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 magnitude.
Optical injection locking is implemented to faithfully transfer the phase noise of a dissipative Kerr microresonator soliton comb in addition to the amplification of the Kerr comb. Unlike Er-doped fiber and semiconductor optical amplifiers, the optical injection locking amplifies the comb mode without degrading the optical signal-to-noise ratio. In addition, we show that the residual phase noise of the optical injection locking is sufficiently small to transfer the relative phase noise of comb modes (equivalent to the repetition frequency) of low phase noise Kerr combs, concluding that the opt…
We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength …
Femtosecond laser pulses interacting with LiNbO3 has been widely applied in intense terahertz generation, excitation and imaging of phonon polaritons and modulating light. It is of great importance to study the nonlinearities induced by femtosecond laser pulses in LiNbO3. Here, we demonstrate that both Kerr nonlinearity and Kerr-like nonlinearity induced by terahertz wave occur under the interaction between laser pulses and LiNbO3 using optical pump-probe techniques. We show that the contribution of Kerr-like nonlinearity to pump-probe spectra varies with the interaction length because of the …
The origin of the Kerr type nonlinearity of the medium as a result of the interaction between photons via the Dirac delta-potential is presented in the formalism adopted from the photon wave function approach. In the view of the result the optical soliton may be treated as a bound state (cluster) of many photons.
The idea of asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity is presented. This idea is based on the symmetry breaking due to the self-trapping of intensive pump pulse inside the structure. As a result, the asymmetric transmission of the secondary (probe) pulses through the perturbed photonic crystal can be observed. The cases of short and long (quasi-continuous) probe pulses are considered.
THz oscillators generated via frequency-multiplication of microwaves are facing difficulty in achieving low phase noise. Photonics-based techniques, in which optical two tones are translated to a THz wave through opto-electronic conversion, are promising if the relative phase noise between the two tones is well suppressed. Here, a THz ($\approx$ 560 GHz) wave with a low phase noise is provided by a frequency-stabilized, dissipative Kerr microresonator soliton comb. The repetition frequency of the comb is stabilized to a long fiber in a two-wavelength delayed self-heterodyne interferometer, sig…
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 investigate the self-Kerr nonlinearity of a four-level N-type atomic system in 87Rb and observe its reversible property with the unidirectional increase of the switching field. For the laser arrangement that the probe field interacts with the middle two states, the slope and the sign of the self-Kerr nonlinearity around the atomic resonance can not only be changed from negative to positive, but also can be changed to negative again with the unidirectional increasing of the switching field. Numerical simulation agrees very well with the experimental results and dressed state analysis is pres…
We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = -10^(-13) m^2/W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the…
Laser frequency combs are coherent light sources that simultaneously provide pristine frequency spacings for precision metrology and the fundamental basis for ultrafast and attosecond sciences. Recently, nonlinear parametric conversion in high-Q microresonators has been suggested as an alternative platform for optical frequency combs, though almost all in 100 GHz frequencies or more. Here we report a low-phase-noise on-chip Kerr frequency comb with mode spacing compatible with high-speed silicon optoelectronics. The waveguide cross-section of the silicon nitride spiral resonator is designed to…
Air turns into a nonlinear medium for electromagnetic waves under exceptionally strong fields. However up to present, its minuscule nonlinear response has limited the exploration to the optical frequency regime owing to the availability of intense near-infrared lasers. Here, we report on the observation of large-amplitude nonlinearity in air induced by an extremely intense light bullet at Terahertz frequencies (0.1-10 THz) provoking strong air birefringence. The observed nonlinearity manifests itself as third order susceptibility. The presented nonlinear observations break the barrier for the …
Self-mode-locking has become an emerging path to the generation of ultrashort pulses with vertical-external-cavity surface-emitting lasers. In our work, a strong Kerr nonlinearity that is so far assumed to give rise to mode-locked operation is evidenced and a strong nonlinearity enhancement by the microcavity is revealed. We present wavelength-dependent measurements of the nonlinear absorption and nonlinear-refractive-index change in a gain chip using the Z-scan technique. We report negative nonlinear refraction up to 1.5E-11 cm2/W in magnitude in the (InGa)As/Ga(AsP) material system close to …
We demonstrated a large enhancement of Kerr electro-optic nonlinearity through cascaded Pockels effects in a domain inversion ferroelectric crystal. We designed a structure that can implement the cascaded Pockels effects and second-harmonic generation simultaneously. The energy coupling between the fundamental lights of different polarizations led to a large nonlinear phase shift, and thus an effective electro-optic nonlinear refractive index. The effective nonlinearity can be either positive or negative, causing the second-harmonic spectra to move towards the coupling center, which in turn, o…
We construct families of optical semi-discrete composite solitons (SDCSs), with one or two independent propagation constants, supported by a planar slab waveguide, XPM-coupled to a periodic array of stripes. Both structures feature the cubic nonlinearity and support intrinsic modes with mutually orthogonal polarizations. We report three species of SDCSs, odd, even, and twisted ones, the first type being stable. Transverse motion of phase-tilted solitons, with potential applications to beam steering, is considered too.
High index dielectric nanoantennas excited at Mie-type resonances have exhibited enormous enhancement of optical nonlinearity. Such nanostructures have been actively studied by researchers in the last years. The present work provides the first numerical analysis study of the optical Kerr effect of nanocomposites consisting of high refractive index (GaP) spheres at the wavelength of 532~nm. This is done by means of three-dimensional finite-difference time-domain (FDTD) simulations. The effective nonlinear refractive index of $0.8$~$μ$m thick nanocomposites and metasurfaces is evaluated. It is s…
The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, t…
In the recent publication [Phys. Rev. B 87, 235319 (2013)], the conventional photon blockade(CPB) was studied for the low frequency mode in a second-order nonlinear system. In this paper, we will study the CPB for the high frequency mode in a second-order nonlinear system with the Kerr nonlinearity filling in the low-frequency cavity. By solving the master equation and calculating the zero-delay-time second order correlation function $g^{(2)}(0)$, strong photon antibunching can be obtained in the high frequency cavity. The optimal condition for strong antibunching is found by analyticcal culat…
Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications i…
A theoretical study of wave propagation in 1D metamaterial is presented. A system of nonlinear evolution equation for electromagnetic waves with both polarizations account is derived by means of projection operators method for general nonlinearity and dispersion. The system describes interaction of opposite directed waves with a given polarization. The particular case of Kerr nonlinearity and Drude dispersion is considered. In such approximation it results in the correspondent systems of nonlinear equations that generalizes the Schäfer-Wayne one. Particular solutions in case of slow-varying en…
We demonstrate optically stable amorphous silicon nanowires with both high nonlinear figure of merit (FOM) of ~5 and high nonlinearity Re(γ) = 1200W-1m-1. We observe no degradation in these parameters over the entire course of our experiments including systematic study under operation at 2 W coupled peak power (i.e. ~2GW/cm2) over timescales of at least an hour.
We review measurements in the literature regarding Kerr nonlinearity of lithium niobate. Of particular interest is to separate the value of the electronic Kerr nonlinearity and the strength of the delayed Raman nonlinearity. The spectral shape of the Raman response in LN is discussed and we restrict ourselves to the case where the pump is polarized along the optical axis. This configuration is important for so-called type 0 noncritical interaction, which is used in QPM devices and in recent supercontinuum generation and few-cycle soliton compression experiments.
We develop one numerical method to compute the optical vortex soliton with self-defocusing Kerr-type nonlocal nonlinearity. With the numerical simulation method, the propagation and interaction properties of such optical vortex solitons are investigated.
Kerr nonlinearity in nanophotonic cavities provides a versatile platform to explore fundamental physical sciences and develop novel photonic technologies. This is driven by the precise dispersion control and significant field enhancement with nanoscale structures. Beyond dispersion and pump engineering, the direct control of Kerr nonlinearity can release the ultimate performance and functionality of photonic systems. Here, we report the in situ control of integrated Kerr nonlinearity through its interplay with the cascaded Pockels nonlinear process. Kerr nonlinearity is tuned over 10~dB dynami…
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…
The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-Q microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counter-intuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy sc…
Spontaneous symmetry breaking in nonlinear systems provides a unified method to understand vastly different phenomena, ranging from Higgs mechanism [1] and superconductivity [2] to ecological stability [3] and genome generation [4]. Spontaneous symmetry breaking is typically considered as the intrinsic property of nonlinear systems with fixed occurrence condition and property, as the form and magnitude of nonlinear interactions cannot be modified [5]. Here, we report the development of reconfigurable Kerr optical nonlinearity to control spontaneous symmetry breaking. This is achieved through t…
We systematically investigate the optical analogs of quantum relativistic Jackiw-Rebbi states in binary waveguide arrays in the presence of Kerr nonlinearity with both self-focusing and self-defocusing cases. The localized profiles of these nonlinear Jackiw-Rebbi states can be calculated exactly by using the shooting method. We show that these nonlinear Jackiw-Rebbi states have a very interesting feature which is totally different from all other well-known nonlinear localized structures, including optical solitons. Namely, the profiles of nonlinear JR states with higher peak amplitudes can tot…
Enhancement of optical Kerr nonlinearity for self-action by electro-magnetically induced transparency in a four-level atomic system including dephasing between the ground states is studied in detail by solving the density matrix equations for the atomic levels. We discern three major contributions, from energy shifts of the ground states induced by the probe light, to the third-order susceptibility in the four-level system. In this four-level system with the frequency-degenerate probes, quantum interference amongst the three contributions can, not only enhance the third-order susceptibility mo…
The propagation of pulses through waveguides with subwavelength features, inhomogeneous transverse structure, and high index contrast cannot be described accurately using existing models in the presence of nonlinear effects. Here we report the development of a generalised full vectorial model of nonlinear pulse propagation and demonstrate that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient $γ,$ $A_{eff}$, and mode orthognality. While new definition…
We study controllable single photon scattering in a one-dimensional waveguide coupling with an additional cavity by second order nonlinear materials in a non-cascading configuration, where the additional cavity is embedded with two-level atom and filled with Kerr-nonlinear materials. Considering the second order nonlinear coupling, we analyze the transmission properties of the three different coupling forms as follows: (i) The two-level atom is excited without the Kerr-nonlinearity. (ii)The Kerr-nonlinearity is excited without the two-level atom. (iii) Both of the two-level atom and Kerr-nonli…
In this study we systematically measure the near-infrared spectral dependence, the sub-picosecond temporal evolution and pulse-width dependence of the effective Kerr coefficient ($n_{2,eff}$) of graphene in hundreds of femtosecond regime. The spectral dependence measured using the Z-scan technique is corroborated by quantum theory to extract a $n_{2,eff} \propto λ^2$ dependence. The temporal evolution extracted using the time-resolved Z-scan measurement shows the nonlinear response peaking at zero delay time and relaxing on a time scale of carrier relaxation. Since the Kerr-type response origi…
We develop one numerical method to compute black and gray solitons with Kerr-type nonlocal nonlinearity. As two examples of nonlocal cases, the gray soliton with exponentially decaying nonlocal response or with Gaussian nonlocal response are discussed. For such two nonlocal cases, the analytical form of the tails of nonlocal gray soliton is presented and the analytical relationship for the maximal transverse velocity of nonlocal gray soliton to the characteristic nonlocal length is obtained.
In this work, we theoretically study the quantum correlations present in an optomechanical system by invoking an additional cross-Kerr coupling between the optical and mechanical mode. Under experimentally achievable conditions, we first show that a significant enhancement of the steady-state entanglement could be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature. Then, we employ Gaussian quantum discord as a witness of the genuine quantumness of the correlation present in the system and discuss its de…
The nonlinear optical properties of the high index nanoparticles are boosted at the anapole state. Researchers intensively study this phenomenon as promising for various applications. In this work, the nonlinear optical Kerr effect of disordered and square lattice metasurfaces of GaP nanodisks is investigated as a function of the disk size in the vicinity of the anapole state at the wavelength of 532 nm. When the sizes of the nanodisks are close to the anapole state, the effective second order refractive index of the metasurface increases exponentially. On approaching the anapole state, the si…
Octave-spanning, self-referenced frequency combs are applied in diverse fields ranging from precision metrology to astrophysical spectrometer calibration. In the past decade, Kerr frequency comb generators have emerged as alternative scheme offering chip-scale integration, high repetition rate and bandwidths that are only limited by group velocity dispersion. The recent observation of Kerr frequency combs operating in the dissipative Kerr soliton (DKS) regime, along with dispersive wave formation, has provided the means for fully coherent, broadband Kerr frequency comb generation with engineer…
We consider interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by the cavity linewidth and nonlinearity, dispersion, and repetition rate, and provide a detailed derivation of the corresponding hierarchy of the coupled mode and of the Lugiato-Lefever-like equations. An effect of the washout of the repetition rate frequencies from the equations governing dynamics of the counter-propagating waves is elaborated in details.
Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.
We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in Photonic Crystal Waveguides (PCWs). In particular, we derive the equations for two modes propagating in PCWs and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analy…
We investigate numerically the effect of Kerr nonlinearity on the transmission spectrum of a one dimensional $δ$-function photonic crystal. It is found that the photonic band gap (PBG) width either increases or decreases depending on both sign and strength of Kerr nonlinearity. We found that any amount of self-focusing nonlinearity $(α>0)$ leads to an increase of the PBG width leading to light localization. However, for defocusing nonlinearity, we found a range of non-linearity strengths for which the photonic band gap width decreases when the nonlinearity strength increases and a critical non…
The main challenge in the recent demonstration of conventional magnon blockade is to increase the nonlinearity of the system especially in comparison with the dissipation channels. One can consider the Kerr nonlinearity through which magnon blockade in a cavity magnonic system is possible provided that the Kerr nonlinearity is much stronger than the cavity and magnonic mode dissipation rates. In the present contribution, we consider a PT-symmetric cavity magnonic system and study the effect of PT-symmetric phase on the magnon statistics and hence magnon blockade. We show that the PT-symmetric …
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…
