In this article for the first time we applied the eclipse Z-scan technique which is by one order of magnitude more sensitive than the conventional Z-scan technique to measure LiNbO3 crystal nonlinear refractive index in the THz range. The obtained value of LiNbO3 nonlinear refractive index is estimated to be order of 10^-11 cm^2/W which is commensurate with known results. This value correlates with the theoretically calculated nonlinear refractive index coefficient of vibrational nature. The influence of thermal nonlinearity on the experimental results can be neglected, since the estimated temperature induced refractive index change equals to 2.6*10^-5, while addition from optical nonlinearity is 2.9*10^-3. The demonstrated heightened sensitivity of eclipse Z-scan allows to hold promise for the properties evaluation of materials exhibiting lower nonlinear refractive indices, thus expanding its applicability in characterizing diverse nonlinear optical materials.
The values of the nonlinear refractive index coefficient for various materials in the terahertz frequency range exceed the ones in both visible and NIR ranges by several orders of magnitude. We report the direct measurement of the nonlinear refractive index coefficient of liquid water by using the Z-scan method with broadband pulsed THz beam. Our experimental result shows that nonlinear refractive index coefficient in water is positive and can be as large as 3.5$\times$10$^{-10}$ cm$^{2}$/W in the THz frequency range, which exceeds the ones for the visible and NIR ranges by 6 orders of magnitu…
Over the last three decades, plasmonics using metallic nanostructures has become central to nanophotonics research. Recently, its targets have been extended to nonlinear optical phenomena. In a nonlinear regime, quantum mechanical effects, as exemplified by electron spill-out on the surface of nanostructures, significantly influence the optical response. Quantum hydrodynamic theory (QHT) is a promising basis for the analysis of nonlinear optical responses involving such quantum mechanical effects. Herein, QHT was applied to calculate the third-order optical nonlinearity of a spherical metallic…
We investigate the optical Kerr nonlinearity and multi-photon absorption (MPA) properties of DSTMS excited by femtosecond pulses at a wavelengths of 1.43 μm, which is optimal for terahertz generation via difference frequency mixing. The MPA and the optical Kerr coefficients of DSTMS at 1.43 μm are strongly anisotropic indicating a dominating contribution from cascaded 2nd-order nonlinearity. These results suggest that the saturation of the THz generation efficiency is mainly related to the MPA process and to a spectral broadening caused by cascaded 2nd-order frequency mixing within DSTMS
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\hbarω=(2/3)E_F$.
To create self-controlled radiation photonics systems, it is necessary to have complete information about the nonlinear properties of the materials used. In this paper, the vibrational mechanism of the giant low-inertia cubic nonlinearity of water in the terahertz frequency range is experimentally proven. Its dominance which manifests itself when the temperature of the liquid changes is demonstrated. The measured nonlinear refractive index in the THz frequency range for water jet at temperatures from 14$^{\circ}$C to 21$^{\circ}$C demonstrates a correlation with the theoretical approach, varie…
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanorib…
The nonlinear responses of different materials provide useful mechanisms for optical switching, low noise amplification, and harmonic frequency generation. However, the nonlinear processes usually have an extremely weak nature and require high input power to be excited. To alleviate this severe limitation, we propose new designs of ultrathin nonlinear metasurfaces composed of patterned graphene micro-ribbons to significantly enhance third harmonic generation (THG) at far-infrared and terahertz (THz) frequencies. The incident wave is tightly confined and significantly boosted along the surface …
Using an enhanced optically heterodyned optical Kerr effect method and a theoretical description of the interactions between an optical beam, a single layer of graphene, and its substrate, we provide experimental answers to questions raised by theoretical models of graphene third-order nonlinear optical response. In particular, we measure separately the time response of the two main tensor components of the nonlinear susceptibility, we validate the assumption that the out-of plane tensor components are small, and we quantify the optical impact of the substrate on the measured coefficients. Our…
Babinet complementary patterns of a spectrally tunable metamaterial incorporating a nematic liquid crystal are normally assumed to exhibit the same tuning range. Here we show that for a hybrid, terahertz liquid crystal-metamaterial, the sensitivity of its resonances to the variations of the refractive index differs substantially for the two complementary patterns. This is due to a mismatch between the alignment of the liquid crystal and the direction of the local electric field induced in the patterns. Furthermore, and more intriguingly, our experimental data indicate that it is possible to sh…
High input intensities are usually required to efficiently excite optical nonlinear effects in ultrathin structures. This problem is particularly critical at terahertz (THz) frequencies because high input power THz sources are not available. The demonstration of enhanced nonlinear effects at THz frequencies is particularly important since these nonlinear mechanisms promise to play a significant role in the development and design of new reconfigurable planar THz nonlinear devices. In this work, we present a novel class of ultrathin nonlinear hybrid planar THz devices based on graphene-covered p…
The active and nonlinear graphene properties are limited due to weak light matter interaction between the ultrathin graphene and the incident light. In this work, we present enhanced nonlinear effects at the low terahertz (THz) range by designing a new patterned graphene hyperbolic metamaterial (GHMM). More specifically, it is demonstrated that the third harmonic generation (THG) can be significantly enhanced by the proposed GHMM due to the field enhancement at the resonance as well as the supported slow light response that fosters strong light matter interaction.
We predict a new type of ultrafast third-order nonlinearity of surface plasmon polaritons (SPP) in planar magneto-plasmonic structures caused by the inverse Faraday effect (IFE). Planar SPPs with a significant longitudinal component of the electric field act via the IFE as an effective transverse magnetic field. Its response to the plasmon propagation leads to strong ultrafast self-action which manifests itself through a third-order nonlinearity. We derive a general formula and analytical expressions for the IFE-related nonlinear susceptibility for two specific planar magneto-plasmonic structu…
We present an experimental and computational study of the nonlinear optical response of conduction electrons to intense terahertz (THz) electric field. Our observations (saturable absorption and an amplitude-dependent group refractive index) can be understood on the qualitative level as the breakdown of the effective mass approximation. However, a predictive theoretical description of the nonlinearity has been missing. We propose a model based on the semiclassical electron dynamics, a realistic band structure, and the free electron Drude parameters to accurately calculate the experimental obse…
Graphene has been shown to exhibit a nonlinear response due to its unique band structure. In this paper, we study the terahertz (THz) response metallic armchair graphene nanoribbons, specifically current density and Rabi oscillations beyond the semiclassical Boltzman model. We performed quantum mathematical modeling by first finding a solution to the unperturbed Hamiltonian for a single Fermion in the dipole gauge and then applying a polarized, THz electrical field. After writing the solution in terms of the four eigenstates of the Dirac system, we numerically calculated the $x$ and $y$ compon…
The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optica…
Photon statistics in a weakly driven optomechanical photonic crystal cavity, with Kerr-type nonlinearity, is analyzed both analytically and numerically. Single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function $g^{(2)}(0)$. The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. The experimental feasibility with state-of-the-art device parameters is discussed. It is observed that photon blockade could be gener…
Optical vector analysis (OVA) having the capability to achieve magnitude and phase responses is essential for fabrication and application of emerging optical devices. However, the conventional OVA often have to make compromises among resolution, dynamic range and bandwidth. Modulation-based OVA promises ultra-high resolution but suffers from measurement errors due to the modulation nonlinearity, narrow bandwidth restricted by the employment of microwave and optoelectronic devices, and difficulties in measuring optical devices with deep notch restricted by small signal modulation or the high-or…
Highly efficient broadband THz upconversion with Dirac materials
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗森多夫赫尔姆霍兹中心）；Universität Würzburg（维尔茨堡大学）；Technische Universität Dresden（德累斯顿工业大学）；Technische Universität Dortmund（多特蒙德工业大学）
We demonstrate that the effective third-order nonlinear susceptibility of a graphene sheet can be enhanced by more than two orders of magnitude by patterning it into a graphene metasurface. In addition, in order to gain deeper physical insights into this phenomenon, we introduce a novel homogenization method, which is subsequently used to characterize quantitatively this nonlinearity enhancement effect by calculating the effective linear and nonlinear susceptibility of graphene metasurfaces. The accuracy of the proposed homogenization method is demonstrated by comparing its predictions with th…
The nonlinear interaction between Near-Infrared (NIR) and Terahertz pulses is principally investigated as a means for the detection of radiation in the hardly accessible THz spectral region. Most studies have targeted second-order nonlinear processes, given their higher efficiencies, and only a limited number have addressed third-order nonlinear interactions, mainly investigating four-wave mixing in air for broadband THz detection. We have studied the nonlinear interaction between THz and NIR pulses in solid-state media (specifically diamond), and we show how the former can be frequency-shifte…
Electrical-control of third-order nonlinearity via Fano interference
Institute of Nuclear Sciences, Hacettepe University（哈契特佩大学核科学研究所）；Department of Nanotechnology and Nanomedicine, Faculty of Science, Hacettepe University（哈契特佩大学理学院纳米技术与纳米医学系）；Department of Physics Engineering, Faculty of Engineering, Hacettepe University（哈契特佩大学工程学院物理工程系）；Department of Physics, Faculty of Arts and Science, Middle East Technical University（中东技术大学文理学院物理学系）；Department of Chemical Engineering, Faculty of Engineering, Hacettepe University（哈契特佩大学工程学院化学工程系）；TUPRAS（土耳其石油炼油公司）；Department of Physics, Faculty of Science, Akdeniz University（安塔利亚大学理学院物理学系）；Department of Physics, Recep Tayyip Erdogan University（雷杰普·塔伊普·埃尔多安大学物理学系）
A non-perturbative model for graphene optical nonlinearity is developed for the study of ultrafast pulse propagation along a monolayer, as in the case of graphene-comprising nanophotonic integrated waveguides. This graphene `hot electron' model (GHEM) builds upon earlier work, based on the Fermi-Dirac framework for 2D semiconductors, which was aimed mainly at steady-state absorptive response of a monolayer under free-space laser-beam illumination. Our extension adapts the GHEM to in-plane light-matter interaction along graphene monolayers under intense ps-pulse excitation that leads to the car…
We present analytic expressions for the electronic contributions to the linear conductivity $σ^{(1)}_{3d}(ω)$ and the third order optical conductivity $σ^{(3)}_{3d}(ω_1,ω_2,ω_3)$ of three dimensional massless Dirac fermions, the quasi-particles relevant for the low energy excitation of topological Dirac semimetals and Weyl semimetals. Although there is no gap for massless Dirac fermions, a finite chemical potential $μ$ can lead to an effective gap parameter, which plays an important role in the qualitative features of interband optical transitions. For gapless linear dispersion in three dimens…
In this paper, we demonstrate NiCo$_2$O$_4$ (NCO) as an efficient new nonlinear optical material with straightforward potential applications in optical limiting devices. We obtain nonlinear absorption coefficient ($β$) and nonlinear refractive index ($n_2$) in parallel by performing Z-scan technique, in both open and closed aperture configurations, respectively. To understand the mechanism responsible for third order optical nonlinearity in NCO, we excited the sample with contrasting laser pulse durations, 7 ns and 120 fs, at two different off-resonant wavelengths. For ns excitation, nonlinear…
We investigate the nonlinear optical properties of BiOBr nanoflakes, a novel two-dimensional (2D) layered material from the Bismuth oxyhalide family. We measure the nonlinear absorption and Kerr nonlinearity of BiOBr nanoflakes at both 800 nm and 1550 nm via the Z scan technique. We observe a large nonlinear absorption coefficient beta = 10^-7 m/W as well as a large Kerr coefficient n2 = 10^-14 m^2/W. We also observe strong dispersion in n2, with it reversing sign from negative to positive as the wavelength varies from 800 nm to 1550 nm. In addition, we characterize the thickness-dependence of…
As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe2) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe2 films is reported. We conduct both open aperture (OA) and closed-aperture (CA) Z scan measurements with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe2 film of \b{et…
