Third-order Nonlinear Processes Research Articles

Multi-wavelength generation in UV and green bands through SRS and parametric processes in silica fibers.

We report on multi-wavelength generation through simultaneous second-order and third-order nonlinear parametric processes following cascaded stimulated Raman scattering (SRS) in silica fibers. The fiber system consists of a short standard step-index silica fiber and a microfiber tapered from it. When this system is pumped with a 130 ps laser at 1040 nm, multiple new wavelengths in the UV (340-370 nm) and green (507-547 nm) bands arise through four-wave mixing (FWM)/sum-frequency generation (SFG) from the pump and its Raman signals. The evolution of these wavelengths with pump power is demonstrated in detail. Matching of frequencies and propagation constants in the involved processes is verified. This work provides a compact and simple method of multi-wavelength generation with fibers.

Generation of second harmonic at wide conversion band in GRIN multimode fibers

Optical poling of multimode graded-index fibers (GRIN) has emerged as a promising technique for creating periodic inscriptions of the second-order nonlinear optical susceptibility χ(2), enabling the generation of a second harmonic in silica fibers. In this work, we investigate the generation of multiple spectral peaks using a continuous broadband source in the infrared domain, generated in the same fiber by a femtosecond laser with a central wavelength different from the one used for the poling process. Building upon theoretical foundations, this work contributes at explaining how second and third-order nonlinear processes participate to the broad generation of the second harmonic in GRIN fibers.

Enhanced terahertz frequency mixing in all-dielectric metamaterial with multiple surface plasmon polaritons resonances

Nonlinear metamaterials hold a promising platform for generating terahertz (THz) waves. In this paper, we present an all-dielectric metamaterial with multiple surface plasmon polariton (SPP) resonances for enhanced THz frequency mixing. The metamaterial is composed of graphene ribbons, a dielectric layer, and a one-dimensional photonic crystal, displaying the multiple absorptions with simultaneous excitation of three SPP resonances. Taking advantage of SPP resonances with high Q factor and strong localized field at the input frequency, the third-order nonlinear processes are remarkably enhanced, including third-harmonic generation and four-wave mixing, producing a variety of frequencies in the THz range. The proposed efficient nonlinear metamaterials offer promising applications for THz frequency synthesis.

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

This paper presents the development of a third-order compact gas-kinetic scheme (GKS) for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme utilizes a time-dependent gas distribution function at a cell interface to not only calculate the fluxes needed for updating the cell-averaged flow variables but also to evaluate the flow variables at the cell interface. This leads to the evolution of cell-averaged gradients of flow variables. The success of this scheme heavily relies on the initial data reconstruction techniques, with an emphasis on their application to the tetrahedral mesh. Employing a conventional second-order unlimited least-square reconstruction directly on the cell-averaged flow variables of von Neumann neighbouring cells can introduce linear instability into the scheme. However, by using the updated cell-averaged gradients, the GKS with a third-order compact smooth reconstruction remains linearly stable under a large CFL number when applied to a tetrahedral mesh. To enhance the robustness of the high-order compact GKS for capturing a discontinuous solution, we propose a novel two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. This innovative approach overcomes the stability issues associated with a second-order compact reconstruction by incorporating a pre-reconstruction step. Additionally, it simplifies the third-order non-linear reconstruction process by adding a single large stencil to those used in the second-order one. A high-order wall boundary condition is achieved by fusing the constrained least-square technique with the WENO procedure, where a quadratic element is used in the reconstruction for cells with a curved boundary. Numerical tests involving both the second-order and third-order compact GKS are presented, encompassing both inviscid and viscous flows at both low and high speeds. The results demonstrate that the proposed third-order compact scheme possesses robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.

High-efficiency optical frequency mixing in an all-dielectric metasurface enabled by multiple bound states in the continuum

We present nonlinear optical four-wave mixing in a silicon nanodisk dimer metasurface. Under the oblique incident plane waves, the designed metasurface exhibits a multiresonant feature with simultaneous excitations of three quasi-bound states in the continuum (BIC). Through employing these quasi-BICs with maximizing electric field energy at the input bump wavelengths, significant enhancement of third-order nonlinear processes including third-harmonic generation, degenerate and nondegenerate four-wave mixing are demonstrated, giving rise to ten frequencies in the visible wavelengths. This work may lead to a new frontier of ultracompact optical mixer for applications in optical circuitry, ultrasensitive sensing, and quantum nanophotonics.

Coherent terahertz radiation from indium tin oxide film via third-order optical nonlinearity

Coherent terahertz (THz) wave emission from indium tin oxide (ITO) in epsilon-near-zero region had been reported recently as a second-order nonlinear process. However, THz radiation from ITO through third-order nonlinear process has not been reported yet. Here, we demonstrate coherent THz radiation from an ITO film via four-wave mixing, a third-order nonlinear process, under the excitation of two-color pulsed laser fields. Experimentally, an in-line phase compensator is utilized to synthesize the asymmetric optical fields to induce photocurrent in an ITO film and consequently emit THz waves. Our experimental results show that THz radiation from ITO films can be coherently controlled by the relative phase between the two-color laser fields. Such a THz wave generation process can be attributed to the fast intra-band nonlinearity in the conduction band. Our demonstration reveals that the fast nonlinearity in ITO can be used to generate THz waves and promotes the investigation of ITO in ultrafast photonics.

Orientation-patterned gallium phosphide for integrated nonlinear photonics

Gallium phosphide has long held promise for integrated nonlinear photonics, owing to its high non-linear figure of merit, broad transparency and compatibility with silicon. The recent development of orientation patterning in gallium phosphide has now brought this promise within grasp. Current research efforts are focused on demonstrating and evaluating a variety of second and third-order non-linear processes on the platform, reducing optical losses, and investigating integration with Si.

Phase dependence of third-order harmonic generation in gases induced by two-color laser field

We experimentally demonstrate third-harmonic generation (THG) in gases ionized by a femtosecond laser pulse superimposed on its second-harmonic (SH). The mechanism of THG has been investigated, and it demonstrates that a third-order nonlinear process dominates at low pump intensity. Asymmetric third-harmonic (TH) spectra are observed at different time delays in two color fields, which are attributed to the process of the four-wave mixing (FWM) of the broad spectrum of pump pulses. A joint measurement on the terahertz (THz) and the TH is performed. It reveals that the optimized phase for the THG jumps from 0 to 0.5π as the pump intensity increases, which is different from the THz being a constant, and indicates that the THG arises from the nonlinearity of the third-order bound electrons to the tunnel-ionization current.

Graphene as a source of entangled plasmons

We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The conversion is activated by applying a dc electric field that induces a density gradient or a current across the ribbon. Another scheme is degenerate four-wave mixing where the counter-propagating plasmons are emitted at the pump frequency. This third-order nonlinear process does not require a symmetry-breaking dc field. We suggest nano-optical experiments for measuring position-momentum entanglement of the emitted plasmon pairs. We estimate the critical pump fields at which the plasmon generation rates exceed their dissipation, leading to parametric instabilities.

Probing electron and hole colocalization by resonant four-wave mixing spectroscopy in the extreme ultraviolet.

Extending nonlinear spectroscopic techniques into the x-ray domain promises unique insight into photoexcited charge dynamics, which are of fundamental and applied interest. We report on the observation of a third-order nonlinear process in lithium fluoride (LiF) at a free-electron laser. Exploring the yield of four-wave mixing (FWM) in resonance with transitions to strongly localized core exciton states versus delocalized Bloch states, we find resonant FWM to be a sensitive probe for the degree of charge localization: Substantial sum- and difference-frequency generation is observed exclusively when in a one- or three-photon resonance with a LiF core exciton, with a dipole forbidden transition affecting details of the nonlinear response. Our reflective geometry–based approach to detect FWM signals enables the study of a wide variety of condensed matter sample systems, provides atomic selectivity via resonant transitions, and can be easily scaled to shorter wavelengths at free-electron x-ray lasers.

An integrated photonic circuit for color qubit preparation by third-order nonlinear interactions

This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.

Efficient mid-infrared wavelength converter based on plasmon-enhanced nonlinear response in graphene nanoribbons

Graphene plasmons with enhanced localized electric field have been used for boosting the light–matter interaction in linear optical nano-devices. Meanwhile, graphene is an excellent nonlinear material for several third-order nonlinear processes. We present a theoretical investigation of the mechanism of plasmon-enhanced third-order nonlinearity susceptibility of graphene nanoribbons. It is demonstrated that the third-order nonlinearity susceptibility of graphene nanoribbons with excited graphene surface plasmon polaritons can be an order of magnitude larger than the intrinsic susceptibility of a continuous graphene sheet. Combining these properties with the relaxed phase matching condition due to the ultrathin graphene, we propose a novel plasmon-enhanced mid-infrared (MIR) wavelength converter with arrays of graphene nanoribbons. The wavelength of signal light is in the MIR range, which can excite the tunable surface plasmons polaritons in arrays of graphene nanoribbons. The efficiency of the converter from MIR to near-infrared wavelength can be remarkably improved by 60 times compared with a graphene sheet without graphene plasmons. This work provides a novel idea for the efficient application of graphene in nonlinear optical nano-devices. The proposed MIR wavelength converter is compact, tunable and has promising potential in graphene-based MIR detectors with high detection efficiency.

Ge2Sb2Te5-based nanocavity metasurface for enhancement of third harmonic generation

The third-order nonlinear processes in nanophotonic devices may have great potentials for developing ultra-compact nonlinear optical sources, ultrafast optical switches and modulators, etc. It is known that the performance of the nonlinear nanophotonic devices strongly relies on the optical resonances and the selection of appropriate nonlinear materials. Here, we demonstrate that the third harmonic generations (THG) can be greatly enhanced at subwavelength scale by incorporating α-Ge2Sb2Te5 (α-GST) into the nanocavity metasurface. Under pumping of a near-infrared femtosecond laser, the THG from the nanocavity metasurface is ∼50 times stronger than that from the bare GST planar film. In addition, the nanocavity metasurface also provides a powerful platform for characterizing the third-order nonlinear susceptibility of the active medium in the cavity. We expect that the GST-based nanocavity metasurface could open new routes for achieving high efficiency nonlinear nanophotonic devices.

Ultrashort pulse compression method in bulk BBO crystal using electro-optically tunable cascaded second-order process: a theoretical analysis

We propose an electro-optically controllable cascaded second-order optical process that mimics as a third-order nonlinear process which is utilized for the compression of ultrashort pulses. Effective compression of optical pulses has been achieved by making efficient use of frequency doubling into an extraordinarily advantageous crystal like beta-barium-borate which is capable of generating shorter pulses within a few cycles. In accordance with simulation, it endeavors ≈ threefold compression in femtosecond pulse, i.e., 47 fs has been achieved by applying a voltage of ∓ 6.2 kV which delivers a phase mismatch (Δk) = ± 117.236 m−1 and effective cascaded refractive index (n2cascade) of ± 3.045 × 10–20 m2/W. This competent compression leads to an increase in the value of peak intensity from 50 to 288 GW/cm2. On account of the decent control in peak intensity, this promising methodology can be utilized for advanced scientific research, and also implemented easily in a large variety of applications in solid-state physics and medical field.

Single-shot diagnosing of spatiotemporal couplings in ultrashort laser pulses by spatiospectral imaging of a third-order nonlinear process.

The impact of spatiotemporal couplings (STCs) on the focal-spot intensity of ultra-intense femtosecond lasers scales up with the larger beam sizes and shorter pulse duration typically implemented to reach petawatt (PW) intensities. The repetition rate of such facilities (${ \lt }{10}\;{\rm Hz}$<10Hz) makes single-shot diagnosing of STCs mandatory. We present here a new, to the best of our knowledge, spatiotemporal diagnostic technique based on the comparison of the spatiospectral intensity of a pulse and its nonlinear third-order effect, in this case, cross-polarized wave generation (XPW), with an imaging spectrometer. The measured XPW spectrum displays specific couplings that depend on both amplitude and phase STCs of the initial pulse to be characterized. We confirm experimentally the ability of our new approach to diagnose common STCs in a laser pulse on the fly.

Shaping nonlinear optical response using nonlocal forward Brillouin interactions

In most practical scenarios, optical susceptibilities can be treated as a local property of a medium. For example, in the context of nonlinear optics we can typically treat the Kerr and Raman response as local, such that optical fields at one location do not produce a nonlinear response at distinct locations in space. This is because the electronic and vibrational disturbances produced within the material are confined to a region that is smaller than an optical wavelength. By comparison, Brillouin interactions, mediated by traveling-wave acoustic phonons, can result in a highly nonlocal nonlinear response as the elastic waves generated in the process can occupy a region in space much larger than an optical wavelength. The unique properties of these interactions can be exploited to engineer new types of processes, where highly delocalized phonon modes serve as an engineerable channel that mediates scattering processes between light waves propagating in distinct optical waveguides. These types of nonlocal optomechanical responses have recently been demonstrated as the basis for information transduction, however the nontrivial dynamics of such systems has yet to be explored. In this work, we show that the third-order nonlinear process resulting from spatially extended Brillouin-active phonon modes involves mixing products from spatially separated, optically decoupled waveguides, yielding a nonlocal susceptibility. Building on these concepts, we illustrate how nontrivial multi-mode acoustic interference can produce a nonlocal susceptibility with a multi-pole frequency response, as the basis for new optical and microwave signal processing schemes within traveling wave systems.

Nonlinear Optical Study in a Set of Dibenzylideneacetone Derivatives with Potential for Optical Frequency Conversion

The search for advanced optical materials, in particular, materials with nonlinear optical responses, has, in the last years, experienced substantial growth due to their vast applications in the photonics field. One of those applications is ultra-fast optical frequency conversion, in the optics communications field. Organic compounds have emerged as promising candidates for raw materials to develop nonlinear optical devices, such as optical converters, due to their intrinsic ultra-fast electronic responses. Also, the easy tailoring of organic molecular structures makes organic materials much more appealing than the inorganic ones. In this work, we have performed a linear and nonlinear optical characterization of a set of dibenzylideneacetone derivatives. The nonlinear optical responses investigated correspond to second- and third-order nonlinear processes, namely, first electronic molecular hyperpolarizability and two-photon absorption cross-section, respectively. The value of the first electronic molecular hyperpolarizability, up to 52 cm4·statvolt−1, could be considered a robust value when compared to the short-sized π-electron backbone length of the studied compounds. Such results suggest that these compounds exhibit the potential to be used as optical frequency converters. Quantum chemical calculations were used to predict the theoretical value of the first molecular hyperpolarizability, as well as to simulate the one- and two-photon absorption spectra for all compounds.

Enhanced third-order nonlinear processes based on Raman resonance

We observe experimentally huge enhanced four-wave mixing based on Raman resonance in an &lt;sup&gt;85&lt;/sup&gt;Rb atomic vapor system. With the decrease of coupling field power or the increase of experimental temperature, the signal tends to be narrowed down in linewidth, and be basically the same spectrum as the stimulated Raman spectroscopy. It is found that the macroscopic polarization interference effect plays a crucial role in determining the nonlinear spectra. Further more, in the Doppler-broadened Λ-type energy level system, there is a strong relationship among electromagnetically induced transparency, four-wave mixing and stimulated Raman spectroscopy. The sharp transparent window in electromagnetically induced transparency can be interpreted as the suppression of Raman gain on the linear absorption of the probe field. However, the four-wave mixing signal is a new field generated by the atomic vapor system, and it comes from the Raman gain which is affected and modified by the absorption and dispersion of the nonlinear optical medium. It shows that in a Λ-type Doppler-broadened system, in essence, both the electromagnetically induced transparency and enhanced four-wave mixing stem from stimulated Raman scattering based on the third-order nonlinear processes, just the spectra of which are from different ways and objects of detection.

Generation of high-energy clean multicolored ultrashort pulses and their application in single-shot temporal contrast measurement.

We demonstrate the generation of 100-μJ-level multicolored femtosecond pulses based on a single-stage cascaded four-wave mixing (CFWM) process in a thin glass plate by using cylinder lenses. The generated high-energy CFWM signals can shift the central wavelength and have well-enhanced temporal contrast because of the third-order nonlinear process. They are innovatively used as clean sampling pulses of a cross-correlator for single-shot temporal contrast measurement. With a simple homemade setup, the proof-of-principle experimental results demonstrate the single-shot cross-correlator with dynamic range of 1010, temporal resolution of about 160 fs and temporal window of 50 ps. To the best of our knowledge, this is the first demonstration in which both the dynamic range and the temporal resolution of a single-shot temporal contrast measurement are comparable to those of a commercial delay-scanning cross-correlator.

Gigantic electric-field-induced second harmonic generation from an organic conjugated polymer enhanced by a band-edge effect

Electric-field-induced second harmonic generation (EFISH), a third-order nonlinear process, arises from the interaction between the electric field of an external bias and that of two incident photons. EFISH can be used to dynamically control the nonlinear optical response of materials and is therefore promising for active nonlinear devices. However, it has been challenging to achieve a strong modulation with EFISH in conventional nonlinear materials. Here, we report a large tunability of an EFISH signal from a subwavelength-thick polymer film sandwiched between a transparent electrode and a metallic mirror. By exploiting the band-edge-enhanced third-order nonlinear susceptibility of the organic conjugated polymer, we successfully demonstrate a gigantic EFISH effect with a modulation ratio up to 422% V−1 at a pumping wavelength of 840 nm. The band-edge-enhanced EFISH opens new avenues for modulating the intensity of SHG signals and for controlling nonlinear electro-optic interactions in nanophotonic devices.