Third-harmonic Generation Process Research Articles

Laser pulse induced second- and third-harmonic generation of gold nanorods with real-time time-dependent density functional tight binding (RT-TDDFTB) method.

In this study, we investigate second- and third-harmonic generation processes in Au nanorod systems using the real-time time-dependent density functional tight binding method. Our study focuses on the computation of nonlinear signals based on the time dependent dipole response induced by linearly polarized laser pulses interacting with nanoparticles. We systematically explore the influence of various laser parameters, including pump intensity, duration, frequency, and polarization directions, on harmonic generation. We demonstrate all the results using Au nanorod dimer systems arranged in end-to-end configurations, and disrupting the spatial symmetry of regular single nanorod systems is crucial for second-harmonic generation processes. Furthermore, we study the impact of nanorod lengths, which lead to variable plasmon energies, on harmonic generation, and estimates of polarizabilities and hyper-polarizabilities are provided.

Adaptive optical third-harmonic generation microscopy for in vivo imaging of tissues

Third-harmonic generation microscopy is a powerful label-free nonlinear imaging technique, providing essential information about structural characteristics of cells and tissues without requiring external labelling agents. In this work, we integrated a recently developed compact adaptive optics module into a third-harmonic generation microscope, to measure and correct for optical aberrations in complex tissues. Taking advantage of the high sensitivity of the third-harmonic generation process to material interfaces and thin membranes, along with the 1,300-nm excitation wavelength used here, our adaptive optical third-harmonic generation microscope enabled high-resolution in vivo imaging within highly scattering biological model systems. Examples include imaging of myelinated axons and vascular structures within the mouse spinal cord and deep cortical layers of the mouse brain, along with imaging of key anatomical features in the roots of the model plant Brachypodium distachyon. In all instances, aberration correction led to enhancements in image quality.

Resonant third-harmonic generation driven by out-of-equilibrium electron dynamics in sodium-based near-zero index thin films

Abstract We investigate resonant third-harmonic generation in near-zero index thin films driven out-of-equilibrium by intense optical excitation. Adopting the Landau weak coupling formalism to incorporate electron–electron and electron–phonon scattering processes, we derive a novel set of hydrodynamic equations accounting for collision-driven nonlinear dynamics in sodium. By perturbatively solving hydrodynamic equations, we model third-harmonic generation by a thin sodium film, finding that such a nonlinear process is resonant at the near-zero index resonance of the third-harmonic signal. Thanks to the reduced absorption of sodium, we observe that third-harmonic resonance can be tuned by the impinging pump radiation angle, efficiently modulating the third-harmonic generation process. Furthermore, owing to the metallic sodium response at the pump optical wavelength, we find that the third-harmonic conversion efficiency is maximised at a peculiar thin film thickness where evanescent back-reflection provides increased field intensity within the thin film. Our results are relevant for the development of future ultraviolet light sources, with potential impact for innovative integrated spectroscopy schemes.

Bridging optical fiber communication and underwater wireless optical communication via third harmonic generation.

In this paper, we propose an optical module, consisting of an Erbium/Ytterbium co-doped fiber amplifier (EYDFA) and a cascaded periodically poled lithium niobate (cascaded-PPLN), to bridge the conventional telecommunication and the emerging underwater wireless optical communication (UWOC). Compared with using two discrete crystals to achieve the third harmonic generation (THG), using a cascaded crystal simplifies the optical system. Under a fundamental power of 5 W at 1550 nm, we have generated an optical power of 6.54 mW at 516 nm, corresponding to a conversion efficiency of 0.1308%. Furthermore, we added a 5-km single-mode fiber (SMF) before the EYDFA, and by adjusting the seed laser power, we successfully maintained the efficiency of the THG process and the output power of the green light. Afterwards, the nonlinearity of the THG process is analyzed, and a simplified nonlinear pre-compensation method has been proposed to tailor the 4-pulse amplitude modulation (PAM4) signals. In such case, the bit error rate (BER) of the modified PAM4 (m-PAM4) can reduce by 69.3% at a data rate of 12 Gbps. Finally, we demonstrate the practicality of our proposed system by achieving a 7-m UWOC transmission in a water tank at a data rate of 13.46 Gbps in an optical dark room. This result demonstrates the feasibility of the hybrid fiber/UWOC system, highlighting its potential for practical implementation.

High Efficiency Third-Harmonic Generation in a Medium with Quadratic Susceptibility Due to Cubic-like Nonlinearity Caused by Cascaded Second-Harmonic Generation

Third-harmonic generation (THG) is of interest for its various applications. We propose using the cascaded second-harmonic generation (SHG) to implement the frequency conversion process, which is similar to that occurring in a medium with cubic susceptibility. Physically, the process is based on consecutive generation of the second-harmonic and the sum frequency in the same crystal with quadratic susceptibility at large phase mismatching between the fundamental wave and the second-harmonic wave. In this case, at phase matching between the fundamental wave and the third-harmonic wave, THG occurs with high efficiency. To demonstrate such a possibility theoretically, we apply the multi-scale method to a set of Schrödinger equations, describing a three-wave interaction with the frequencies ω,2ω and 3ω in a medium with quadratic susceptibility, to derive modified equations describing the frequency tripling process. These equations are solved without using the fundamental wave energy non-depletion approximation. A THG efficiency equal to 94.5% is predicted theoretically. The analytical solution is confirmed by computer simulation results. We study how various factors, such as the incident pulse intensity, phase mismatching between interacting waves, group velocity mismatching of the pulses, and second-order dispersion of the wave packets influence the THG process.

Theoretical Study on Nonreciprocity for Third-Harmonic Generation Process in Nonlinear Photonic Crystals

Based on the nonlinear coupled wave equations, the nonreciprocal response of the third-harmonic generation process has been theoretically investigated in nonlinear photonic crystals with a defect embedded. The simulation results have shown that complete nonreciprocity for third-harmonic generation can be achieved under specific conditions, and the arbitrary nonreciprocal response can be realized by adjusting the structure parameters, including the crystal length, the defect position and the defect width. These findings hold great potential for implementing practical nonlinear optical isolating devices.

Effects of conduction band non-parabolicity and matrix material on THG process in GaAs QD

We investigate theoretically the third harmonic generation (THG) process in the singly charged GaAs quantum dot (QD). The effective mass approximation is used to obtain the energy levels and the wavefunctions. The potential is considered to be of finite type, with and without the effect of non-parabolicity of the conduction band. The effect of the conduction band nonparabolicity is included using the Kane’s model. Within the framework of the density matrix approach, THG nonlinear optical process is investigated in THz region for different dot radii of GaAs QD embedded in three different matrices, viz: Ga1-yAlyAs, Al2O3 and Si3N4.

Direct sampling of ultrashort laser pulses using third-harmonic generation with perturbation in ambient air.

We propose a simple and robust all-optical pulse sampling method to characterize the temporal profiles of ultrashort laser pulses. The method is based on a third-harmonic generation (THG) process with perturbation in ambient air, which requires no retrieval algorithm and can be potentially applied to electric field measurement. The method has been successfully used to characterize multi-cycle and few-cycle pulses with a spectral range from 800 nm to 2200 nm. Considering the broad phase-matching bandwidth of THG and extremely low dispersion of air, this method is suitable for ultrashort pulse characterization even for single-cycle pulses in the near- to mid-infrared range. Thus, the method provides a reliable and highly accessible approach for pulse measurement in ultrafast optics research.

Modeling of dual frequency combs and bistable solitons in third-harmonic generation

Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for optical frequency combs in a dissipative and nonlinear χ(3)-based cavity system with parametric coupling between fundamental and third-harmonic waves. We investigate temporally dispersive dual-comb generation of phase-matched combs with broad bandwidth and anomalous dispersion of the fundamental field, individuating conditions for accessing a multistable regime that simultaneously supports two types of coupled bright cavity solitons. These bistable cavity solitons coexist for the same pump power and frequency detuning, while featuring dissimilar amplitudes of their individual field components. Third-harmonic generation frequency combs grant telecom pump laser sources a simultaneous and direct access to both the near-infrared and the visible regions, which may prove advantageous for the development of optical clocks and sensing applications.

Enhanced terahertz third-harmonic generation in graphene–metal metasurface with bound states in the continuum

We propose a graphene–metal metasurface with bound states in the continuum (BICs) for the enhancement of terahertz (THz) third-harmonic generation (THG). With the adjustment of graphene Fermi level, the parameter-tuned BICs produced by the graphene–metal metasurface can make the transition to distinct quasi-BICs. It enables strong confinement of the localized field in monolayer graphene. By exploiting the large third-order nonlinearity of graphene, the efficient THG process at the quasi-BICs can be boosted under low pump threshold. With the 50 kW/cm2 of fundamental THz incidence, a THG conversion efficiency as high as ∼3% is achievable at the quasi-BICs regime. This renders the BIC metasurfaces very attractive for THz nonlinear photonics.

Amplification and interaction of two optical waves with third harmonic spectral delay

In the present paper the parametric interaction between two optical waves, which are propagating in few-mode optical fibers, is investigated. This occurs under the influence of the processes of third harmonic generation, self-phase modulation and cross-phase modulation. The generation of third-harmonic or THz generation in femtosecond region is described by a system of two coupled nonlinear differential equations. A new analytical solution of this system, which characterizes the periodic energy exchange between the two waves, is found. Depending on the wavenumber mismatch Δk, the obtained result can be used for studying different optical processes of generation of signal wave in nonlinear dispersive media. The mentioned effects are strongly related to modern optical sensors, parametric amplifiers and communication systems.

Investigation on the optical characteristic of calcite crystal and α-BBO crystal in direct third-harmonic generation process

Calcite crystal and α-BBO crystal of which the microstructure possesses symmetric center with delocalized π bond were selected to produce phase-matched direct third-harmonic. In order to obtain a high third-order nonlinear conversion efficiency, the parameters including the walk-off angles, phase-matching angles, acceptance angles, acceptance wavelengths and group-velocity index in calcite crystal and α-BBO crystal were calculated within I (ooo→e), II (ooe→e) and III (oee→e) phase-matching types. The tinier walk-off angle and the larger acceptance angle in α-BBO crystal may lead to a better third-order nonlinear interaction in UV region. The smaller phase-matching angle in calcite crystal makes it possible to produce third-harmonic with shorter wavelength even in deep UV region. In the experiment, phase-matching angles and phase-mismatching angles of type-II which was the most efficient phase-matching type were measured in calcite crystal and α-BBO crystal. The results may provide a reference for further study on direct third-harmonic generation.

Enhanced third-harmonic generation via gold nanospheres localized surface plasmonic resonance

In the progress of nanoengineering of noble metals, the extreme nonlinear optics within nanometric volumes is of great research interest in recent years. In particular, plasmonic nanostructures offer unique route for enhancing high-order harmonic generation and other nonlinear optical progress. Here, we report that strong third harmonic emission in zinc oxide (ZnO) microbelts (MBs) via a strong localization of electromagnetic field caused by localized surface plasmon resonances. In MB/Au-nanoparticles composite, it was demonstrated that the intensity of third-harmonic generation (THG) was enhanced by a factor of five compared to bare MB. Additionally, the polarization characteristics of THG in the same system were illustrated in detail. With respect to the bare MB, the polarization degree of THG was improved significantly. The nonlinear polarization features can be attributed to the crystal structure and the ensemble of anisotropic plasmonic hot spots on the surface of Au nanoparticles. Finally, intrinsic enhancement process of THG was explored comprehensively by finite difference time domain method. The simulation results are consistent with our experimental observation.

High efficiency and large optical anisotropy in the high-order nonlinear processes of 2D perovskite nanosheets

Abstract Nonlinear nanophotonic devices have brought about great advances in the fields of nano-optics, quantum science, biomedical engineering, etc. However, in order to push these nanophotonic devices out of laboratory, it is still highly necessary to improve their efficiency. Since obtaining novel nanomaterials with large nonlinearity is of crucial importance for improving the efficiency of nonlinear nanodevices, we propose the two-dimensional (2D) perovskites. Different from most previous studies which focused on the 2D perovskites in large scale (such as the bulk materials or the thick flakes), herein we studied the 2D perovskites nanosheets with thickness of ∼50 nm. The high-order nonlinear processes including multi-photon photoluminescence and third-harmonic generation (THG) have been systematically investigated, and it is found the THG process can have a high conversion efficiency up to ∼8 × 10−6. Also, it is observed that the nonlinear responses of 2D perovskites have large optical anisotropy, i.e., the polarization ratio for the incident polarization dependence of nonlinear response can be as high as ∼0.99, which is an impressive record in the perovskite systems. Our findings reveal the properties of high efficiency and huge optical anisotropy in the nonlinear processes of 2D perovskite nanosheets, shedding light on the design of advanced integrated nonlinear nanodevices in future.

Excitonic effects on the linear and nonlinear optical properties of solid C60 fullerene, insights from many-body first-principles calculations

We perform the many-body Bethe-Salpeter equation eigenstates based sum-over-states calculations for the linear and nonlinear optical properties of solid C60 fullerene. Excitonic and local field effects are included in the calculations. We calculate the one-photon absorption (OPA), third harmonic generation (THG), degenerate four-wave mixing (DFWM), and electric-field-induced second harmonic generation (ESHG) spectra of solid C60 fullerene. The overall agreement between the theoretical and experimental results is good for all calculated spectra. The OPA spectrum shows that the solid C60 fullerene has a large excitonic binding energy of 0.35 eV. The position and intensity of spectral peaks are modified significantly. By tracing the sum-over-states progress, we determine the type of nonlinear polarization resonances for the characteristic peaks of the THG process, which may clear up a discrepancy in two experimental results. The calculated DFWM spectrum is in excellent agreement with the available experimental results in terms of line shape and peak positions, and thus the two-photon absorption peaks can be well understood on the basis of the excitonic states of solid C60 fullerene. The dynamic ESHG spectrum is given as a reference for the future experiment.

Efficient third-harmonic generation in asymmetric InxGa1-xN/InN double quantum wells

We report on enhanced third-harmonic generation based on intersubband transitions in an asymmetric InxGa1-xN/InN double quantum well. We give a comprehensive account of the influences of different structural parameters such as doping concentration, thickness of layers, and indium mole composition of barriers on the intersubband transition quantities and then their nonlinear response. The conduction band parameters are computed by the numerical solution to Schrödinger and Poisson equations within nonparabolic band approximation. More importantly, the participation of each electron scattering process, e.g., LO phonon scattering in the electron relaxation time and linewidth values, is calculated, so that it can be considered a reference to provide a heterostructure with optimum functionality. Finally, two optimized double quantum wells are designed at the fundamental photon energies of 117 and 144 meV, which exhibit remarkable third-order susceptibility up to 1.2×10−3 and 10−3μm2/V2, respectively. This study opens a new path to design a suitable InxGa1-xN/InN heterostructure for a third-harmonic generation process from the far- to near-infrared band, which promises various applications in optoelectronic devices.

Three-step model for third-harmonic generation in air by nanosecond lasers

Understanding the phenomena involved in harmonic generation in plasmas by high-power pulsed lasers is a paramount task for developing new techniques for generation of coherent radiation in ultrashort bursts. Although first experiments on harmonic generation involved nanosecond lasers and inspired further interest in the subject, numerical simulations on harmonic generation are currently mainly oriented toward ultrashort fs lasers. This paper presents a combined theoretical–experimental approach to the generation mechanisms and the properties of third-harmonic (TH) radiation generated by infrared nanosecond laser pulses in air-breakdown plasma. The paper indicates that, at the microscopic level, the generation of TH can be described by a three-step model, which involves breakdown of nitrogen molecules in the air. First, the nitrogen molecules undergo cascade-impact ionization; then, the ionized molecules are quasi-resonantly excited through three-photon absorption; in the third step, the nitrogen molecules de-excite to the fundamental level with associated emission of TH radiation. At the macroscopic level, the three-step model is implemented considering that the breakdown plasma is a conductive nonlinear medium whose third-order susceptibility and complex conductivity depend upon the cubic root of the driving laser intensity. The 2D numerical simulations performed in the frame of this model are in good agreement with the experimental data in terms of TH generation efficiency, collimation, and polarization of TH radiation, indicating the validity of the theoretical model presented here. The model enables realistic calculations with affordable computing power for prediction and control of the TH generation process driven by nanosecond laser pulses. The results are important from the fundamental and practical points of view, thus providing an efficient tool for prediction of nonlinear optical phenomena in laser-produced plasmas and for noncontact diagnosis of harmonic-generating plasmas.

Ultrafast Third-Order Nonlinear Optical Response Excited by fs Laser Pulses at 1550 nm in GaN Crystals.

The ultrafast third-order optical nonlinearity of c-plane GaN crystal, excited by ultrashort (fs) high-repetition-rate laser pulses at 1550 nm, wavelength important for optical communications, is investigated for the first time by optical third-harmonic generation in non-phase-matching conditions. As the thermo-optic effect that can arise in the sample by cumulative thermal effects induced by high-repetition-rate laser pulses cannot be responsible for the third-harmonic generation, the ultrafast nonlinear optical effect of solely electronic origin is the only one involved in this process. The third-order nonlinear optical susceptibility of GaN crystal responsible for the third-harmonic generation process, an important indicative parameter for the potential use of this material in ultrafast photonic functionalities, is determined.

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these signatures manifest in the nonlinear Kerr effect and in third-harmonic generation processes. We show that the resonant nonlinear spectral response of topological fermions can be traced to specific Dirac cones in these materials, enabling characterization of topological invariants in any phase by detecting the cross-polarized component of the electromagnetic field. By shedding light on the unique processes involved in harmonic generation via topological phenomena our findings open an encouraging path towards the development of novel nonlinear systems based on two-dimensional semiconductors of the graphene family.

Conversion of spin and orbital angular momentum in the third harmonic generation process in the bulk of an isotropic medium

The interaction between spin and orbital components of the angular momentum of an elliptically polarized beam with helicoidal phase profile and arbitrary axially symmetric intensity profile in the third-harmonic generation process is investigated. The third-harmonic beam is generated in an isotropic medium with cubic nonlinearity within undepleted pump approximation. The conservation of the total projections of both the spin angular momentum and orbital angular momentum components in four-wave mixing is demonstrated for interacting waves.