Third Harmonic Research Articles

Determination of plasma properties in liquid jets through time-resolved experiments on third harmonic reflection dynamics.

The study of plasma in liquid jets represents a significant area of research encompassing plasma science, dynamics, and properties. This paper presents experimental studies on plasma formation processes in liquid jets of water, ethanol, and isopropyl based on the dynamics of the third harmonic (TH) reflection from the induced plasma. Through time-resolved experiments, and theoretical estimations using the Keldysh theory, plasma properties including density and frequency for all three media are evaluated. Isopropyl demonstrates the highest values of the characteristics mentioned. These findings hold significant potential for advancing our understanding of plasma-based radiation sources, e.g., terahertz generation.

Coherent beam combining of femtosecond third-harmonic generators: towards high-power, high-beam-quality UV light generation.

Coherent beam combining (CBC) of two femtosecond third-harmonic (TH) generators is proposed and demonstrated. By applying phase modulation to one of the fundamental laser pulses, the feedback loop effectively eliminates both phase and pointing errors between the two TH femtosecond laser beams. The system delivers 345-nm femtosecond laser pulses with 22-W average power at 1-MHz repetition rate. The average combining efficiency is 91.5% over approximately 1 h of testing. The beam quality of the combined ultraviolet (UV) laser beam is near-diffraction-limited with M2 factors of M X2=1.36, M Y2=1.24, which are similar to those of the individual channels. This scheme exhibits promising potential for increasing high-beam-quality UV laser power.

Efficient Cascaded Third‐Harmonic Generation in Sampled‐Grating Periodically‐Poled Lithium Niobate Waveguides

AbstractPeriodically poled thin‐film lithium niobate (PPTFLN) waveguides enable efficient quadratic nonlinear processes due to the strong light confinement and the utilization of the largest nonlinear coefficient d33 of lithium niobate. Here, an efficient third harmonic (TH) generation is reported with a normalized conversion efficiency of 6481% W−2 cm−4 in a sampled‐grating PPTFLN waveguide under the pump of a continuous laser, which is improved by 4 orders of magnitude compared with reported results. Such an efficient TH generation is realized by cascaded second‐harmonic (SH) generation and sum‐frequency (SF) generation supported by a sampled‐grating domain structure with two Fourier coefficients of 0.44 and 0.37, respectively. Phase matching conditions for the SH and cascaded SF processes are simultaneously achieved by finely tuning the geometric dispersion, domain structure, and operating temperature of the PPTFLN waveguides.

Enhanced nonlinear effects in femtosecond laser-inscribed depressed cladding waveguides in sapphire crystals.

High-performance depressed cladding waveguides can be fabricated in crystals using ultrafast laser inscription. The investigation of nonlinear phenomena, which manifest during the transmission of high peak power femtosecond pulses within waveguides, holds significant importance for their practical integration into waveguide lasers and waveguide-based components, among other pioneering applications. In this study, the depressed cladding waveguides were successfully prepared in sapphire crystal by a femtosecond laser. The nonlinear phenomena occurring in this waveguide were investigated. The experimental results show that the nonlinearity in the depressed cladding waveguides is significantly enhanced compared with that of the bulk. This enhancement notably manifests through augmented nonlinear losses (NLs) and the third harmonic (TH) blueshift increase. Meanwhile, we theoretically investigate the influence of nonlinear effects on the TH, such as self-phase modulation (SPM), cross-phase modulation (XPM), and group delay. Our results reveal that the phase mismatch between the TH and the pump pulses is the main reason for the asymmetric broadening and blueshift of the TH spectrum. Our study reveals the unique nonlinear properties of the waveguides and lays the foundation for further relevant studies and applications of such waveguides.

Polarization of the third harmonic emission from the filamentation of femtosecond cylindrical vector beams.

We experimentally generate a third harmonic (TH) vector optical field in deep ultraviolet wavelength range using femtosecond vector laser beams. The generated TH beams are characterized by analyzing the Stokes parameters with different input laser energies. The results show that the TH predominantly preserves the vector polarization distribution of the fundamental frequency beam. Moreover, the intensity profile of the TH exhibits a multiple-ring structure. A hybrid polarization pattern is observed in the TH, where the ellipticity is influenced by the input laser energy. Our work provides an effective and straightforward method for producing TH vector optical fields, which may facilitate potential applications such as micro/nanofabrication and super-resolution microscopy.

Sub-cycle pulse revealed with carrier-envelope phase control of soliton self-compression in anti-resonant hollow-core fiber.

The influence of the carrier-envelope phase (CEP) of a pump pulse on the multioctave supercontinuum (SC) generation in a gas-filled anti-resonant hollow-core fiber (AR HCF) by soliton self-compression (SSC) has been explored. We have shown an octave-wide third harmonic generation (THG) in the visible-to-near-infrared range during the pulse compression down to a sub-cycle duration. The CEP of a multi-cycle pump pulse provides control of interference between the third harmonic (TH) and the SC that indicates the coherent synthesis of a sub-cycle pulse with a duration of about 0.4 optical cycles and a peak power of more than 2 GW at the fiber output.

Excitation of third harmonic terahertz surface plasmon over a rippled graphene-free space interface

We examined the third harmonic (TH) terahertz (THz) surface plasmon waves (SPWs) generation over a graphene surface deposited on a rippled dielectric substrate (SiO2) by obliquely incidenting a p-polarized laser beam on a graphene surface with frequency ω0 and wave numbers k0x and k0z at an incident angle θ. Laser beam exerts ponderomotive force on free electrons of the graphene surface and produce nonlinear second harmonic (SH) oscillatory velocity v→2ω0 at frequency 2ω0. SH oscillatory velocity couples with perturbed ripple electron density to produce TH nonlinear current density J→3ω0nl at frequency 3ω0. Ripple wave number (q) provides an extra wave number to develop resonant TH THz SPWs at frequency 3ω0 and wave number kz=3k0z+q. The required ripple wave number for the excitation of THz TH SPWs is lower for the higher Fermi energy of the graphene sheet as compared to lower Fermi energy. Graphene sheet’s Fermi energy and angle of incidence laser beam significantly modify the amplitude of TH THz SPWs.

Non-linear propagation effects of intense femtosecond pulses on below bandgap harmonics in solids

The non-linear propagation of the intense near-infrared (NIR) driving field in crystals poses a challenge and can offer an opportunity to control the spectral properties of harmonics in solids. Here, we have investigated the non-linear propagation effects in wide bandgap dielectrics such as Magnesium Oxide (MgO), Chromium (Cr) doped MgO (Cr: MgO), Sapphire (Sa) crystals, and fused silica (FS). Furthermore, we have generated second and third harmonics (TH) and measured the linear polarization dependence of harmonics in these thin solids to explore the non-linear response at a strong field. We observe spectral shifts and broadening of the driving field spectrum which is imprinted on the harmonics. We attribute these effects to the strong photoionization, generation of free-carrier density, and self-phase modulation effects. This work shows the sensitivity to control the spectral profile of harmonics by manipulating the driving field, showing the possibility of new tailored solid-state ultraviolet sources for optical diagnostics.

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.

Chiral Third-Harmonic Metasurface for Multiplexed Holograms.

Chiral nonlinear metasurfaces could natively synergize nonlinear wavefront manipulation and circular dichroism, offering enhanced capacity for multifunctional and multiplexed nonlinear metasurfaces. However, it is still quite challenging to simultaneously enable strong chiral response, precise wavefront control, high nonlinear conversion efficiency, and independent functions on spins and chirality. Here, we propose and experimentally demonstrate multiplexed third-harmonic (TH) holograms with four channels based on a chiral Au-ZnO hybrid metasurface. Specifically, the left- and right-handed circularly polarized (LCP and RCP) components of the TH holographic images can be designed independently under the excitation of an LCP (or RCP) fundamental beam. In addition, the TH conversion efficiency is measured to be as large as 10-5, which is 8.6 times stronger than that of a bare ZnO film with the same thickness. Thus, our work provides a promising platform for realizing efficient and multifunctional nonlinear nanodevices.

Investigation of Nonlinear Optical Processes in Mercury Sulfide Quantum Dots.

The authors report the third-harmonic generation, nonlinear refraction, and nonlinear absorption in HgS quantum dot (QD) suspensions and films using the nanosecond and femtosecond pulses. High conversion efficiency (7 × 10−4) towards the third harmonic (TH) of the 900–1700 nm, 150 fs laser in the thin (70 nm) films containing HgS QDs deposited on the glass substrates is obtained. The authors analyze spectral dependencies of the TH, nonlinear refractive indices, and nonlinear absorption coefficients of QDs in the 500–1700 nm range and discuss the relation between the TH process and the low-order nonlinear optical properties of these quantum dots.

Nonintrusive temperature measurement of a combustion field by femtosecond laser-induced third harmonic generation

We report a comparative experimental investigation of femtosecond laser-induced third harmonic generation (THG) in an ethanol flame and in air. It was found that the third harmonic (TH) signal produced in the presence of a combustion field can be greatly enhanced, in comparison to that generated in air, and that the enhancement factor depends strongly on the experimental parameters, such as the focal length, relative position of the flame and filament, and laser repetition frequency. Moreover, by replacing the flame with a point temperature controller, a similar signal enhancement of THG was observed, and the TH signal exhibited a nonlinear growth with the heating temperature. Further analysis indicated that the observed enhancement of THG originates from the suppression of Gouy-phase-induced destructive interference due to the disturbed gas density under high-temperature heating. The high sensitivity of the TH signal to the combustion temperature helps formulate an effective and straightforward approach to achieve nonintrusive temperature measurements in the combustion field.

Tunable Lifetime and Nonlinearity in Two Dimensional Materials Plasmonic-Photonic Absorber.

We investigate a framework of local field, quality factor and lifetime for tunable graphene nanoribbon plasmonic-photonic absorbers and study the second order and third order nonlinear optical response of surface plasmons. The energy exchange of plasmonic-photonic absorber occurs in two main ways: one way is the decay process of intrinsic loss for each resonant mode and another is the decay process of energy loss between graphene surface plasmon (GSP) mode and the external light field. The quality factor and lifetime of the plasmonic-photonic absorber can be obtained with using the coupled mode theory (CMT) and finite difference time domain (FDTD) method, which are effectively tunable with changing Fermi energy, carrier mobility and superstrate refractive index. The evolutions of total energy and lifetime of GSP are also shown, which are helpful for the study of micro processes in a two-dimensional material plasmonic-photonic absorber. The strongly localized fundamental field induces a desired increase of second harmonic (SH) wave and third harmonic (TH) wave. The manipulation of the quality factor and lifetime of the GSP makes graphene an excellent platform for tunable two-dimensional material plasmonic-photonic devices to realize the active control of the photoelectric/photothermal energy conversion process and higher harmonic generation.

Enhanced third harmonic generation in ultrathin free-standing β-Ga2O3 nanomembranes: study on surface and bulk contribution.

Third harmonic generation (THG) has proven its value in surface and interface characterization, high-contrast bio-imaging, and sub-wavelength light manipulation. Although THG is observed widely in general solid and liquid substances, when laser pulses are focused at nanometer-level ultra-thin films, the bulk THG has been reported to play the dominant role. However, there are still third harmonics (TH) generated at the surface of the thin-films, not inside the bulk solid - so-called surface TH, whose relative contribution has not been quantitatively revealed to date. In this study, we quantitatively characterized the surface and bulk contributions of THG at ultra-thin β-Ga2O3 nanomembranes with control of both the laser and thin-nanomembranes parameters, including the laser peak power, polarization state, number of layers, and nanomembranes thicknesses. Their contributions were studied in detail by analyzing the TH from freestanding β-Ga2O3 nanomembranes compared with TH from β-Ga2O3 nanomembranes on glass substrates. The contribution of the TH field from the β-Ga2O3-air interface was found to be 5.12 times more efficient than that from the β-Ga2O3-glass interface, and also 1.09 times stronger than the TH excited at bulk 1-μm-thick β-Ga2O3. Besides, TH from the β-Ga2O3-air interface was found to be 20% more sensitive to the crystalline structure than that from the β-Ga2O3-glass interface. This research work deepens our understanding of surface and bulk THG from crystalline materials and provides new possibilities towards designing highly efficient nonlinear optical materials for bio-imaging, energy-harvesting, and ultrafast laser development.

Intensity-dependent nonlinear optical properties in an asymmetric Gaussian potential quantum well-modulated by external fields

In this paper, the effects of external electric, magnetic and non-resonant intense laser fields on the nonlinear optical rectification (NOR), second-harmonic (SH), and third harmonic (TH) generation in a GaAs quantum well with asymmetrical Gaussian potential are theoretically investigated. Firstly, the energy eigenvalues and eigenfunctions of a single electron confined in the structure are obtained by using the diagonalization method within the framework of the effective-mass and parabolic band approaches. Then, using these energy eigenvalues and eigenfunctions, expressions derived within the compact density matrix approximation have been employed to calculate the coefficients of the nonlinear optical response in the structure. The obtained simulation results show that the influence of the external fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation in the system. As a result, it has been seen that the amplitude and position of the peaks of nonlinear optical rectification, second and third harmonic coefficients can be controlled by changing the applied external fields.

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.

Third optical harmonic generation reveals circular anisotropy in tilted silicon nanowire array.

In this Letter, we report on the circular anisotropy of third-harmonic (TH) generation in an array of silicon nanowires (SiNWs) of approximately 100 nm in diameter tilted to the crystalline silicon substrate at an angle of 45°. Numerical simulations of the scattering at the fundamental and TH frequencies of circularly polarized light by a single SiNW and an ansatz structure composed of 13 SiNWs used as a geometrical approximation of the real SiNW array indicate asymmetric scattering diagrams, which is a manifestation of the photonic spin Hall effect mediated by the synthetic gauge field arising due to the special guided-like mode structure in each SiNW. Despite strong light scattering in the SiNW array, the experimentally measured TH signal demonstrated significant dependence on the polarization state of incident radiation and the SiNW array spacial orientation in regard to the wave vector direction.

Supercontinuum-induced multi-wavelength third-harmonic generation in a suspended-core microstructured optical fiber.

In this paper, we reported a multi-wavelength third-harmonic generation (THG) induced by supercontinuum (SC) in an in-house fabricated suspended-core microstructured optical fiber (MOF). The adjustment of pump wavelength and pump power exerted an influence on SC which simultaneously emitted third harmonic (TH) waves in the visible light range. At the pump wavelength of 1220 nm and the average pump power of 450 mW, a multi-wavelength TH spectrum (373∼589 nm) with over twenty distinct peaks was observed under the phase matching (PM) condition between the fundamental mode and the higher-order modes. To the best of our knowledge, this is the first report on THG in optical fibers with so great a number of wavelengths. The maximal THG conversion efficiency ∼6.791 × 10-4 was obtained at 1480 nm, 350 mW, which is highly competitive compared with the values reported previously. Furthermore, theoretical simulation has been carried out, which corresponded well with the experimental observation. This multi-wavelength THG in the suspended-core MOF may provide a unique pathway towards tailored multi-wavelength ultrafast light sources for applications in sensing and imaging technologies.

Coherently enhanced third-harmonic generation in cascaded microfibers.

A scheme using cascaded silica microfibers is proposed for efficient third-harmonic (TH) generation. By tuning the phase difference via input pump power, the TH from the microfibers could overlap coherently, yielding great output enhancement. Conversion efficiency ∼20% is demonstrated analytically and numerically. Moreover, as the TH output features are dominated by behavior analogous to optical interference, the influence of random diameter deviation of each microfiber is reduced, and the conversion process could be well controlled.

Enhanced nonlinear optical responses of graphene in multi-frequency topological edge modes.

We propose a hybrid structure where graphene is inserted to the interface of two one-dimensional photonic crystals (1D PCs). The two PCs are designed to have opposite topological properties, and at the interface, topological edge modes exist. The edge modes exist at both the fundamental frequency (FF) and the third harmonic (TH) frequency. This double resonant structure will enhance the nonlinear responses of graphene greatly, including Kerr nonlinearity and TH generation. We discuss these two kinds of nonlinearities both at terahertz (THz) and near-infrared (NIR) frequencies. The influence of Kerr nonlinearity on the resonant frequencies is considered, when we calculate the TH generation. At THz frequency, low-threshold bistability (about 8MW/cm2) is obtained and the TH generation efficiency of 2.5% is achieved with incident intensity of 10MW/cm2. At NIR frequency, the nonlinear conductivities of graphene are about 7 orders lower. Bistability is unlikely to happen with incident intensity below 1GW/cm2. The TH generation efficiency is only about 5×10-6 with incident intensity of 25MW/cm2. The proposed structure is more suitable to work as a low-threshold saturable absorber at NIR frequency. These results may be helpful both for a better understanding of graphene's nonlinear responses in a double resonant structure and for potential applications in THz nonlinear devices and NIR nanophotonics.