Effective Third-order Susceptibility Research Articles

Enhancement of third-order optical nonlinearity in effective epsilon-near-zero metamaterials of dielectric/metal/dielectric sandwich nanostructures

We report the enhancement of third-order optical nonlinearity in dielectric/metal/dielectric sandwiches driven by the epsilon-near-zero (ENZ) effect. The lithium niobate (LN) and Au are chosen as the typical dielectric and metal, respectively. The sandwich nanostructure consists of two layers of LN film (90 nm) and an insertion of Au layer of different thicknesses (9, 13, and 17 nm). The ENZ wavelength of LN/Au/LN (LAL) sandwiches is experimentally obtained with a modulation from 0.96 μm (Au layer 17 nm) to 1.33 μm (Au layer 9 nm). The nonlinear refractive index n2 and nonlinear absorption coefficient β are determined at variable near infrared wavelengths using the Z-scan method. The maximum n2=2.31×10−14(6.76×10−15)m2/W and β=−9.20×10−8(−1.94×10−8)m/W are obtained in the LAL sandwich with a 13 nm Au layer of ENZ wavelength 1.088 μm at the wavelength 1.064 μm with a pulse duration of 25 ps (120 fs). The n2 is around 19 and 25 times larger than those in the pure LN film of thickness 180 nm measured at the picosecond and femtosecond time domains, respectively. The enhancement of n2 in LAL sandwiches follows the numerical results obtained from the ENZ effect. Especially, the LN layer and the Au layer have comparable contributions to the effective third-order susceptibility χeff(3), which leads to the reconfigurable χeff(3) by changing the thickness of each layer and further to modulate the n2 and β of the samples. The results offer a promising way to attain large and reconfigurable optical nonlinearities for application in all-optical photonic devices at a specified wavelength.

Third harmonic generation in monoclinic 2D KNbO3 with high power endurance

Two-dimensional (2D) KNbO3 is prepared by topotactic transition from 2D KNbO2 at 530 °C in air, which has a single spontaneous polarization (Ps) direction along the [101¯]pc zone axis. The strong Ps anisotropy leads to a negligible second harmonic generation of 2D KNbO3 with laser vertically incident on the sample. However, a strong third harmonic generation is observed. The effective third-order susceptibility of 2D KNbO3 with the order of ∼10−19 m2 V−2 is estimated by comparing it with the χeff(3) of graphene. The robust power tolerance of 2D KNbO3 endows it great potential in the application of high-power third harmonic generation 2D devices.

Enhanced Third Harmonic Generation in Lead Bromide Perovskites with Ruddlesden-Popper Planar Faults.

Lead halide perovskites provide a test bed for exploring nonlinear optical properties. Although the underlying centrosymmetric crystal structure of 3D lead halide perovskites precludes the phenomenon of second harmonic generation, the third and higher-order harmonic generation are allowed. In this work, we probe the third harmonic generation (THG) from CsPbBr3 nanocrystals (NCs) and compare it to the THG from CsPbBr3 NCs with Ruddlesden-Popper planar faults (RP-CsPbBr3), formed via postsynthetic fusion-growth. The THG from CsPbBr3 NCs is negligible compared with that of RP-CsPbBr3 NCs within a wide range of femtosecond excitation wavelengths. We further compare the THG from a thin film of RP-CsPbBr3 with that of a single crystal of methylammonium lead bromide (MAPbBr3). The THG efficiency of RP-CsPbBr3 is found to be three times greater than that of MAPbBr3. An effective third-order susceptibility of the order of 10-18 m2 V-2 is obtained for a RP-CsPbBr3 film, opening up the prospect of inorganic halide perovskite NCs with planar defects for a range of nonlinear optical applications.

Fifth-order optical nonlinear response of semiconducting 2D LTMD MoS2.

The effective fifth-order susceptibility, ${\chi}_{\rm eff}^{(5)}$, of two-dimensional (2D) semiconducting layered transition metal dichalcogenide (LTMD) molybdenum disulfide (${\rm MoS}_2$) is reported here for the first time, to the best of our knowledge. Using the $ Z $-scan technique with a laser operating at 800 nm, 1 kHz, 100 fs, we investigated the nonlinear behavior of ${\rm MoS}_2$ suspended in acetonitrile (concentration, 70 µg/ml). The effective nonlinear refractive index ${{n}_{4,{eff}}} = - ({7.6 \pm 0.5}) \times {10^{- 26}}\; {{\rm cm}^4}/{{\rm W}^2}$, proportional to ${\rm Re}{\chi}_{\rm eff}^{(5)}$, was measured for monolayer ${\rm MoS}_2$ nanoflakes, prepared by a modified redox exfoliation method. We also determined the value of the nonlinear refractive index ${{n}_2} = + ({4.8 \pm 0.5}) \times {10^{- 16}}\;{{\rm cm}^2}/{\rm W}$, which is related to the material's effective third-order optical susceptibility real part, ${Re\chi}_{\rm eff}^{(3)}$. For comparison, we also investigated the nonlinear response of tungsten disulfide (${\rm WS}_2$) monolayers, prepared by the same method and suspended in acetonitrile (concentration, 40 µg/ml), which only exhibited the third-order nonlinear effect in the same intensity range, up to ${120}\;{{{\rm GW}/{\rm cm}}^2}$. Nonlinear absorption was not observed in either ${\rm MoS}_2$ or ${\rm WS}_2$.

Simple model for the nonlinear optical response of dimer-doped waveguides

We put forth a simple model that allows us to obtain the nonlinear coefficient of a waveguide doped with dimers of Ag and Au, and study its unique nonlinear optical properties through the recently introduced photon-conserving nonlinear Schrödinger equation. We calculate the doped-waveguide effective third-order susceptibility based on the Maxwell Garnett model and its extension to nonlinear optics. In particular, our model captures the nature of the plasmon hybridization in an equivalent single nanoparticle whose dielectric function and size are derived. As a result, we obtain a gap-dependent nonlinear coefficient significantly higher than that of waveguides doped with single nanoparticles. Finally, a modulation-instability analysis reveals a complex nonlinear response from the waveguide depending upon the dimer gap, including the emergence of ultra-narrow gain bands. We believe these findings to be of singular relevance in the engineering of photonic devices based on nanoparticle-doped waveguides.

Acousto-optic modulation in ion implanted semiconductor plasmas having SDDC

Abstract The present paper is aimed to the exploration of acousto-optic (AO) modulational amplification in ion implanted semiconductors. The AO modulational process has been treated as a four wave parametric mixing process and the effective third-order acousto-optic susceptibility characterizing the instability process has been deduced. By considering that the origin of modulational interaction lies in the third order AO susceptibility arising from the nonlinear induced current density and using the coupled mode theory, an analytical investigation of an intense laser beam in a strain dependent dielectric constant (SDDC) semiconductor crystal is presented. We found a significant change in threshold and gain characteristics with changes in charge imbalance parameter. The presence of colloidal grains (CGs) plays an effective role in changing the threshold intensity and effective gain constant.

Effect of high index sphere size on effective refractive index of random nanocomposites

The linear and nonlinear optical properties of random composites are investigated with the use of the three-dimensional finite-difference time-domain (FDTD) simulations of light propagation. An effective linear refractive index of the mixture as a function of the GaP spherical inclusion size is constructed. This dependence is non-monotonic reaching a maximum just below the first optical resonance. It is shown that the effective Kerr third-order susceptibility of the nanocomposite grows by orders near the optical resonance.

Highly Enhanced Third-Harmonic Generation in 2D Perovskites at Excitonic Resonances.

Two-dimensional hybrid organic-inorganic Ruddlesden-Popper perovskites (RPPs) have attracted considerable attention due to their rich photonic and optoelectronic properties. The natural multi-quantum-well structure of 2D RPPs has been predicted to exhibit a large third-order nonlinearity. However, nonlinear optical studies on 2D RPPs have previously been conducted only on bulk polycrystalline samples, in which only weak third-harmonic generation (THG) has been observed. Here, we perform parametric nonlinear optical characterization of 2D perovskite nanosheets mechanically exfoliated from four different lead halide RPP single crystals, from which we observe ultrastrong THG with a maximum effective third-order susceptibility (χ(3)) of 1.12 × 10-17 m2 V-2. A maximum conversion efficiency of 0.006% is attained, which is more than 5 orders of magnitude higher than previously reported values for 2D materials. The THG emission is resonantly enhanced at the excitonic band gap energy of the 2D RPP crystals and can be tuned from violet to red by selecting the RPP homologue with the requisite resonance. Due to signal depletion effects and phase-matching conditions, the strongest nonlinear response is achieved for thicknesses less than 100 nm.

Degenerate Four-Wave Mixing in a Multiresonant Germanium Nanodisk

Dielectric nanoantennas excited at Mie resonances are becoming suitable candidates for nonlinear optical effects due to their large intrinsic nonlinearity and capability to highly confine electromagnetic fields within subwavelength volumes. In this work, we show that a single Ge nanodisk, recently demonstrated as an efficient source of third-harmonic generation (THG), can also be exploited for four-wave mixing (FWM) phenomena. The high field enhancement inside the disk yields effective third-order susceptibilities as high as 2 × 10–8 esu (2.8 × 10–16 m2/V2), which were determined by single pump wavelength THG measurements tuned to high-order Mie modes. A similar nonlinear optical response is observed in the case of degenerate FWM where two different pump wavelengths are coupled to a single high-order resonant mode. However, when the two pump wavelengths are coupled to different high-order modes, the FWM process is partially suppressed due to a diminished near-field spatial overlap of the mixed wavelengths...

Quadratic electro-optic Kerr effect in doped graphene

We theoretically investigate one of the third-order nonlinear optical (NLO) effects, namely, the quadratic electro-optic Kerr effect (EOKE), in doped graphene. To avoid the screening of an in-plane external dc electric field by the graphene’s electrons, we propose to use ‘low-amplitude’ ( cm−1) terahertz radiation pulses focused onto the graphene sample collinearly with a normally incident optical beam of frequency ω. Using the Dirac cone approximation for the π-electron energy bands of graphene, we calculate the real part of the effective third-order NLO susceptibility , describing the EOKE in doped graphene under the above conditions. The results obtained show that a large electro-optic modulation of the graphene’s refractive index n (up to ) can be achieved by proper tuning the Fermi level of charge carriers in the graphene sample via electrostatic gating. Furthemore, a change of sign of the electro-optic Kerr coefficient of doped graphene can occur in the spectral range below the photon energy threshold value of , corresponding to the onset of the fundamental (single-photon) interband absorption in the graphene. These theoretical findings open up new opportunities for practical exploitation of the EOKE in graphene-based NLO devices.

Rapid and Large-Area Characterization of Exfoliated Black Phosphorus Using Third-Harmonic Generation Microscopy.

Black phosphorus (BP) is a layered semiconductor that recently has been the subject of intense research due to its novel electrical and optical properties, which compare favorably to those of graphene and the transition metal dichalcogenides. In particular, BP has a direct bandgap that is thickness-dependent and highly anisotropic, making BP an interesting material for nanoscale optical and optoelectronic applications. Here, we present a study of the anisotropic third-harmonic generation (THG) in exfoliated BP using a fast scanning multiphoton characterization method. We find that the anisotropic THG arises directly from the crystal structure of BP. We calculate the effective third-order susceptibility of BP to be ∼1.64 × 10-19 m2 V-2. Further, we demonstrate that multiphoton microscopy can be used for rapid, large-area characterization indexing of the crystallographic orientations of many exfoliated BP flakes from one set of multiphoton images. This method is therefore beneficial for samples of areas ∼1 cm2 in future investigations of the properties and growth of BP.

Nonlinear optical model for strip plasmonic waveguides

This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett.41, 317 (2016)OPLEDP0146-959210.1364/OL.41.000317]. The first effect is the nonlinear power saturation of the plasmonic mode, and the second effect is the spectral broadening of the plasmonic mode. Both nonlinear plasmonic effects can be used for practical applications and their appropriate model will be important for further developments in communication approaches.

Four-wave-mixing experiments with seeded free electron lasers.

The development of free electron laser (FEL) sources has provided an unprecedented bridge between the scientific communities working with ultrafast lasers and extreme ultraviolet (XUV) and X-ray radiation. Indeed, in recent years an increasing number of FEL-based applications have exploited methods and concepts typical of advanced optical approaches. In this context, we recently used a seeded FEL to demonstrate a four-wave-mixing (FWM) process stimulated by coherent XUV radiation, namely the XUV transient grating (X-TG). We hereby report on X-TG measurements carried out on a sample of silicon nitride (Si3N4). The recorded data bears evidence for two distinct signal decay mechanisms: one occurring on a sub-ps timescale and one following slower dynamics extending throughout and beyond the probed timescale range (100 ps). The latter is compatible with a slower relaxation (time decay > ns), that may be interpreted as the signature of thermal diffusion modes. From the peak intensity of the X-TG signal we could estimate a value of the effective third-order susceptibility which is substantially larger than that found in SiO2, so far the only sample with available X-TG data. Furthermore, the intensity of the time-coincidence peak shows a linear dependence on the intensity of the three input beams, indicating that the measurements were performed in the weak field regime. However, the timescale of the ultrafast relaxation exhibits a dependence on the intensity of the XUV radiation. We interpreted the observed behaviour as the generation of a population grating of free-electrons and holes that, on the sub-ps timescale, relaxes to generate lattice excitations. The background free detection inherent to the X-TG approach allowed the determination of FEL-induced electron dynamics with a sensitivity largely exceeding that of transient reflectivity and transmissivity measurements, usually employed for this purpose.

Widely Tunable Intracavity Phasematched Cascaded Second-Order Interaction for the Generation of Multicolor Radiation

A theoretical and experimental study of all-solid-state barium borate (BBO)-based optical parametric oscillator with wide tunability from visible to near-infrared by means of intracavity second-order cascaded nonlinear interaction has been demonstrated for simultaneous generation of multicolor radiation. Radiations in the wavelength range of 600-661 nm in the visible and 892-1322 nm in the near-infrared range are generated by a combination of optical parametric oscillation and simultaneous second harmonic generation in BBO crystal. The effective third-order susceptibility is measured to be 885.18 pm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which is greater than intrinsic third-order susceptibility by one order of magnitude.

Synthesis and optical properties of a D–A–D cationic cyclopentadienyl iron complex containing double arylazo chromophores

A D–A–D cationic cyclopentadienyl iron complex containing double arylazo chromophores (Fc-diazo) with methoxyl group (Fc-diazo-OMe) was obtained via nucleophilic substitution and well characterized by IR, UV–visible, 1H NMR, and 13C NMR spectroscopy, and MS. UV–Vis absorption and nonlinear optical property of Fc-diazo-OMe were investigated by comparison of Fc-diazo with no methoxyl group (Fc-diazo-H). Quantum chemical calculations of the orbital energy, geometric structure of Fc-diazo-OMe, and Fc-diazo-H were conducted by using density functional methods at the B3PW91/Lanl2dz level. Charge transfer from the highest occupied molecular orbital to the lowest unoccupied molecular orbital was found based on density functional theory. The substitution of the methoxyl group greatly improves the NLO property of Fc-diazo. Fc-diazo-OMe shows effective two-photon absorption, coefficient and third-order nonlinear susceptibility for potential applications as optical materials, while Fc-diazo-H barely shows NLO ability.

Nonlinearity management of photonic composites and observation of spatial-modulation instability due to quintic nonlinearity

We present a procedure for nonlinearity management of metal-dielectric nanocomposites (MDNCs). Varying the volume fraction occupied by silver nanoparticles (NPs) suspended in acetone we could investigate the nonlinear (NL) response of the MDNC. In particular, we could cancel the NL refractive index related to the effective third-order susceptibility, ${\ensuremath{\chi}}_{\mathrm{eff}}^{(3)}$, and thus the NL refractive behavior of the MDNC was due to the effective fifth-order susceptibility, ${\ensuremath{\chi}}_{\mathrm{eff}}^{(5)}$. Hence, in a cross-phase modulation experiment, we demonstrated the effect of spatial-modulation instability due to ${\ensuremath{\chi}}_{\mathrm{eff}}^{(5)}$. The experimental results are corroborated with numerical calculations based on a generalized Maxwell-Garnet model that includes the direct contributions of the NPs and the host medium as well as cascade contributions due to the third- and fifth-order susceptibilities of the NPs.

Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna

The ability to convert low-energy quanta into a quantum of higher energy is of great interest for a variety of applications, including bioimaging, drug delivery and photovoltaics. Although high conversion efficiencies can be achieved using macroscopic nonlinear crystals, upconverting light at the nanometre scale remains challenging because the subwavelength scale of materials prevents the exploitation of phase-matching processes. Light-plasmon interactions that occur in nanostructured noble metals have offered alternative opportunities for nonlinear upconversion of infrared light, but conversion efficiency rates remain extremely low due to the weak penetration of the exciting fields into the metal. Here, we show that third-harmonic generation from an individual semiconductor indium tin oxide nanoparticle is significantly enhanced when coupled within a plasmonic gold dimer. The plasmonic dimer acts as a receiving optical antenna, confining the incident far-field radiation into a near field localized at its gap; the indium tin oxide nanoparticle located at the plasmonic dimer gap acts as a localized nonlinear transmitter upconverting three incident photons at frequency ω into a photon at frequency 3ω. This hybrid nanodevice provides third-harmonic-generation enhancements of up to 10(6)-fold compared with an isolated indium tin oxide nanoparticle, with an effective third-order susceptibility up to 3.5 × 10(3) nm V(-2) and conversion efficiency of 0.0007%. We also show that the upconverted third-harmonic emission can be exploited to probe the near-field intensity at the plasmonic dimer gap.

Third harmonic generation in graphene and few-layer graphite films

We observe optical third harmonic generation from graphene and few-layer graphite flakes produced by exfoliation. The emission scales with the cube of the intensity of the incident near-infrared femtosecond pulses and has a wavelength that is one-third of the incident wavelength, both consistent with third harmonic generation. We extract an effective third-order susceptibility for graphene that is on the order of 10${}^{\ensuremath{-}16}$ m${}^{2}$/V${}^{2}$, which is comparable to that for materials that are resonantly excited, but larger than for materials that are transparent at the fundamental and third harmonic wavelengths.

Effective third-order susceptibility of silicon-nanocrystal-doped silica

We derive approximate analytic expressions for the effective susceptibility tensor of a nonlinear composite, consisting of silicon nanocrystals embedded in fused silica. Two types of composites are considered: by assuming that (i) the crystallographic axes of different crystallites are the same, or (ii) crystallites are oriented randomly. In the first case, the tensor properties of the effective third-order susceptibility are shown to coincide with those of the bulk silicon. In the second case, however, the tensor properties of the susceptibility of the composite material are found to be quite different due to drastic modification of light interaction with optical phonons inside the composite. The newly derived expressions should be useful for modeling nonlinear optical phenomena in silica fibers and waveguides doped with silicon nanocrystals.

Enhancement of the nonlinear effects in composite plasmonic nanoparticles

Features of the second- and third-order nonlinear effects in composite plasmonic core/shell nanoparticles placed into a polymer matrix are investigated. Resonant enhancement of the effective third-order susceptibility is observed, as well as the appearance of a coherent magnetization-induced component of the second harmonic.