Nonlinear Optical Experiments Research Articles

Linear response of molecular polaritons.

In this article, we show that the collective light-matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A-C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

On-target delivery of intense ultrafast laser pulses through hollow-core anti-resonant fibers.

We report the flexible on-target delivery of 800 nm wavelength, 5 GW peak power, 40 fs duration laser pulses through an evacuated and tightly coiled 10 m long hollow-core nested anti-resonant fiber by positively chirping the input pulses to compensate for the anomalous dispersion of the fiber. Near-transform-limited output pulses with high beam quality and a guided peak intensity of 3 PW/cm2 were achieved by suppressing plasma effects in the residual gas by pre-pumping the fiber with laser pulses after evacuation. This appears to cause a long-term removal of molecules from the fiber core. Identifying the fluence at the fiber core-wall interface as the damage origin, we scaled the coupled energy to 2.1 mJ using a short piece of larger-core fiber to obtain 20 GW at the fiber output. This scheme can pave the way towards the integration of anti-resonant fibers in mJ-level nonlinear optical experiments and laser-source development.

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support.

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov etal. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.

Matter-wave gap solitons and vortices of dense Bose–Einstein condensates in Moiré optical lattices

Optical lattices provide a key enabling and controllable platform for exploring new physical phenomena and implications of degenerate quantum gases both in the quantum and nonlinear regimes. Based on the Gross–Pitaevskii/nonlinear Schrödinger equation with competing cubic–quintic nonlinearity, we show, numerically and theoretically, the nonlinear localization of dense Bose–Einstein condensates (BECs) in a novel two-dimensional twisted periodic potential called Moiré optical lattices which, in essence, build a bridge between the perfect optical lattices and aperiodic ones. Our theory reveals that the Moiré optical lattices display a wider second gap and flat-band feature, and support two kinds of localized matter-wave structures like gap solitons and topological states (gap vortices) with vortex charge s=1, all populated inside the finite gaps of the linear Bloch-wave spectrum. We demonstrate, by means of linear-stability analysis and direct perturbed evolutions, that these localized structures have wide stability regions, paving the way for studying flat-band and Moiré physics in shallow optical lattices and for finding robust coherent matter waves therein. The twisted periodic structures can be readily implemented with currently available optical-lattice technique in BECs and nonlinear optics experiments where the results predicted here are observable.

Dynamical evolutions of optical smooth positons in variable coefficient nonlinear Schrödinger equation with external potentials

We construct the optical smooth positon solutions for the generalized variable coefficient nonlinear Schrödinger equation with longitudinally varying dispersion, nonlinearity, linear and harmonic potentials. By employing the similarity transformation technique, we derive this solution along with the homogeneous smooth positon solutions of the basic NLS equation and the integrable requirement. The dynamical properties of the constructed second- and third-order positon solutions are investigated considering the two physical scenarios. In the first situation, we consider a longitudinally variable linear potential while keeping the dispersion parameter constant. In the second scenario, we take into account three different types of modulated dispersion parameters, namely quadratic, exponential, and linear, to analyze the various features in the intensity profile of inhomogeneous optical smooth positons. In both situations, we observe a wide range of significant nonlinear phenomena in the intensity profiles of positons. These phenomena include amplification, deformation, compression, prolongation, suppression, and distortion. Our findings could make a significant contribution to intriguing nonlinear optics experiments focused on investigating optical positons.

Post-2000 nonlinear optical materials and measurements: data tables and best practices

In its 60 years of existence, the field of nonlinear optics has gained momentum especially over the past two decades thanks to major breakthroughs in material science and technology. In this article, we present a new set of data tables listing nonlinear-optical properties for different material categories as reported in the literature since 2000. The papers included in the data tables are representative experimental works on bulk materials, solvents, 0D–1D–2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, hybrid waveguiding systems, and materials suitable for nonlinear optics at THz frequencies. In addition to the data tables, we also provide best practices for performing and reporting nonlinear-optical experiments. These best practices underpin the selection process that was used for including papers in the tables. While the tables indeed show strong advancements in the field over the past two decades, we encourage the nonlinear-optics community to implement the identified best practices in future works. This will allow a more adequate comparison, interpretation and use of the published parameters, and as such further stimulate the overall progress in nonlinear-optical science and applications.

Synthesis, structural and spectral investigations of an optically active E-N′-(3,4-dimethoxybenzylidene)− 4-fluorobenzohydrazide crystal

Hydrazines represent a group of compounds with pronounced pharmacological activities, along with their possible use of optically active materials. In this contribution, E-N′-(3,4-dimethoxybenzylidene)− 4-fluorobenzohydrazide (DBF) was synthesized and chemically characterized by X-ray crystallography, IR, Raman, UV–VIS, and NMR spectroscopies. The intermolecular interactions governing the stability of the crystal were investigated by the Hirshfeld surface analysis. The structure optimization was performed starting from a crystallographic one. The highest resemblance between experimental and theoretical bond lengths and angles was obtained for the structure at M06–2X/6–311 + +G(d,p) level of theory. The Natural Bond Orbital (NBO) and Quantum Theory of Atoms in Molecules (QTAIM) analyses outlined the most important intramolecular interactions. The IR and Raman spectra vibrational peaks were assigned based on the Potential Energy Distribution (PED) analysis. Theoretical methods with high correlation factors and low mean absolute error reproduced the NMR chemical shifts. The excited state optimization of DBF with a difference of several nm modelled the peak at 330 nm in the experimental UV–VIS spectrum. The Condensed Fukui functions outlined the most active positions for electrophilic, neutrophilic, and radical attacks. The non-linear optical (NLO) Z-scan experiment determined the absorption coefficient and nonlinear refractive index, concluding that DBF can be used as NLO material. The ECOSAR prediction of toxicity showed that the material could be potentially dangerous for aquatic organisms.

Compact Metasurface-Based Optical Pulse-Shaping Device.

Dispersion is present in every optical setup and is often an undesired effect, especially in nonlinear-optical experiments where ultrashort laser pulses are needed. Typically, bulky pulse compressors consisting of gratings or prisms are used to address this issue by precompensating the dispersion of the optical components. However, these devices are only able to compensate for a part of the dispersion (second-order dispersion). Here, we present a compact pulse-shaping device that uses plasmonic metasurfaces to apply an arbitrarily designed spectral phase delay allowing for a full dispersion control. Furthermore, with specific phase encodings, this device can be used to temporally reshape the incident laser pulses into more complex pulse forms such as a double pulse. We verify the performance of our device by using an SHG-FROG measurement setup together with a retrieval algorithm to extract the dispersion that our device applies to an incident laser pulse.

An Alternative Method to Determine the Quantum Yield of the Excited Triplet State Using Laser Flash Photolysis

The excited triplet state of a molecule (T1) is one of the principal intermediate products in various photochemical processes due to its high reactivity and relatively long lifetime. The T1 quantum yield (φT) is one of the most important characteristics in the study of photochemical reactions. It is of special interest to determine the φT of various photoactive compounds (photosensitizer, PS) used in photodynamic therapy (PDT). PDT is an effective medical technique for the treatment of serious diseases, such as cancer and bacterial, fungal and viral infections. This technique is based on the introduction of a PS to a patient’s organism and its further excitation by visible light, producing reactive oxygen species (ROS) via electron or energy transfer from the PS T1 state to the biological substrate or molecular oxygen. Therefore, information on the φT value is fundamental in the search for new and effective PSs. There are various experimental methods to determine φT values; however, these methods demonstrate a high discrepancy between φT values. This stimulates the analysis of various factors that can affect the determined φT. In this study, we analyze the effect of the intensity profile of the exciting laser pulse on the calculation of the φT value obtained by the Laser Flash Photolysis technique. The φT values were determined by analyzing the variation of a sample transient absorption in the function of the exciting laser pulse intensity, in combination with the spectral and kinetic PS characteristics obtained in nonlinear optical experiments by solving the rate equations of a five-level-energy diagram. Well-studied PSs: meso-tetra(4-sulfonatophenyl) (TPPS4) porphyrins, its zinc complex (ZnTPPS4) and the zinc complex of meso-tetrakis(N-methylpyridinium-4-yl) (ZnTMPyP) were chosen as test compounds to evaluate the proposed model. The φT values were determined through a comparison with the φT,TMPyP = 0.82 of meso-tetrakis(N-methylpyridinium-4-yl) (TMPyP), used as a standard. The obtained results (φT,TPPS4=0.75±0.02, φT,ZnTMPyP=0.90±0.03), and φT,ZnTPPS4=0.89±0.03) are highly compatible with the medium φT values obtained using the known methods.

Self‐Referencing 3D Characterization of Ultrafast Optical‐Vortex Beams Using Tilted Interference TERMITES Technique (Laser Photonics Rev. 17(4)/2023)

3D Reconstruction of Ultrafast Vortex Pulses Ultrafast optical-vortex beams carrying orbital angular momentum are of particular importance in many nonlinear-optics experiments. In article number 2200697, Jinyu Pan, Zhiyuan Huang, Meng Pang, Yuxin Leng, and colleagues developed a novel total electrical-field measurement set-up based on a tilted optical interferometer, which can be used to reconstruct, in a self-referenced manner, the spatio-temporal information of ultrafast vortex pulses.

Laguerre–Gaussian vortex beam for reduced thermal effects in nonlinear optical studies

Interaction of an intense laser beam with a material induces many thermal effects. In this work, thermo-optic effects induced by fundamental Gaussian and Laguerre–Gaussian vortex (LGV) laser beams in a sample in nonlinear optical (NLO) experiments are compared and their impact on the accuracy of determining the nonlinear susceptibility is examined. A solution of saturable absorber dye IR 26 in dichloroethane with the technique of z-scan to determine its third order nonlinear susceptibility was used as a model system. The LGV beams were generated by passing the Hermite–Gaussian beams from an Ar-ion laser through a cylindrical lens mode converter. Pump–probe setup was used to study the thermo-optic effects. Experiments and simulations suggest that the LGV beam is advantageous to reduce the thermal effects.

The nonlinear effects and applications of gain doped whispering-gallery mode cavities

Whispering-gallery mode (WGM) cavities formed by dielectric structures have attracted intensive interest in various fields. The high-quality factor and smaller mode volume associated with the optical modes have inspired experiments in nonlinear optics, nanophotonics, and quantum information science. Moreover, they are also used in optical biosensors and other significant applications. To further reduce the material loss of the resonator, optical gain materials, such as erbium and ytterbium, are doped into the dielectric structure to increase the nonlinear effect and enhance the interaction between light and matter. Here in this review, we outline the most recent advancements in gain-doped optical WGM microcavities. Moreover, we introduce the dynamics of the gain in WGM resonators, the integration of gain media into WGM microcavities with various shapes, and the fabrication and applications of the gain microcavities. Also, the applications of the gain cavity based on the whispering-gallery mode have been introduced, e.g., ultra-sensitive sensors, low-threshold lasers, and high-performance optical systems.

Application of the pyrazolone derivatives as effective modulators in the opto-electronic networks

Materials engineering plays a pivotal role in the modern technologies and individual solutions for various applications. In this contribution we describe two pyrazolone-based organic chromophores that differ slightly in structure, but represent a significantly various spectroscopic response. Based on the quantum-chemical calculations, namely TD-DFT model, HOMO-LUMO maps estimation, we have implemented both derivatives in the 2nd and 3rd order nonlinear optical (NLO) experiments. Pyrazolone-based organic systems occurred to be sensitive and appealing all-optical modulators as well as SHG and THG signals generators. The presence of a small methoxy group or its lack in the dye structure directly affects the kinetics of photoinduced birefringence, and its magnification. Moreover, it allows to determine the ease modulation of higher harmonic of the light induction according to the provided experimental polarization spatial conditions. Such approach enables to design and implement individually adjusted organic components to the complex opto-electronic networks and highly effective photonic architectures.

Magneto-optical Spectroscopy with RAMBO: A Table-Top 30 T Magnet

Optically probing materials in high magnetic fields can provide enlightening insight into field-modified electronic states and phases, while optically driving materials in high magnetic fields can induce novel nonequilibrium many-body dynamics of spin and charge carriers. While there are high-field magnets compatible with standard optical spectroscopy methods, they are generally bulky and have limited optical access, which prohibit performing state-of-the-art ultrafast and/or nonlinear optical experiments. The Rice Advanced Magnet with Broadband Optics (RAMBO), a unique 30-T pulsed mini-coil magnet system with direct optical access, has enabled previously challenging experiments using femtosecond optical pulses, including time-domain terahertz spectroscopy, in cutting-edge materials placed in strong magnetic fields. Here, we review recent experimental advances made possible by the first-generation RAMBO setup. After summarizing technological aspects of combining optical spectroscopic techniques with the mini-coil magnet, we describe results of magneto-optical studies of a wide variety of materials, providing new insight into the states and dynamics of four types of quasiparticles in solids - excitons, plasmons, magnons, and phonons - in high magnetic fields.

Optical second harmonic signature of phase coexistence in ferroelectric|dielectric heterostructures

An exotic coexistence of polar states is known to occur in $\text{ferroelectric}|\text{dielectric} {\mathrm{PbTiO}}_{3}|{\mathrm{SrTiO}}_{3}$ ($\mathrm{PTO}|\mathrm{STO}$) heterostructures. In the PTO layers with a thickness of 10--20 unit cells, in-plane-polarized regions order alongside the so-called vortex phase with a whirl-like arrangement of electric dipoles. We investigate the optical signature of these polar phases noninvasively using optical second harmonic generation (SHG) on $\mathrm{PTO}|\mathrm{STO}$-based heterostructures. We identify the phase coexistence down to a single $\mathrm{PTO}|\mathrm{STO}$ bilayer. By comparing the SHG yield in dependence of the number of PTO layers, we further find that interlayer coupling plays an important role in setting the final polarization state. Our nonlinear optical experiments demonstrate the potential of this noninvasive approach for the identification and understanding of complex noncollinear ordering of dipole moments in oxide heterostructures and lays the groundwork for their operando investigation.

The Penrose process in nonlinear optics

Penrose process is a mechanism by which energy may be extracted from the rotation of a Kerr black hole. The goal of this Perspective is to describe the elements that combine to allow a tabletop nonlinear optics experiment involving laser propagation in a medium to provide a versatile platform for elucidating the intimate details of the Penrose process. Key elements include propagation in a thermo-optic medium viewed as a photon fluid, rotating black hole geometries in a photon superfluid, and the Zel'dovich effect, and we highlight connections to the work of Roger Penrose throughout. In addition, we point out how the Penrose process has led to the notion of geometry-induced phase-matching in nonlinear optics, thereby highlighting the synergy between the fields of nonlinear optics and analog black holes.

Perspectives on nonlinear optics of graphene: Opportunities and challenges

The first nonlinear-optical experiments with graphene date back over a decade, and a wide range of research breakthroughs has been reported since then, particularly on the third-order nonlinearities of the material. Graphene has been shown to exhibit extraordinary saturable absorption properties as well as extremely strong nonlinear refraction effects, both of which hold promise for practical use in nonlinear-optical devices. In this Perspective, after providing a very brief overview of the state of the art, I elaborate on the most relevant material parameters for future research and development activities in this domain, while also highlighting specific features of graphene’s linear and nonlinear-optical properties that are sometimes overlooked in experiments. Finally, I present my view on what the opportunities and remaining challenges are in the practical exploitation of graphene for nonlinear-optical applications.

Laser Light Durability and Nonlinear Optical Properties of Acrylate Polymer−Chalcogenide Glass−Gold Nanocomposites

Synthesis of acrylate‐based nanocomposites (NCs) for photonic applications is performed, and the influence of gold and chalcogenide glass nanoparticles (NPs) on optical parameters of NC layers at high laser intensities is investigated, whereas the polymerization, recording of optical gratings or other elements, and variations of their functional parameters in As2S3 and Au‐containing NC layers are possible at low, 532 nm laser light intensities in the absorption edge range; optical stability under high intensity illumination and threshold laser damage intensities in NIR optical transmission range are important for nonlinear optical experiments, measurements of n2. Hence, these parameters are determined and show the increase in NCs’ stability due to the addition of Au NPs, as well as increase in n2 in gold‐ and chalcogenide‐containing NCs. Thus, the functionality of such NCs and optical elements on their basis can be extended to high‐intensity applications and nonlinear optics.

Tailored Multi-Color Dispersive Wave Formation in Quasi-Phase-Matched Exposed Core Fibers.

Widely wavelength‐tunable femtosecond light sources in a compact, robust footprint play a central role in many prolific research fields and technologies, including medical diagnostics, biophotonics, and metrology. Fiber lasers are on the verge in the development of such sources, yet widespan spectral tunability of femtosecond pulses remains a pivotal challenge. Dispersive wave generation, also known as Cherenkov radiation, offers untapped potentials to serve these demands. In this work, the concept of quasi‐phase matching for multi‐order dispersive wave formation with record‐high spectral fidelity and femtosecond durations is exploited in selected, partially conventionally unreachable spectral regions. Versatile patterned sputtering is utilized to realize height‐modulated high‐index nano‐films on exposed fiber cores to alter fiber dispersion to an unprecedented degree through spatially localized, induced resonances. Nonlinear optical experiments and simulations, as well as phase‐mismatching considerations based on an effective dispersion, confirm the conversion process and reveal unique emission features, such as almost power‐independent wavelength stability and femtosecond duration. This resonance‐empowered approach is applicable to both fiber and on‐chip photonic systems and paves the way to instrumentalize dispersive wave generation as a unique tool for efficient, coherent femtosecond multi‐frequency conversion for applications in areas such as bioanalytics, life science, quantum technology, or metrology.

Measurement of Penrose Superradiance in a Photon Superfluid.

The superradiant amplification in the scattering from a rotating medium was first elucidated by Sir Roger Penrose over 50years ago as a means by which particles could gain energy from rotating black holes. Despite this fundamental process being ubiquitous also in wave physics, it has only been observed once experimentally, in a water tank. Here, we measure this amplification for a nonlinear optics experiment in the superfluid regime. In particular, by focusing a weak optical beam carrying orbital angular momentum onto the core of a strong pump vortex beam, negative norm modes are generated and trapped inside the vortex core, allowing for amplification of a reflected beam. Our experiment demonstrates amplified reflection due to a novel form of nonlinear optical four-wave mixing, whose phase-relation coincides with the Zel'dovich-Misner condition for Penrose superradiance in our photon superfluid, and unveil the role played by negative frequency modes in the process.