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We report atomic-like Autler–Townes splitting controlled by destructive and constructive natural non-Hermitian quantization in Eu3+: BiPO4. For the first time, we explored destructive and constructive AT splitting in different regions. Fluorescence (FL), spontaneous four-wave mixing (SFWM), and shot noise signals exhibit different kinds of AT splitting. FL signal exhibits three level dip AT splitting through destructive quantization, SFWM signals exhibit peak and multi-dip AT splitting through constructive quantization, and shot noise signals exhibit a two-level dip AT splitting. These kinds of AT splitting originate through single photon dressing and double photon–phonon dressing, which can be controlled by adjusting experimental parameters. Our atomic-like Autler–Townes-splitting technique is useful for making a spectral router. [ABSTRACT FROM AUTHOR]

We report atomic-like Autler–Townes splitting controlled by destructive and constructive natural non-Hermitian quantization in Eu3+: BiPO4. For the first time, we explored destructive and constructive AT splitting in different regions. Fluorescence (FL), spontaneous four-wave mixing (SFWM), and shot noise signals exhibit different kinds of AT splitting. FL signal exhibits three level dip AT splitting through destructive quantization, SFWM signals exhibit peak and multi-dip AT splitting through constructive quantization, and shot noise signals exhibit a two-level dip AT splitting. These kinds of AT splitting originate through single photon dressing and double photon–phonon dressing, which can be controlled by adjusting experimental parameters. Our atomic-like Autler–Townes-splitting technique is useful for making a spectral router. [ABSTRACT FROM AUTHOR]

A bipartite system is defined as two microscopic entities being able to exchange energy. When excited by light, the complete optical response functions at first (polarizabilities) and second orders (first hyperpolarizabilities) of such a system are determined using the diagrammatic theory of optics. The generality of the method is ensured by the free choice of light–matter and matter–matter interaction Hamiltonians and by the arbitrary number of quanta involved in the energy exchange. In the dipolar approximation, the optical response functions of the system (i.e., of the interacting entities) are linked to the responses of the interaction-free entities by transfer matrices. These universal matrices identically modify the optical response functions at all orders in the electromagnetic field, allowing the implementation of matter–matter interactions in higher-order processes, such as stimulated or spontaneous Raman scattering and four-wave mixing. This formalism is then applied to various composite systems: dimers, multimers and lattices of nanoparticles and molecules, dense molecular layers, and substrate-induced image dipoles. [ABSTRACT FROM AUTHOR]

In this article, we use spatially modulated control fields to increase the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, motivated by similar works in atomic systems. Using a simplified version of the propagation equations, we show analytically that for control fields with a constant amplitude and linearly varying mixing angles with the propagation distance, a conversion efficiency close to unity can be achieved even for relatively short propagation distances. Subsequently, we confirm these results by numerically simulating the full set of propagation equations. [ABSTRACT FROM AUTHOR]

Significant progress has been achieved in leveraging atomic systems for the effective operation of quantum networks, which are essential for secure and long-distance quantum communication protocols. The key elements of such networks are quantum nodes that can store or generate both single and entangled photon pairs. The primary mechanisms leading to the production of single and entangled photon pairs revolve around established techniques such as parametric down-conversion, four-wave mixing, and stimulated Raman scattering. In contrast to solid-state platforms, atomic platforms offer a more controlled approach to the generation of single and entangled photon pairs, owing to the progress made in atom manipulation techniques such as trapping, cooling, and precise excitation schemes facilitated by the use of lasers. This review article delves into the techniques implemented for generating single and entangled photon pairs in atomic platforms, starting with a detailed discussion of the fundamental concepts associated with single and entangled photons and their characterization techniques. The aim is to evaluate the strengths and limitations of these methodologies and offer insights into potential applications. Additionally, the article will review the extent to which these atomic-based systems have been integrated into operational quantum communication networks. [ABSTRACT FROM AUTHOR]

The rapid growth of online services and the global transition to digital platforms, accelerated by the COVID-19 pandemic and the emergence of AI-based services, have led to a surge in demand for high-capacity optical communication networks (OCNs). However, this transition exacerbates the issue of fiber nonlinearity, notably four-wave mixing (FWM), which can significantly impact signal integrity in long-distance OCN transmissions with multiple channels. To address this challenge, this paper presents a novel approach leveraging a convolutional neural network (CNN)-based digital signal processing (DSP) model to mitigate the nonlinear effects of FWM on signal quality. The proposed CNN model, designed with three convolutional layers and trained on a comprehensive dataset of simulated OCN transmissions, demonstrates significant improvement in reducing nonlinear distortions caused by FWM. Our method is compared with traditional compensation techniques, such as digital back-propagation and Volterra series-based equalizers, showing a reduction in power penalties by 1 dB and an enhancement in the power budget by 2 dB. Simulation results indicate that the bit error rates (BERs) remain consistently below the critical threshold of 10−9 across various transmission distances, outperforming conventional methods. The simulation analysis, conducted on a 100 km multi-channel OCN testbed, confirms the CNN equalizer's efficacy in reducing crosstalk and improving power efficiency, with a demonstrated 15% reduction in required launch power. Moreover, the analytical models used to evaluate the CNN-based DSP model show high accuracy in predicting performance, underscoring the model's capability to achieve high-quality transmission with lower power requirements. These findings advocate for the integration of our CNN-based DSP model into OCNs, offering a fruitful solution for managing multi-channel, long-distance, and high-data-rate optical transmissions in real-world systems. [ABSTRACT FROM AUTHOR]

We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a four-wave mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute–solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, the complete frequency space is considered through the pump–probe detuning, without restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation. [ABSTRACT FROM AUTHOR]

Distributed optical fiber sensors with the capability of dynamic temperature and strain discrimination can be used for various applications, including perimeter security, structural health monitoring, and seismic sensing, as they can access the tolerance of the structures and sites to natural hazards, such as earthquakes, fires, and overflows. Here, we propose a hybrid Brillouin/Rayleigh sensing system that combines distributed phase matching measurement via Brillouin dynamic grating and inhomogeneity-induced Rayleigh scatting in polarization-maintaining fiber. Due to the high birefringence of polarization-maintaining fibers imposed by the stress-rods, the detection of Brillouin dynamic gratings results in opposite signs of spectral shifts under the changed temperature and strain, giving a high discrimination accuracy. In addition, the usage of a single chirped probe pulse signal allows a single end detection system for Rayleigh of the probe wave and idler wave from stimulated Brillouin scattering enhanced four-wave mixing, which simplified the sensing system significantly. Driven by the high spatial resolution ability of distributed phase matching measurement without phonon lifetime limitation, an intensity-based analysis approach for Rayleigh traces is carried out to resolve the external perturbation applied in a short section that is smaller than the spatial distinctness associated pulse width. In the proof-of-concept experiments, a simultaneous strain and temperature variation within a 40 cm fiber section are successfully discriminated with noise equivalent discrimination errors for strain and temperature of 112.2 nɛ and 10.9 m °C. The spatial resolution here is 2 m, and the maximum system's sampling rate is up to 100 kHz without average, corresponding to the sensing distance of 1 km. [ABSTRACT FROM AUTHOR]

A dense wavelength division multiplexing (DWDM) system improves the capacity of an optical communication system. On the other hand, nonlinear effects are critical issues that limit the performance of the DWDM system. The nonlinear effects of self-phase modulation, cross-phase modulation, and four-wave mixing affect optical communication's capacity. This paper focuses on mitigating the nonlinear effect of cross-phase modulation in the DWDM system with a suitable technique. [ABSTRACT FROM AUTHOR]

The sensitivity of molecular spectroscopy based on surface‐enhanced coherent anti‐Stokes Raman scattering (SECARS) is limited by the spectrally overlapping background from nonresonant four‐wave mixing (FWM). While the SECARS signal is mediated by the molecular vibrational eigenstates and exhibits long lifetime (a few picoseconds), the FWM background stems from the instantaneous electronic polarization and decays rapidly with the vanishment of excitation. Therefore, CARS and FWM can be separated by time‐resolved CARS (trCARS) using ultrashort pulsed lasers. The broad spectral bandwidth also enables broadband CARS (BCARS) for simultaneous identification of multiple vibrational signatures. This work combines trCARS and BCARS with an optimized plasmonic system to demonstrate time‐resolved surface‐enhanced BCARS) and show its capability in obtaining background‐suppressed broadband vibrational spectra from a monolayer of 4‐Aminothiophenol (4‐ATP) molecules self‐assembled on a gold grating. The vibrational dephasing time of the ring‐breathing mode for the 4‐ATP monolayer on the gold grating (≈1.00 ± 0.17 ps) is significantly shortened compared to that for 4‐ATP powder on a glass substrate (2.10 ± 0.05 ps). This work presents an effective method to suppress FWM background and investigate the vibrational dynamics of molecules in the vicinity of plasmonic nanostructures. [ABSTRACT FROM AUTHOR]

A theory of degenerate four‐wave mixing (DFWM) and phase conjugation is developed for metallic nanohybrids, which consist of an ensemble of interacting metallic nanoshells and noninteracting quantum dots (QDs). It is considered that three incident waves are applied to the metallic nanohybrid, and they produce a fourth output mixed wave. These waves induce dipoles in metallic nanoshells, generating surface plasmon polaritons, and interact with each other via the dipole–dipole interactions (DDI). In DFWM, the input and output waves travel in opposite directions, and this retroreflective nature is responsible for the phenomenon of phase conjugation. The analytical expressions for the input transmitted and output reflected wave intensities are calculated in the presence of the surface plasmon polaritons (SPPs) and the DDI polaritons. It is demonstrated that the phase conjugation, the phase coherent phenomena, and the intensities of both input transmitted and output reflected waves are enhanced due to SPPs and DDI polaritons. These findings indicate that the nanohybrid acts as a phase conjugate device and a phase coherent optical amplifier, which can be applied to fabricate optical nanoamplifiers, phase conjugate mirrors, and nanosensors by measuring the intensity of the output reflected wave. [ABSTRACT FROM AUTHOR]

The advent of free electron lasers has opened the opportunity to explore interactions between extreme ultraviolet (EUV) photons and collective excitations in solids. While EUV transient grating spectroscopy, a noncollinear four-wave mixing technique, has already been applied to probe coherent phonons, the potential of EUV radiation for studying nanoscale spin waves has not been harnessed. Here we report EUV transient grating experiments with coherent magnons in Fe/Gd ferrimagnetic multilayers. Magnons with tens of nanometers wavelengths are excited by a pair of femtosecond EUV pulses and detected via diffraction of a probe pulse tuned to an absorption edge of Gd. The results unlock the potential of nonlinear EUV spectroscopy for studying magnons and provide a tool for exploring spin waves in a wave vector range not accessible by established inelastic scattering techniques. [ABSTRACT FROM AUTHOR]

We proposed a coherent radiation scheme based on double-stimulated Raman scattering (SRS) induced cascaded four-wave mixing (FWM) in a mixed methanol–ethanol solution. The SRS of methanol has two characteristic vibrational peaks, which are attributed to the symmetric stretching vibration of –CH3 and the antisymmetric stretching vibration of –CH3. The addition of ethanol enhances the antisymmetric stretching vibration mode, and intensities of two peaks were similar when the volume ratio of methanol to ethanol was 7.5:2.5. Resonant amplification of the two SRS signals is achieved by refocusing the scattered light, and the stronger self-focusing effect not only converges the two beams but also generates a plasma-enhanced SRS process, realizing cascaded FWM. The frequency difference Δ ω between two FWM beams matches the frequency difference Δ Ω between the vibrational energy levels of the symmetric and antisymmetric stretching vibrations, and the stimulated excitation enhances FWM signals. The output coherent radiation light is a large broadband ranging from 592 to 668 nm and 721 to 797 nm, with a wavelength interval of about 3 nm. The intensity of light radiated at different wavelengths is not the same, with the strongest light at the center of the wavelength (630 and 759 nm). This technique has the potential to contribute to the development of a multi-wavelength cascaded Raman laser. [ABSTRACT FROM AUTHOR]

Recently, dense wavelength division multiplexing passive optical networks (DWDM-PONs) have become a considerable choice for 5G and beyond fronthaul implementations. Formerly, we have proposed a full-duplex bidirectional DWDM-PON architecture convenient for those implementations and analyzed the combined dual impact of four-wave mixing (FWM) and stimulated Raman scattering (SRS) nonlinear impairments on the proposed architecture. Meanwhile, a detailed literature analysis showed us that the combined quadruple impact of self phase modulation (SPM), cross phase modulation (XPM), FWM and SRS on the performance of bidirectional DWDM-PONs have never been researched up to now. In this paper, quadruple impact of SPM, XPM, FWM and SRS on the performance of both uplink channels (ULCs) and downlink channels (DLCs) of the formerly proposed DWDM-PON has been analyzed with simulations. Simulations have been performed in O-band region for ULCs and in C-band region for DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs having 12.5 GHz, 25 GHz, 50 GHz, 100 GHz equally-spaced channels. The quadruple impact of optical nonlinear impairments on the DWDM-PON performance has been analyzed with signal-to-crosstalk ratio (SXR) simulations performed under varying channel input powers and channel lengths. Results show that under the quadruple nonlinear impact reliable bidirectional transmission with an SXR over 23 dB can be achieved for channel input powers below 0.58 mW and 0.16 mW in 2 × 15- and 2 × 63-channel DWDM-PONs, respectively, for all channel spacing values and 25 km transmission lengths. Moreover, results also imply that variations in channel lengths do not significantly affect SXR at both ULCs and DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs for lengths exceeding 50 km. The thorough analysis presented in the paper will give a new insight for analysis of conventional and next generation PONs. [ABSTRACT FROM AUTHOR]

A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics. [ABSTRACT FROM AUTHOR]

On-chip light generation in the mid-infrared (mid-IR) region of the electromagnetic spectrum is gaining considerable attention due to its various potential applications in free-space communication, mid-IR spectroscopy, sensing, and thermal Imaging. In this work, we have designed a dispersion-engineered silicon nitride (SiN)-coated tellurium oxide (TeO2) hybrid waveguide on silica (SiO2) substrate with barium fluoride (BaF2) as cladding for nonlinear applications. Strong modal confinement, broad dispersion characteristic, and high nonlinearity were achieved in the proposed hybrid waveguide design, which are important features for obtaining desired nonlinear applications. Through numerical simulations, we found that the dispersion curve is nearly flat within the dispersion range of −40.60 ps/nm/km to 33.15 ps/nm/km for a spectral bandwidth of 1.55–4.25 µm with a zero-dispersion wavelength (ZDW) around 1.80 µm, which is suitable for generating nonlinear effects such as four-wave mixing, self-phase modulation, and Raman scattering. Such types of on-chip hybrid waveguide devices can be pumped using a commercially available fiber laser operating at a wavelength of 2 µm. The design of the hybrid waveguide was optimized to achieve very low modal confinement loss ranging from 0.1 × 10−4 to 35 dB/cm, with a spectral bandwidth of 1.5–4 µm. Additionally, a high nonlinear coefficient value of 1372 W−1 km−1 was achieved at a pumping wavelength of 1.5 µm in hybrid waveguide. The results of such hybrid waveguides can be helpful to experimentalists working in this field for developing nonlinear hybrid waveguide devices. These nonlinear hybrid waveguide devices have potential nonlinear applications, including four-wave mixing, Raman scattering, and supercontinuum spectrum spanning the near-IR to mid-IR. Further, the on-chip hybrid waveguide structure can be significantly help to expand the functionality of future photonics integrated circuits. [ABSTRACT FROM AUTHOR]

A systematic spectroscopic study of the dicarbon molecule C2 has important applications in various research fields, such as astrochemistry and combustion. In the short vacuum ultraviolet (VUV) wavelength region, recent theoretical calculations have predicted many absorption band systems of C2, but only few of them have been verified experimentally yet. In this work, we employed a tunable VUV laser radiation source based on the two-photon resonance-enhanced four-wave mixing method and a time-of-flight mass spectrometer to investigate the absorption bands of C2 in the VUV range of 64 000–66 000 cm−1. The electronic transition 23Σg−(v′)–a3Πu(v″) of C2 has been observed and identified experimentally for the first time. The term value Te for the 23Σg− state is determined to be 66 389.9 ± 0.5 cm−1 above the ground state X1Σg+, and the vibrational and rotational constants are also determined. The experimentally measured spectroscopic parameters in this study are in excellent agreement with the theoretical results based on high-level ab initio calculations. [ABSTRACT FROM AUTHOR]

This work presents a theoretical analysis of the helical phase steering via a four-wave mixing (FWM) process in a closely cycled double-ladder atomic system. Our focus is to understand the contribution of the two-photon resonant process governed by a probe field and a driving laser in the control of the helical phase. The theoretical analysis allows us to understand the helical phase can be effectively steered when the two-photon resonant condition Δ = − δ is satisfied. Moreover, we investigate the superposition modes of the FWM field and a same-frequency Gaussian beam, which testify the two-photon resonant condition Δ = − δ plays an important role in the steering of the helical phase. [ABSTRACT FROM AUTHOR]

We analytically investigate the Fano-type optical response and the four-wave mixing (FWM) process by exploiting the magnetoelasticity of a ferromagnetic material. The deformation of the ferromagnetic material plays the role of mechanical displacement, which is simultaneously coupled to both optical and magnon modes. We report that the magnetostrictively induced displacement leads to realization of Fano profiles in the output field and is effectively well-tuned through adjusting the system parameters, such as effective magnomechanical coupling, magnon detuning, and cavity detuning. It is found that the magnetoelastic interaction also gives rise to the FWM phenomenon. The number of the FWM signals mainly depends upon the effective magnomechanical coupling and the magnon detuning. Moreover, the FWM spectrum exhibits suppressive behavior upon increasing (decreasing) the magnon (cavity) decay rate. The present scheme will open new perspectives in highly sensitive detection and quantum information processing. [ABSTRACT FROM AUTHOR]

Abstract We present theoretical and experimental evidence of high-gain far-detuned nonlinear frequency conversion, extending towards both the visible and the mid-infrared, in a few-mode graded-index silica fiber pumped at 1.064 $$\upmu \hbox {m}$$ μ m , and more specifically achieving gains of hundreds of dB per meter below 0.65 $$\upmu \hbox {m}$$ μ m and beyond 3.5 $$\upmu \hbox {m}$$ μ m . Interestingly, our findings highlight the potential of graded-index fibers for enabling high-gain wavelength conversion into the strong-loss spectral region of silica. Such advancements require an accurate interpretation of intramodal and intermodal four-wave mixing processes.

A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics.

Intermodal four-wave mixing (FWM) in photonic waveguides offers a promising approach for efficient terahertz (THz) wave generation, crucial for advanced photonic systems. This study explores the potential of germanium (Ge) waveguides, leveraging their distinct dispersion profiles in transverse electric (TE), and transverse magnetic (TM) modes to achieve phase-matching for FWM. We conducted a numerical analysis of two waveguide geometries, ridge and plane, to optimize THz generation efficiency. Also, by optimizing waveguide geometry, it is possible to achieve higher conversion efficiency and broader THz bandwidth. The results demonstrate that Ge waveguides, particularly when utilizing same-phase laser pulses, can significantly enhance THz radiation and exhibit lower losses compared to traditional silicon-based designs. The findings suggest that integrating these optimized Ge waveguides with existing photonic components could lead to more versatile and efficient THz systems. [ABSTRACT FROM AUTHOR]

Context: In this study, we evaluate the geometrical, absorption, optoelectronic, electronic, nonlinear optical (NLO) and thermodynamic properties of dibenzo[b,def]chrysene molecule derivatives by means of DFT and TD-DFT simulations. In view of the aim of producing new high-performance materials for non-linear optics (NLO) by doping test, two types of doping were used. We obtained six derivatives by doping with organic dopants (Nitro, amide and ticyanoethenyl) and mixed alkali metal (potassium) and organic dopants. Doping with organic dopants produced molecules A, B and C, respectively when substituting one hydrogen with nitro (NO2), amide (CONH2) and tricyanoethenyl (C5N3) groups, while mixed doping involved considering A, B and C and then substituting two hydrogens with two potassiums to obtain compounds D, E and F respectively. The negative values of the various interaction energies calculated for all the doped molecules show that they are all stable, but also that molecules C and F are the most stable in the case of both dopings. The gap energies calculated at the B3LYP level of theory are all below 3 eV, which means that all the molecules obtained are semiconductors. Better still, compounds C and F, with gap energies of 1.852 eV and 1.204 eV, respectively, corresponding to decreases of 35.67% and 58.18% in gap energy compared with the pristine molecule, are more reactive than the other doped molecules. Mixed doping is therefore a highly effective way of narrowing the energy gap and boosting the semiconducting character and reactivity of organic materials. Optoelectronic properties have also been improved, with refractive index values higher than those of the reference material, glass. This shows that our compounds could be used under very high electric field conditions of the order of 4.164 × 109 V.m−1 for C and 7.410 × 109 V.m−1 for F the highest values at the B3LYP level of theory. The maximum first-order hyperpolarizability values for both types of doping are obtained at the CAM-B3LYP level of theory by C: β mol = 92.088 × 10−30esu and by F: β mol = 129.449 × 10−30esu, and second-order values are also given by these same compounds. These values are higher than the reference value, which is urea, making our compounds potential candidates for high-performance NLO applications. In dynamic mode and at a frequency of 1064 nm, at the CAM-B3LYP level of theory, the highest dynamic hyperpolarizability coefficients were obtained by C and F. Hyper-Rayleigh scattering β HRS , coefficients of the electro-optical Pockel effect (EOPE), EFISHG, third-order NLO-response degree four-wave mixing γ DFWM , quadratic nonlinear refractive index n2 were also calculated. The maximum values of n2 are obtained by C (6.13 × 10–20 m2/W) and F (6.60 × 10–20 m2/W), these values are 2.24 times higher than that of fused silica which is the reference for degenerate four-wave mixing so our molecules could also have applications in optoelectronics as wavelength converters, optical pulse modulators and optical switches. Methods: Using the DFT method, we were able to determine the optimized and stable electronic structures of doped dibenzo[b,def]chrysene derivatives in the gas phase. We limited ourselves to using the proven B3LYP and CAMB3LYP levels of theory for calculating electronic properties, and non-linear optics with the 6-311G + + (d,p) basis set, which is a large basis set frequently used for these types of compound. Gaussian 09 software was used to run our calculations, and Gauss View 6.0.16 was used to visualize the output files. TD-DFT was also used to determine absorption properties at the B3LYP level of theory, using the same basis set. [ABSTRACT FROM AUTHOR]

Optical nonlinearities are one of the most fascinating properties of two-dimensional (2D) materials. While tremendous efforts have been made to find and optimize the second-order optical nonlinearity in enormous 2D materials, opportunities to explore higher-order ones are elusive because of the much lower efficiency. Here, we report the giant high odd-order optical nonlinearities in centrosymmetric correlated van der Waals insulator manganese phosphorus triselenide. When illuminated by two near-infrared femtosecond lasers, the sample generates a series of profound four-and six-wave mixing outputs. The near-infrared third-order nonlinear susceptibility reaches near the highest record values of 2D materials. Comparative measurements to other prototypical nonlinear optical materials [lithium niobate, gallium(II) selenide, and tungsten disulfide] reveal its extraordinary wave mixing efficiency. The wave mixing processes are further used for nonlinear optical waveguide with multicolor emission. Our work highlights the promising prospect for future research of the nonlinear light-matter interactions in the correlated 2D system and for potential nonlinear photonic applications. [ABSTRACT FROM AUTHOR]

Silicon carbide (SiC) electronics has seen a rapid development in industry over the last two decades due to its capabilities in handling high powers and high temperatures while offering a high saturated carrier mobility for power electronics applications. With the increased capacity in producing large-size, single-crystalline SiC wafers, it has recently been attracting attention from academia and industry to exploit SiC for integrated photonics owing to its large bandgap energy, wide transparent window, and moderate second-order optical nonlinearity, which is absent in other centrosymmetric silicon-based material platforms. SiC with various polytypes exhibiting second- and third-order optical nonlinearities are promising for implementing nonlinear and quantum light sources in photonic integrated circuits. By optimizing the fabrication processes of the silicon carbide-on-insulator platforms, researchers have exploited the resulting high-quality-factor microring resonators for various nonlinear frequency conversions and spontaneous parametric down-conversion in photonic integrated circuits. In this paper, we review the fundamentals and applications of SiC-based microring resonators, including the material and optical properties, the device design for nonlinear and quantum light sources, the device fabrication processes, and nascent applications in integrated nonlinear and quantum photonics. [ABSTRACT FROM AUTHOR]

High-order wave mixing in solid-state platforms gather increasing importance due to the development of advanced lasers and integrated photonic circuit for both classical and quantum information. However, the high-order wave mixing is generally inefficient in solids under weak pump. Here, we observed the presence of phase matching of five-wave mixing (5WM) propagating in a zinc oxide (ZnO) microwire. The 5WM signal is enhanced by 2–3 orders of magnitude under the phase matching conditions, reaching an absolute conversion efficiency of 1.7 × 10−13 when the peak pumping power density is about 106 W/cm2. The propagation of multiple nonlinear signals, including sum frequency generation, third harmonic generation, four-wave mixing etc., benefited from both the large nonlinear coefficients and the wide transparent window of ZnO, implies the possibility of developing cascaded nonlinear process under higher pumping. This study enriches the ZnO platform for integrated nonlinear nanophotonics. [ABSTRACT FROM AUTHOR]

Dielectric metasurfaces supporting quasi-bound states in the continuum (qBICs) enable high field enhancement with narrow-linewidth resonances in the visible and near-infrared ranges. The resonance emerges when distorting the meta-atom's geometry away from a symmetry-protected BIC condition and, usually, a given design can sustain one or two of these states. In this work, we introduce a silicon-on-silica metasurface that simultaneously supports up to four qBIC resonances in the near-infrared region. This is achieved by combining multiple symmetry-breaking distortions on an elliptical cylinder array. By pumping two of these resonances, the nonlinear process of degenerate four-wave mixing is experimentally realized. By comparing the nonlinear response with that of an unpatterned silicon film, the near-field enhancement inside the nanostructured dielectric is revealed. The presented results demonstrate independent geometric control of multiple qBICs and their interaction through wave mixing processes, opening new research pathways in nanophotonics, with potential applications in information multiplexing, multi-wavelength sensing and nonlinear imaging. [ABSTRACT FROM AUTHOR]

The numerical solution of the generalized nonlinear Schrödinger equation by simple splitting methods can be disturbed by so-called spurious instabilities. We analyze these numerical instabilities for an arbitrary splitting method and apply our results to several well-known higher-order splittings. We find that the spurious instabilities can be suppressed to a large extent. However, they never disappear completely if one keeps the integration step above a certain limit and applies what is considered to be a more accurate higher-order method. The latter can be used to make calculations more accurate with the same numerically stable step, but not to make calculations faster with a much larger step. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the impact of classical optical communications in quantum key distribution (QKD) over hollow-core fiber (HCF), multi-core fiber (MCF) and single-core fiber (SCF) and propose wavelength allocation schemes to enhance QKD performance. Firstly, we theoretically analyze noise interference in QKD over HCF, MCF and SCF, such as spontaneous Raman scattering (SpRS) and four-wave mixing (FWM). To mitigate these noise types and optimize QKD performance, we propose a joint noise suppression wavelength allocation (JSWA) scheme. FWM noise suppression wavelength allocation and Raman noise suppression wavelength allocation are also proposed for comparison. The JSWA scheme indicates a significant enhancement in extending the simultaneous transmission distance of classical signals and QKD, reaching approximately 100 km in HCF and 165 km in MCF under a classical power per channel of 10 dBm. Therefore, MCF offers a longer secure transmission distance compared with HCF when classical signals and QKD coexist in the C-band. However, when classical signals are in the C-band and QKD operates in the O-band, the performance of QKD in HCF surpasses that in MCF. This research establishes technical foundations for the design and deployment of QKD optical networks. [ABSTRACT FROM AUTHOR]

The non‐Hermitian singularity control of multimode entanglement in the energy‐level cascaded four‐wave mixing system within a single atomic vapor is of great significance and importance. In this study, a non‐Hermiticity system by means of quasi‐quantization of energy‐band based on non‐Hermiticity systems is constructed. By employing atomic coherence in the non‐Hermiticity system, high‐dimensional quantized photon correlations underdressed field‐induced parity‐time (PT) symmetry and symmetry breaking through the quantization of energy levels are studied. Such a phenomenon happens at microscopic (nanoscale) when the eigenvalues of dressed energy‐level and multimode entanglement are considered for both real and imaginary parts symmetry breaking. Double dressing effect is observed with more coherent channels and larger information capacity than single dressing in the energy‐level cascaded four‐wave mixing system. The study found that the splitting of the real part is larger than an imaginary part in a second‐order system, and the imaginary part splitting is also greater than the real part splitting in a third‐order system. The real part (in phase) is constructive dressing quantization, and the imaginary (out of phase) is destructive dressing quantization. Exceptional points (EP points) can be used to enhance sensitivity detection of entanglement quantum state. [ABSTRACT FROM AUTHOR]

Time lenses can measure ultrafast signals but are based on single-mode fibers (SMFs). To develop multimode time lenses that are based on a four-wave mixing process, we must have full control of the nonlinear interaction between the modes. Specifically, we need to generate an idler from each mode without any cross-talk between the modes. Here, as a first step toward a multimode time lens, we study how stable a short pulse is traveling in a multimode fiber, and how pulses at different modes interact with each other. We utilize a single-mode-based time lens to measure the dynamics of these pulses in the time and spectral domains. We found that there is cross-talk between the modes and that the pulses are not stable and excite other modes, rather than staying in the same modal order. These findings indicate that developing a multimode time-lens may be more challenging than expected. [ABSTRACT FROM AUTHOR]

In this paper, two-and-three channel all-optical AND logic gates based on four-wave mixing in a highly nonlinear fiber for 120 Gbps on–off keying signals were designed, simulated, and investigated. Simulation results show low bit error rate and consequently fairly high Q-factor at the receiving end in both two and three inputs AND gates, as well as the logic operation, is confirmed by the open eye diagrams with moderate power penalties for both designs. [ABSTRACT FROM AUTHOR]

Dirac fermion in topological materials exhibits intriguing nonlinear optical responses. However, their direct correlation with the linearly dispersed band remains elusive experimentally. Here, we take topological semimetal ZrSiS as a paradigm, unveiling three unique nonlinear optical signatures of Dirac fermion. These signatures include strong quadrupolar response, quantum interference effect, and exponential divergent four-wave mixing (FWM), all of which are described by the prominent third-order nonlinear optical susceptibility. Resonantly enhanced by linear bands, quadrupolar second harmonic generation in centrosymmetric bulk overwhelms the electric-dipole contribution at the surface with inherent inversion symmetry breaking. Furthermore, owing to the interference between multiple resonant transition pathways within linear bands, difference-frequency FWM is several orders of magnitude stronger than sum-frequency FWM and third harmonic generation. The difference-frequency FWM further displays an inverse-square divergence toward degenerate excitation, whose scaling law perfectly matches with the long-sought behavior of Dirac fermion. These signatures lay the solid foundation toward the practical applications of topological materials in nonlinear optoelectronics and photonics. [ABSTRACT FROM AUTHOR]

This paper introduces a method for achieving tunable frequency conversion in the mid-infrared range, leading to the development of an optical gate circuit capable of selectively outputting three distinct frequencies for high switching efficiency. The process involves pumping a second-order soliton and a weak probe wave on either side of the zero-dispersion wavelength in an optical fiber. Nonlinear optical interactions result in four-wave mixing under certain conditions, leading to the generation of new spectral components in a hybrid glass photonic crystal fiber. By adjusting the center wavelength of the probe, the energy conversion efficiency and the maximum frequency shift induced by the soliton-probe interaction can be precisely controlled. This novel method of manipulating complex soliton dynamics via light-light interactions enables the construction of all-optical logic gates with advanced functionalities. Additionally, using the same mechanism, it is possible to observe tunable quasi-discrete supercontinuum formation with ultrashort pulse trains. [ABSTRACT FROM AUTHOR]

Electromechanical transduction gain of 21 dB is realized in a micro-cantilever resonant force sensor operated in the unresolved-sideband regime. Strain-dependent kinetic inductance weakly couples cantilever motion to a superconducting nonlinear resonant circuit. A single pump generates motional sidebands and parametrically amplifies them via four-wave mixing. We study the gain and added noise, and we analyze potential benefits of this integrated amplification process in the context force sensitivity. [ABSTRACT FROM AUTHOR]

The conservation of spectral asymmetry is a fundamental feature of the ideal four‐wave mixing process as it exists in a medium combining quadratic chromatic dispersion and third‐order nonlinearity. The robustness of this invariant in an experimental configuration where the excitation conditions of an optical fiber are sequentially updated, mimicking infinite propagation is tested in this paper. This theoretical and experimental study reveals the high sensitivity of the asymmetry to very slight deviations from the ideal case, and the idealized system behaves as an intermediate case between the ideal case of noncascaded four‐wave mixing and propagation in a system governed by the nonlinear Schrödinger equation is shown. [ABSTRACT FROM AUTHOR]

Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology of waveguide cross section and scattering. Here, we study the polarization conversion mechanism in 1-THz-FSR X-cut lithium niobate microrings with multiple-resonance condition, that is the conversion can be implemented by birefringence of waveguides, which will also introduce an avoided-mode crossing. In the experiment, we find that this mode crossing results in severe suppression of one sideband in local nondegenerate four-wave mixing and disrupts the cascaded four-wave mixing on this side. Simultaneously, we propose one two-dimensional method to simulate the eigenmodes (TE and TM) in X-cut microrings, and the mode crossing point. This work will provide one approach to the design of polarization converters and simulation for monolithic photonics integrated circuits, and may be helpful to the studies of missed temporal dissipative soliton formation in X-cut lithium niobate rings. [ABSTRACT FROM AUTHOR]

Multipartite quantum entanglement plays a vital role in both fundamental science and quantum applications. The cascaded four‐wave mixing (FWM) process is an effective method to prepare multipartite entanglement, however, the physical nature of entanglement based on different cascading paths, i.e., simultaneous cascaded FWM (SC‐FWM) and ordinal cascaded FWM (OC‐FWM), has not yet been conclusively determined. In this article, tunable continuous‐variable (CV) triple‐mode entanglement is proposed to be generated by using both the SC‐FWM and OC‐FWM schemes. The simulation results reveal that the absorption/dispersion properties of the two nonlinear processes can be efficiently tuned by varying the optical parameters (i.e., the photon detuning and the nonlinear susceptibility), resulting in triple‐mode CV entanglement with tunable properties. Compared with the OC‐FWM scheme, the SC‐FWM scheme has a broader entanglement bandwidth and a higher degree of entanglement, where the tripartite entanglement region is 4.38% larger than that of the OC‐FWM scheme. Furthermore, these results indicate that the SC‐FWM scheme has a more compact and stable mode structure with better entanglement performance. Such tunable optical triple‐mode entanglement may find applications in specific quantum communication protocols and pave the way for implementing and manipulating multichannel quantum networks. [ABSTRACT FROM AUTHOR]

Optical fiber networks need to transmit various types of client data with different requirements of bandwidth, reach, latency, and capacity by interconnecting backbone, metro, and local access networks. Since the optimal modulation format usually differs, it should be efficiently converted at the intermediate node connecting different networks. Among the multilevel modulation format, 8-ary quadrature amplitude modulation (8QAM) is a candidate for terrestrial networks thanks to the good balance between spectral efficiency and transmission distance. In this paper, we propose modulation format conversion systems from binary phase shift keying (BPSK) to 8QAM using coherent interference in delay interferometer and its reverse conversion system using four-wave mixing in a single highly nonlinear fiber. Conversion performances are numerically evaluated based on bit error rate, constellation diagrams, 8QAM and BPSK propagation lengths, and parameters in electrical signal regeneration. As a result, error-free format conversion is achieved for both conversion systems. [ABSTRACT FROM AUTHOR]

We have previously demonstrated that in the context of two-dimensional (2D) coherent electronic spectroscopy measured by phase modulation and phase-sensitive detection, an incoherent nonlinear response due to pairs of photoexcitations produced via linear excitation pathways contributes to the measured signal as an unexpected background [Grégoire et al., J. Chem. Phys. 147, 114201 (2017)]. Here, we simulate the effect of such incoherent population mixing in the photocurrent signal collected from a GaAs solar cell by acting externally on the transimpedance amplifier circuit used for phase-sensitive detection, and we identify an effective strategy to recognize the presence of incoherent population mixing in 2D data. While we find that incoherent mixing is reflected by the crosstalk between the linear amplitudes at the two time-delay variables in the four-pulse excitation sequence, we do not observe any strict phase correlations between the coherent and incoherent contributions, as expected from modeling of a simple system. [ABSTRACT FROM AUTHOR]

The dicarbon radical, C2, is one of the most abundant molecules in the universe, and has been widely observed in various energetic environments. Even though numerous experimental and theoretical investigations on C2 have been done during the last two centuries, spectroscopic study of C2 in vacuum ultraviolet (VUV) region has been rare. The only three known absorption band systems in VUV region were identified by Herzberg and co-workers in 1969 by VUV spectrograph, namely the electronic transitions F1Πu(v′)–X1Σg+(v″), f3Σg−(v′)–a3Πu(v″) and g3Δg(v′)–a3Πu(v″) (Herzberg-Lagerqvist-Malmberg transitions). In this study, we employ a two-photon resonance-enhanced four-wave mixing based VUV laser source and a time-of-flight mass spectrometer for reinvestigating the above three electronic transitions of C2 through a resonant (1VUV + 1′UV) photoionization scheme. Besides those vibronic transitions as identified by Herzberg and co-workers, many more absorption bands belonging to the electronic transitions f3Σg−(v′)–a3Πu(v″) and g3Δg(v′)–a3Πu(v″) are observed with their spectroscopic parameters determined. The rather astrophysically important F1Πu state is not observed here by the resonant (1VUV + 1′UV) photoionization scheme, which must be due to its fast predissociation process. Instead, our study shows that the vibronic band g3Δg(v′ = 2)–a3Πu(v″ = 0) exactly overlaps with F1Πu(v′ = 0)–X1Σg+(v″ = 0), which was not realized in previous studies. The potential implications of these findings to astronomical observations are discussed. [ABSTRACT FROM AUTHOR]

A chiral analog of transient absorption spectroscopy, transient circular dichroism (TCD) spectroscopy is an emerging time-resolved method. Both spectroscopic methods can probe the electronic transitions of a sample, and TCD is additionally sensitive to the dynamic aspects of chirality, such as those induced by molecular excitons. Here, we develop a theoretical description of TCD for electronic multi-level models in which the pump pulse is linearly polarized and probe pulse is alternately left- and right-circularly polarized. We derive effective response functions analogous to those often used to describe other four-wave mixing methods and then simulate and analyze TCD spectra for three representative multi-level electronic model systems. We elaborate on the presence and detection of the spectral signatures of electronic coherences. [ABSTRACT FROM AUTHOR]

This review is about anthraquinone dyes. One of the advantages of organic NLOphores materials is the variety of chromophores explored for a wide range of potential applications in optoelectronics and biology. The second and third harmonic generations, as well as hyper‐Rayleigh scattering (HRS), the Z‐scan technique, degenerate four‐wave mixing (DFWM), and density functional theory (DFT), are all covered in this review. The most active sites for establishing enhanced NLO properties were found to be positions 2 and 6 of the anthraquinone core. The structural characteristics of dyes are used to divide them into subcategories. In each section, structures with a higher NLO response are highlighted. Researchers will benefit from this review when designing and synthesizing NLOphores. [ABSTRACT FROM AUTHOR]

Direct bandgap semiconductors possess a unique attribute: the presence of a free exciton state with a high total oscillator strength. This property makes them highly promising for applications in ultrafast optical signal processing and optical computing. One such protocol for optical computing is based on four‐wave mixing (FWM). In this study, the nonlinear optical effect in polycrystalline thin films of halide perovskite MAPbI3 (MA+ = CH3NH3+$_3^+$) at low temperatures is demonstrated. Through analyzing the spectroscopy of the FWM signal, studying the photoluminescence excitation spectra, and comparing the findings with results from MAPbI3 single crystals, it has been discovered that the strongest nonlinear response is observed at the free exciton resonance and in the region of shallow defect states. Surprisingly, the presence of FWM in cross‐linear excitation geometry has been observed, indicating potential involvement of other nonlinear or many‐body effects. The observations of FWM with free excitons even in highly defective MAPbI3 thin films demonstrate the robustness of the exciton resonance and highlight the practical prospects for utilizing this material in optical computing. [ABSTRACT FROM AUTHOR]

Ultralow-noise microwaves are essential in a wide variety of scientific and technological applications, such as metrology, radars, and communications. Here, we propose and demonstrate a scheme for generating an ultralow-noise microwave signal using a Brillouin optical frequency comb (OFC), which is based on the stimulated Brillouin scattering in combination with a frequency-shifted optical injection locking mechanism. The generated two intra-cavity Brillouin lasers are used as the intra-cavity pump for the eventual formation of the OFC and thus the microwave signal via the cascaded four-wave mixing process. Exploiting the cascaded narrowing effect in the Brillouin cavity assisted by the frequency-shifted optical injection locking, the proposed microwave signal source exhibits ultralow phase noise. Experimental results show that the phase noise of the microwave signal is equivalent to below −115 dBc / Hz for a 200-GHz carrier at 10 kHz offset. The system can work in stable operation without the need for any active feedback loop. [ABSTRACT FROM AUTHOR]

Four-wave mixing process (FWM) in the non-degenerate category can be produced by the interaction of the radiation field with the third-order nonlinear optical media. In our present paper, to describe the non-degenerate four-wave mixing process we have used the fully quantum mechanical bosonic Hamiltonian. Heisenberg’s equations of motion for various modes involving pump, signal and idler are constructed. The corresponding differential equations are coupled and nonlinear. Due to non-linearity, the solution of these equations in closed set analytical form is not possible. To solve these coupled nonlinear differential equations we use the Sen-Mandal perturbative technique. Interestingly, this approach provides a broader and more general set of solutions that may be applicable across a wider range of conditions. The Sen-Mandal perturbative technique allows a more general solution that can result in a more accurate and general representation of the system that is more advantageous than the well-known short-time approximation method. The obtained solutions have been used to study the intermodal entanglement, normal order anti-bunching and normal order squeezing for various modes under the non-degenerate four-wave mixing process. The non-degenerate FWM is one of the processes for generating entanglement, squeezing and anti-bunching etc. [ABSTRACT FROM AUTHOR]

Four-wave mixing techniques, such as coherent anti-Stokes Raman spectroscopy (CARS), laser-induced grating spectroscopy (LIGS), and degenerate four-wave mixing (DFWM), have been widely used in combustion diagnostics due to their advantages of high signal-to-noise ratio (S/N), coherent signal, and spatial resolution. In this work, a nano-second pulsed laser is utilized to generate mid-infrared (near 3 µm) pump beams, exciting the rovibrational transitions of nascent water in flames. Combined LIGS and DFWM measurements are demonstrated in premixed laminar CH4/O2/N2 flames with equivalence ratios from 0.6 to 1.5, to achieve precise thermometry in a wide range of flame conditions. The flame temperatures were also measured by thermocouple as a reference, and the results from LIGS and DFWM align well with the trends shown in the thermocouple measurements. In fuel-lean flames, where the mass-to-specific-heat ratio variation is minimal, LIGS provides temperature data with a precision better than 16 K (0.8%). In fuel-rich flames, where the increased H2 concentration in the flame introduces uncertainty in gas constants thus affecting the accuracy of LIGS thermometry, DFWM is instead employed for temperature measurement since it is less sensitive to the gas composition within the measured volume. The high-precision LIGS temperatures in lean flames serve as temperature reference during the DFWM calibration of the degree of saturation, and a precision better than 90 K (4.5%) is achieved for DFWM thermometry. In addition to temperature, a theoretical model is employed to fit LIGS signal time waveforms, extracting the local speed of sound and thermal diffusivity with precisions better than 0.5% and 1.3%, respectively. These high-precision measurements contribute additional data for flame research and simulation calculations. This way, the combined use of DFWM and LIGS proves the potential for accurate thermometry and diagnostics of other thermodynamic parameters across a wide range of flame conditions. [ABSTRACT FROM AUTHOR]