Higher-order Nonlinear Processes Research Articles

Dissipative phase transitions in n-photon driven quantum nonlinear resonators

We investigate and characterize the emergence of finite-component dissipative phase transitions (DPTs) in nonlinear photon resonators subject to n-photon driving and dissipation. Exploiting a semiclassical approach, we derive general results on the occurrence of second-order DPTs in this class of systems. We show that for all odd n, no second-order DPT can occur while, for even n, the competition between higher-order nonlinearities determines the nature of the criticality and allows for second-order DPTs to emerge only for n=2 and n=4. As pivotal examples, we study the full quantum dynamics of three- and four-photon driven-dissipative Kerr resonators, confirming the prediction of the semiclassical analysis on the nature of the transitions. The stability of the vacuum and the typical timescales needed to access the different phases are also discussed. We also show a first-order DPT where multiple solutions emerge around zero, low, and high-photon numbers. Our results highlight the crucial role played by strong and weak symmetries in triggering critical behaviors, providing a Liouvillian framework to study the effects of high-order nonlinear processes in driven-dissipative systems, that can be applied to problems in quantum sensing and information processing.

Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics.

Physical properties are commonly represented by tensors, such as optical susceptibilities. The conventional approach of deriving non-vanishing tensor elements of symmetric systems relies on the intuitive consideration of positive/negative signflipping after symmetry operations, which could be tedious and prone to miscalculation. Here, we present a matrix-based approach that gives a physical picture centered on Neumann's principle. The principle states that symmetries in geometric systems are adopted by their physical properties. We mathematically apply the principle to the tensor expressions and show a procedure with clear physical intuition to derive non-vanishing tensor elements based on eigensystems. The validity of the approach is demonstrated by examples of commonly known second and third-order nonlinear susceptibilities of chiral/achiral surfaces, together with complicated scenarios involving symmetries such as D6 and Oh symmetries. We then further applied this method to higher-rank tensors that are useful for 2D and high-order spectroscopy. We also extended our approach to derive nonlinear tensor elements with magnetization, which is critical for measuring spin polarization on surfaces for quantum information technologies. A Mathematica code based on this generalized approach is included that can be applied to any symmetry and higher order nonlinear processes.

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.

Chirped self-similar solitary waves in optical fibers governed with self-frequency shift and varying parameters

We demonstrate that when self-frequency shift effect is the dominant higher-order nonlinear process affecting ultrashort light pulse propagation in an inhomogeneous optical fiber media, a novel class of self-similar solitary waves that are characterized by a nonlinear chirp existed. The solitary wave profiles are of bright, dark, kink, and gray type, illustrating the potentially rich set of chirped self-similar pulses in the inhomogeneous fiber system. Compared with the cubic nonlinear Schrödinger equation with distributed coefficients, the phase of these chirped pulses exhibits a nonlinear structure which makes them more suitable for diverse physical applications. The application of obtained chirped self-similar pulses is also discussed in a periodic distributed amplification system. The results show that one may control the propagation dynamics of the presented nonlinearly chirped pulses by an appropriate choice of the dispersion and nonlinearity parameters.

Modeling and nonlinear analysis of chaotic wave processes in electrochemically active neuronal media based on matrix decomposition

A general model of the origin and evolution of chaotic wave processes in electrochemically active neuronal media based on the proposed method of matrix decomposition of operators of nonlinear systems has been developed. The mathematical models of Hodgkin – Huxley and FitzHugh – Nagumo of an electrochemically active neuronal media are considered. The necessary conditions for self-organization of chaotic self-oscillations in the FitzHugh – Nagumo model are determined. Computer modeling based on the matrix decomposition of chaotic wave processes in electrochemically active neuronal media has shown the interaction of higher-order nonlinear processes leading to stabilization (to a finite value) of the amplitude of the chaotic wave process. Mathematically, this is expressed in the synchronous “counteraction” of nonlinear processes of even and odd orders in the general vector-matrix model of an electrochemically active neuronal media being in a chaotic mode. It is noted that the state of hard self-excitation of nonlinear oscillations in an electrochemically active neuronal media leads to the appearance of a chaotic attractor in the state space. At the same time, the proposed vector-matrix model made it possible to find more general conditions for the appearance and evolution of chaotic wave processes in comparison with the initial Landau turbulence model and, as a result, to explain the occurrence of consistent nonlinear phenomena in an electrochemically active neuronal media.

Approximating higher-order nonlinear QED processes with first-order building blocks

Higher-order tree-level processes in strong laser fields, i.e., cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e., nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particle-in-cell codes. However, the locally-constant-field (LCF) approximation and these particle-in-cell codes cannot be used when the intensity is only moderately high, which is a regime that is experimentally relevant. We have shown that one can still use a sequence of first-order processes to estimate higher orders at moderate intensities provided the field is sufficiently long. An important aspect of our new ``gluing'' approach is the role of the spin and polarization of intermediate particles, which is more nontrivial compared to the LCF regime.

Higher-order coherent anti-Stokes Raman scattering microscopy realizes label-free super-resolution vibrational imaging

Coherent Raman scattering (for example, coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering) microscopy has emerged as a powerful tool for label-free biomolecular imaging in biological and biomedical systems, but its spatial resolution is diffraction limited. Here, we report a higher-order coherent anti-Stokes Raman scattering (HO-CARS) microscopy to break the diffraction limit for label-free, super-resolution vibrational imaging. The resolution enhancement of HO-CARS microscopy has been analysed and demonstrated in biological samples (for example, live HeLa and buccal cells). The HO-CARS technique provides an inherent high resonant to non-resonant background ratio compared with conventional CARS microscopy. We affirm that under a tight focusing, the HO-CARS signal originating from the higher-order nonlinear process (χ(5), χ(7)) dominates over the cascaded lower-order nonlinear process (χ(3)), yielding much richer spectroscopic information. This study illustrates that HO-CARS microscopy can be an appealing tool for label-free, super-resolution imaging in biological and biomedical systems with high image contrast. Higher-order (fifth and seventh order) coherent anti-Stokes Raman scattering microscopy is demonstrated to break the diffraction limit for label-free super-resolution vibrational imaging for live cells such as HeLa and buccal cells.

High-harmonic generation at the nanoscale boosted by bound states in the continuum

This paper combines the concept of bound states in the continuum with engineering of epsilon-near-zero substrates to boost multi-frequency and multi-step cascaded nonlinear processes at the nanoscale. High-order nonlinear processes such as four-wave mixing, third- and fifth-harmonic generation in all-dielectric subwavelength resonators are shown to be enhanced in comparison with the state-of-the-art results.

Tailored UV Emission by Nonlinear IR Excitation from ZnO Photonic Crystal Nanocavities

For many applications in photonics, e.g., free-space telecommunication, efficient UV sources are needed. However, optical excitation of such sources requires photons of even higher energies, which are difficult to integrate into photonic circuits. Here, we present photonic crystal devices based on zinc oxide (ZnO) that allow excitation using highly abundant sources in the near-infrared (NIR). These devices offer control of generating tailored photonic modes in the UV range via higher order nonlinear processes by combining the wide electronic band gap and pronounced nonlinear effects in ZnO with the adjustable properties of photonic crystal (PhC) membranes. Two different techniques for fabricating such ZnO-based PhC membranes are discussed, including the presentation of a novel bottom-up approach. Furthermore, dispersive theoretical simulations are introduced to determine the size and position of the photonic band gap, leading to an optimized cavity with only one dominant mode. This is followed by an evalu...

Nonlinear optical memory: theory and experiment

The present work explores new possibilities for the selective storage of optical information through higher-order nonlinearities in a sample of cold cesium atoms obtained from a magneto-optical trap. Particularly, we demonstrate the storage of a third-, fifth-, and seventh-order nonlinear atom–light interaction into the coherences and populations of the Zeeman structure of the hyperfine cesium 6S1/2, F=3 ground state. Two writing beams create coherence and population gratings associated with high-order nonlinear processes, which can be selectively retrieved by a reading beam after a controllable storage time. Each kind of grating can store only specific orders of the nonlinear interaction, leading to special features in each signal. Applications of this nonlinear memory to herald multiphotons are discussed.

Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers

Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS2 (1L-MoS2): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS2 is approximately three times higher than that for graphene, which was reported to have a large χ(3). We explain this by calculating the nonlinear response functions of 1L-MoS2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

Measurement of deflection on germanium and gold prisms using 1.7 MeV laser Compton scattering γ-rays

We measured the refractive index of germanium and gold prisms at 1.7 MeV to explore if there are refractive index enhancements to 6th power of atomic number due to high order nonlinear process of Delbrück scattering in quantum electrodynamics. We measured the deflection by prisms using imaging plates and laser Compton scattering γ-rays with linear and random polarization. We used crystal and polycrystalline prisms for Au. The measured upper limit of the refractive index, δ, for crystal Ge, crystal Au, or polycrystal Au prisms is 4.0×10−8, 2.9×10−7, or 2.4×10−7. We could not find any signature for high order nonlinear process. This result does not support the hypothesis suggested by Habs et al. (2012) [3].

Effects of higher-order nonlinear processes on harmonic-generation phase matching

We experimentally and theoretically reinvestigate the significant third-harmonic enhancement via plasma generation using time-resolved methods with two-color, copropagating femtosecond laser pulses. By measuring plasma densities with digital in-line holography and using carrier-resolved unidirectional pulse propagation equations to model the experiment, we show that a fifth-order nonlinearity contributes to third-harmonic generation mainly via phase matching. In particular, our study confirms that self- and cross-phase modulation including higher-order nonlinear processes can play a crucial role in harmonic-generation phase matching, which has recently been proposed by Weerawarne $et\phantom{\rule{4pt}{0ex}}al.$ [Phys. Rev. Lett. 114, 093901 (2015)] and should be potentially applicable to high-order harmonic generation.

Higher-order stimulated Raman scattering in an aqueous solution of magnesium sulfate pumped by 532 nm laser pulses

We report on the generation of higher-order stimulated Raman scattering (SRS) in a saturated aqueous solution of MgSO4, pumped by a 532 nm frequency-doubled Nd:YAG laser operating with multiple longitudinal modes. The first- (∼561.4 nm), second- (∼594 nm), and third-order (∼630 nm) Stokes components of SRS were observed, and were attributed to the symmetric vibrations of the [SO4] tetrahedral structural groups. Two possible physical mechanisms for generating higher-order SRS were analyzed. The results point to an efficient method for generating new laser wavelengths from a liquid blended media system through a higher-order nonlinear SRS process.

Supercontinuum in ionization by relativistically intense and short laser pulses: Ionization without interference and its time analysis

Ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong-field quantum electrodynamics. Our main focus is on the formation of ionization supercontinua. More specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. These supercontinua extend over hundreds of driving photon energies, thus corresponding to high-order nonlinear processes. The corresponding polar-angle distributions show asymmetries which are attributed to the radiation pressure experienced by photoelectrons. Moreover, our time analysis shows that the electrons comprising the supercontinuum can form pulses of short duration. While we present the fully numerical results, their interpretation is based on the saddle-point approximation for the ionization probability amplitude.

Two-color resonant filamentation in gases

In this paper, it is shown that two-photon resonance involving a fundamental field and one of its odd harmonic strongly influences the filamentation process, i.e., the nonlinear propagation of an ultrashort and ultraintense laser field. This particular situation happens, for instance, when a 400 nm fundamental field propagates together with its third harmonic in krypton. Using three-dimensional ab initio calculations, the optical response of krypton is evaluated and the underlying nonlinear refractive indices are extracted. It is found that the resonance also exacerbates higher-order nonlinear processes. Injecting the retrieved higher-order Kerr indices in a nonlinear propagation solver, it is found that the resonance leads to an enhanced defocusing cross-phase modulation that strongly participates to the filament stabilization. This work sheds a light on the mechanism of filamentation, in particular, in the ultraviolet range, where two-color two-photon resonances are expected to occur in many atomic gases.

Nonlinear optical memory for manipulation of orbital angular momentum of light.

We report on the demonstration of a nonlinear optical memory (NOM) for storage and on-demand manipulation of orbital angular momentum (OAM) of light via higher-order nonlinear processes in cold cesium atoms. A spatially resolved phase-matching technique is used to select each order of the nonlinear susceptibility associated, respectively, with time-delayed four-, six-, and eight-wave mixing processes. For a specific configuration of the stored OAM of the incident beams, we demonstrated that the OAM of the retrieved beam can be manipulated according to the order of the nonlinear process chosen by the operator for reading out the NOM. This demonstration indicates new pathways for applications in classical and quantum information processing where OAM of light is used to encode optical information.

Coherent phonon-induced optical modulation in semiconductors at terahertz frequencies

The coherent modulation of electronic and vibrational nonlinearities in atoms and molecular gases by intense few-cycle pulses has been used for high-harmonic generation in the soft x-ray and attosecond regime, as well as for Raman frequency combs that span multiple octaves from the terahertz to petahertz frequency regions. In principle, similar high-order nonlinear processes can be excited efficiently in solids and liquids on account of their high nonlinear polarizability densities. In this paper, we demonstrate the phononic modulation of the optical index of Si and GaAs for excitation and probing near their direct band gaps, respectively at ∼3.4 and ∼3.0 eV. The large amplitude coherent longitudinal optical (LO) polarization due to the excitation of LO phonons of Si (001) and LO phonon–plasmon coupled modes in GaAs (001) excited by 10 fs laser pulses induces effective amplitude and phase modulation of the reflected probe light. The combined action of the amplitude and phase modulation in Si and GaAs generates phonon frequency combs with more than 100 and 60 THz bandwidth, respectively.

Cascaded Phase Matching and Nonlinear Symmetry Breaking in Fiber Frequency Combs

We report theoretical, numerical, and experimental studies of cascaded phase matching in fiber frequency combs and show how this mechanism is directly connected to the dynamics of supercontinuum generation. In particular, linking cascaded four-wave mixing with direct higher-order nonlinear processes allows us to derive a simple phase matching condition that governs nonlinear symmetry breaking in the presence of higher-order dispersion. We discuss how this mechanism provides a physical interpretation of soliton-induced Cherenkov radiation and associated spectral recoil in terms of phase-matched frequency mixing pumped by bichromatic pump pairs in the soliton spectrum. Theoretical and numerical predictions are confirmed via experiments using both quasicontinuous wave and picosecond pulse excitation.

Evidence of Autler–Townes splitting in high-order nonlinear processes

We demonstrate Autler-Townes (AT) splitting of four-wave mixing in an electromagnetically induced transparency window, which results from the destructive interference between a three-photon process and a five-photon process. The primary and secondary AT splittings are achieved via induced atomic coherence in a four-level Y-type atomic system. Theoretical calculations fit well with the experimentally measured results. Such controlled multichannel splitting of nonlinear optical signals can have potential applications in optical communication and quantum information processing.