-up) combs that oscillate at a spacing equal to the FSR of the micro cavity resonance.

We present an extraction algorithm for spectral phase interferometry for direct field reconstruction (SPIDER) in the so-called X-SPIDER configuration. Our approach largely extends the measurable time windows of pulses without requiring any modification to the experimental X-SPIDER setup.

We demonstrate a novel mode locked ultrafast laser, based on an integrated high-Q microring resonator. Our scheme exhibits stable operation of two slightly shifted spectral optical comb replicas. It generates a highly monochromatic radiofrequency modulation of 65.8MHz with a linewidth < 10kHz, on a 200GHz output pulse train.

Ultrashort pulsed lasers, operating through the phenomenon of mode-locking, have had a significant role in many facets of our society for 50 years, for example, in the way we exchange information, measure and diagnose diseases, process materials, and in many other applications. Recently, high-quality resonators have been exploited to demonstrate optical combs. The ability to phase-lock their modes would allow mode-locked lasers to benefit from their high optical spectral quality, helping to realize novel sources such as precision optical clocks for applications in metrology, telecommunication, microchip-computing, and many other areas. Here we demonstrate the first mode-locked laser based on a microcavity resonator. It operates via a new mode-locking method, which we term filter-driven four-wave mixing, and is based on a CMOS-compatible high quality factor microring resonator. It achieves stable self-starting oscillation with negligible amplitude noise at ultrahigh repetition rates, and spectral linewidths well below 130  kHz.

We report on the observation of Type I third-harmonic generation induced by a train of femtosecond laser pulses in nematic liquid crystals. We find that as the average power of the train is increased, the frequency conversion process is enhanced as a consequence of the tight confinement of the pulses into a nonlocal spatial soliton.

We demonstrate sub-picosecond wavelength conversion in the C-band via four wave mixing in a 45cm long high index doped silica spiral waveguide. We achieve an on/off conversion efficiency (signal to idler) of + 16.5dB as well as a parametric gain of + 15dB for a peak pump power of 38W over a wavelength range of 100nm. Furthermore, we demonstrated a minimum gain of + 5dB over a wavelength range as large as 200nm.

We present the first system penalty measurements for all-optical wavelength conversion in an integrated ring resonator. We achieve wavelength conversion over a range of 27.7 nm in the C-band at 2.5 Gb/s by exploiting four wave mixing in a CMOS compatible, high index glass ring resonator at approximately 22 dBm average pump power, obtaining < 0.3 dB system penalty.

We observe second harmonic generation via random quasi-phase-matching in a 2.0 mum periodically poled, 1-cm-long, z-cut lithium tantalate. Away from resonance, the harmonic output profiles exhibit a characteristic pattern stemming from a stochastic domain distribution and a quadratic growth with the fundamental excitation, as well as a broadband spectral response. The results are in good agreement with a simple model and numerical simulations in the undepleted regime, assuming an anisotropic spread of the random nonlinear component.

We observe attraction, repulsion and energy exchange between two self-trapped beams in a heavy-metal-oxide glass exhibiting a Kerr-like response with multiphoton absorption. The coherent interaction between spatial solitons is controlled by their relative phase and modelled by a nonlinear dissipative Schrödinger equation.

We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

We demonstrate two-dimensional spatial solitons excited by near-infrared picosecond pulses in Kerr-like heavy metal oxide glasses with a nonlinearity one order of magnitude larger than in fused silica. Solitons were obtained at 820 nm owing to the presence of multiphoton absorption, which prevented catastrophic collapse.

We tested some cardiovascular reflexes (Valsalva ratio, deep-breathing, postural hypotension) in 53 subjects suffering from diabetes type I in childhood with an average disease length of 13 +/- 6 years, in order to estimate possible damage to the autonomic nervous system without clinical symptomatology. A rather high percentage of signs of neurovegetative involvement combined with the progressive increase of further complications during the course of the disease, suggests early neurologic damage. We confirm the sensitivity of adopted tests and deep-breathing in particular.