Nonlinear Optical Interactions Research Articles

Nonlinear optical interactions in focused beams and nanosized structures

Thin-film materials from μm thickness down to single-atomic-layered 2D materials play a central role in many novel electronic and optical applications. Coherent, nonlinear optical (NLO) μ-spectroscopy offers insight into the local thickness, stacking order, symmetry, or electronic and vibrational properties. Thin films and 2D materials are usually supported on multi-layered substrates leading to (multi-)reflections, interference, or phase jumps at interfaces during μ-spectroscopy, which all can make the interpretation of experiments particularly challenging. The disentanglement of the influence parameters can be achieved via rigorous theoretical analysis. In this work, we compare two self-developed modeling approaches, a semi-analytical and a fully vectorial model, to experiments carried out in thin-film geometry for two archetypal NLO processes, second-harmonic and third-harmonic generation. In particular, we demonstrate that thin-film interference and phase matching do heavily influence the signal strength. Furthermore, we work out key differences between three and four photon processes, such as the role of the Gouy-phase shift and the focal position. Last, we can show that a relatively simple semi-analytical model, despite its limitations, is able to accurately describe experiments at a significantly lower computational cost as compared to a full vectorial modeling. This study lays the groundwork for performing quantitative NLO μ-spectroscopy on thin films and 2D materials, as it identifies and quantifies the impact of the corresponding sample and setup parameters on the NLO signal, in order to distinguish them from genuine material properties.

Electro-optically tunable cascaded second-order nonlinearity induced (2 + 1)D spatial optical soliton using bulk β-barium borate crystal: a theoretical approach

This paper deals with the development of an effective theoretical approach to generate spatial optical soliton in exceptionally beneficial bulk beta-barium-borate crystal by utilizing cascaded second-order nonlinearity through electro-optic tuning. The proposed methodology paves the way for novel nonlinear optical interactions conceptualized in bulk material depending upon an effective nonlinear refractive index for a broad range of crystal lengths. The development of ( 2 + 1 ) D spatial bright soliton has been analytically demonstrated at 800 nm wavelength of the incident continuous-wave optical radiation, and the implication of tunable electro-optic effect to the crystal’s nonlinear response is also presented here. Involvement of the generalized nonlinear Schrödinger equation has been utilized to develop the necessary and sufficient criteria for self-trapping optical beams considering both linear and nonlinear absorption losses. In conformity with the findings of the simulation, the beam diameter of a generated spatial soliton within this anisotropic crystal is near 56 µm while maintaining precise peak intensity ∼ 0.8 G W / c m 2 .

Short-period domain patterning by ion beam irradiation in lithium niobate waveguides produced by soft proton exchange

The lithium-niobate-based waveguides have emerged as one of the key platforms for enabling integrated optical technologies. The most common method for creating waveguides in lithium niobate is soft proton exchange (SPE) method. The range of the waveguides applications can be expanded further by creation of near-surface periodical structure of stripe ferroelectric domains within a waveguide (periodical poling) to realize various types of nonlinear optical interactions for creation of frequency conversion devices. However, the joint use of these two procedures (SPE and periodical poling) remains a challenging task. In this paper, we propose a focused ion beam (i-beam) periodical poling technique realized after SPE process for creation of an integrated optical frequency conversion device. The choice of i-beam poling parameters is based on the study of the features of domain structure evolution in lithium niobate after SPE process. We have found that SPE process leads to formation of shallow structure of isolated nanodomains. The revealed isotropic domain growth was caused by the sideways domain wall motion by step generation as a result of merging with these nanodomains. This type of domain kinetics is preferable for periodical poling as it decreases the probability of fast merging of stripe domains due to formation of fast domain walls. Eventually, we have created the 1-mm-long 2-μm-period domain structure in a channel waveguide. The obtained second harmonic generation efficiency for pulse pumping at 756 nm was up to 6·107% W−1 cm−2 for average power and 300 % W−1 cm−2 for peak power indicating the high quality of periodical poling.

Rainbow Cherenkov Second-Harmonic Radiation

Nonlinear Cherenkov radiation, an intriguing noncollinear optical parametric process with versatile longitudinal phase matching, is commonly realized in engineered nonlinear photonic structures. Here, we report on the observation of ultrabroadband rainbow Cherenkov second-harmonic generation (UBR CSHG) in a single periodically poled lithium niobate (PPLN) nonlinear crystal driven by a near-infrared high-peak-power ultrashort femtosecond pump laser. Multiple colored nonlinear radiation bands along the direction of Cherenkov conical angles are simultaneously exhibited, leading to a beautifully colorful rainbow picture never reported before. We systematically analyze the multicolor spectral characteristics of the UBR CSHG in the whole conical direction and explicitly clarify their phase-matching conditions. We show that this UBR CSHG interaction is subject to remarkable spectral broadening owing to both the third-order nonlinearity effect induced by the high-peak-power ultrashort pump laser and the reciprocal lattice vector of the PPLN crystal, which eventually enables the generation of three bright dominating colors---red, orange-yellow, and green bands---and their automatic dispersion in space. The experimental results suggest rich physics of nonlinear optical interactions and indicate the possibility to engineer broadband nonlinear frequency conversion for applications in compact colored laser sources and others.

Domain dynamics in coercive-field engineered sub-µm periodically poled Rb-doped KTiOPO4

Nonlinear optical interactions involving counter-propagating photons are of great interest for both classical and quantum optical applications. However, their use is sparsely spread due to the fact that they require quasi-phase-matched devices with sub-µm periods. A recent breakthrough has been the fabrication of bulk sub-µm domain gratings in Rb-doped KTiOPO4 by creating a grating of low- and high- coercive field regions in the crystal via periodic ion exchange, so-called coercive-field engineering. Here, we investigate the physical mechanisms behind this method and study the interplay between the ion-exchanged grating properties and the ferroelectric domain dynamics. Furthermore, we investigate the scalability of the method by studying the domain morphology of sub-µm periodically poled crystals with periods ranging from 755 to 433 nm and correlating it to that of the ion-exchanged regions. We show that the formation of sub-µm domain gratings is governed by the depth, shape, and critical ion-concentration of the ion-exchanged volume and that it is independent of the poling period. These findings are crucial for further scaling the coercive field engineering technique to even shorter poling periods and larger aperture periodically poled crystals.

Demonstrating quantum properties of triple photons generated by chi ^3 processes

Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states.Graphic abstract

Complete characterization of ultrafast optical fields by phase-preserving nonlinear autocorrelation

Nonlinear autocorrelation was one of the earliest and simplest tools for obtaining partial temporal information about an ultrashort optical pulse by gating it with itself. However, since the spectral phase is lost in a conventional autocorrelation measurement, it is insufficient for a full characterization of an ultrafast electric field, requiring additional spectral information for phase retrieval. Here, we show that introducing an intensity asymmetry into a conventional nonlinear interferometric autocorrelation preserves some spectral phase information within the autocorrelation signal, which enables the full reconstruction of the original electric field, including the direction of time, using only a spectrally integrating detector. We call this technique Phase-Enabled Nonlinear Gating with Unbalanced Intensity (PENGUIN). It can be applied to almost any existing nonlinear interferometric autocorrelator, making it capable of complete optical field characterization and thus providing an inexpensive and less complex alternative to methods relying on spectral measurements, such as frequency-resolved optical gating (FROG) or spectral phase interferometry for direct electric-field reconstruction (SPIDER). More importantly, PENGUIN allows the precise characterization of ultrafast fields in non-radiative (e.g., plasmonic) nonlinear optical interactions where spectral information is inaccessible. We demonstrate this novel technique through simulations and experimentally by measuring the electric field of ~6-fs laser pulses from a Ti:sapphire oscillator. The results are validated by comparison with the well-established FROG method.

Extremely large nondegenerate nonlinear index and phase shift in epsilon-near-zero materials [Invited

Epsilon-near-zero (ENZ) materials have emerged as viable platforms for strong nonlinear optical (NLO) interactions. The NLO phase shift in materials exhibiting an ENZ condition is extremely large; however, direct experimental measurements of the magnitude and time dynamics of this phenomenon, particularly nondegenerate NLO phase shifts, have so far been lacking. Here, we directly measure the NLO phase shift of an Indium-Tin-Oxide (ITO) thin film using three different techniques. By characterizing the excitation-induced, time-resolved beam deflection (BD) of a probe beam, we measure the nondegenerate NLO effects, allowing a separate determination of the effects of excitation and probe wavelengths on the NLO phase shift as they are varied across the ENZ region. These experiments reveal that having the probe pulse centered at ENZ greatly contributes to this enhancement; however, the NLO phase shift is less sensitive to the excitation wavelength, which only slightly enhances the nonlinearity for obliquely incident TM-polarized light. We also find that the spectral shift of the probe pulse induced by the excitation follows both the magnitude and time dynamics of the NLO phase shift measured via the BD experiments. We observe large, ultrafast cross-phase modulation in agreement with a redistribution of carriers in the conduction band. Finally, using the Z-scan method, we measure the degenerate nonlinear refraction at ENZ near normal incidence. The results of all three measurements agree, revealing a gigantic sub-picosecond NLO phase shift in ITO. At its largest, we consistently measure an effective induced index change greater than the linear index.

Spectroscopic characterization of rare events in colloidal particle stochastic thermodynamics.

Given the remarkable developments in synthetic control over chemical and physical properties of colloidal particles, it is interesting to see how stochastic thermodynamics studies may be performed with new, surrogate, or hybrid model systems. In the present work, we apply stochastic dynamics and nonlinear optical light-matter interaction simulations to study nonequilibrium trajectories of individual Yb (III):Er (III) colloidal particles driven by two-dimensional dynamic optical traps. In addition, we characterize the role of fluctuations at the single-particle level by analyzing position trajectories and time-dependent upconversion emission intensities. By integrating these two complementary perspectives, we show how the methods developed here can be used to characterize rare events.

Observation of a triangular-lattice pattern in nonlinear wave mixing with optical vortices

Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.

Angular Quasi-Phase-Matching in Periodically Poled Uniaxial and Biaxial Crystals

This article deals with a general description of Angular Quasi-Phase-Matching (AQPM) in uniaxial and biaxial crystals for second-order nonlinear optical interactions. Such an exhaustive and generalized angular-dependent approach of AQPM reveals new directions of propagation with efficient parametric frequency conversion. These AQPM solutions are studied by depicting the corresponding topologies and associated symmetries. The theoretical overview is fully validated and illustrated by measurements. We clearly demonstrate the benefits of such a generalized approach, both in the case of two emblematic periodically poled (PP) crystals: 5%MgO-doped PPLiNbO3 (5%MgO:PPLN) and Rb-doped PPKTiOPO4 (PPRKTP). These developments should stimulate new potential applications in nonlinear frequency conversion.

Carrier-envelope phase effect on light bullet dynamics

A light bullet (LB) is a wave packet of a few optical cycles that is extremely compressed in space and time, which is formed in the bulk transparent dielectric during femtosecond filamentation under anomalous group velocity dispersion. We demonstrate for the first time that the carrier-envelope phase shift during propagation of a near single-cycle LB causes synchronous oscillations of the spatial, temporal and energy parameters of its core with the period decreasing with increasing carrier wavelength. When analyzing the structure of color centers and induced plasma channels in fluorides, it was experimentally found that LB parameter oscillations lead to a periodic change in the nonlinear optical interaction with the dielectric.

Enhanced Chemical Sensing with Multiorder Coherent Raman Scattering Spectroscopic Dephasing.

Molecular vibrational spectroscopy is widely used in various sensing and imaging applications, providing intrinsic information at the molecular level. Nonlinear optical interactions using ultrashort laser pulses facilitate the selective coherent excitation of molecular vibrational modes by focusing energy into specific molecular bonds, boosting the signal level for multiple orders of magnitude. The dephasing of such coherence, which is susceptible to the local molecular environment, however, is often neglected. The unique capability of vibrational dephasing dynamics to serve as a unique probe for complex molecular interactions and the effect of local nano- and microenvironments are beyond the reach of conventional, intensity-based spectroscopy. Here, we developed a novel multiorder coherent Raman spectroscopy platform with a special focus on the temporal evolution of molecular vibrational dephasing, termed as time-resolved coherent Raman scattering (T-CRS) spectroscopy. By utilizing a high dynamic range detection, molecular vibrational dynamics and the environmental effects are demonstrated with multidimensional spectroscopic sensing, which promises a new range of applications in biology, materials, and chemical sciences.

Coherent contributions to population dynamics in a semiconductor microcavity

Multidimensional coherent spectroscopy (MDCS) is used to separate coherent and incoherent nonlinear contributions to the population-time dynamics in a GaAs-based semiconductor microcavity encapsulating a single InGaAs quantum well. In a three-pulse four-wave-mixing scheme, the second delay time is the population time that in MDCS probes excited-state coherences and population dynamics. Nonlinear optical interactions can mix these contributions, which are isolated here for the lower- and upper-exciton polariton through the self- and mutual-interaction features. Results show fast decays and oscillations arising from the coherent response, including a broad stripe along the absorption energy axis, and longer time mutual-interaction features that do not obey a simple population decay model. These results are qualitatively replicated by Bloch equation simulations for the $1s$ exciton strongly coupled to the intracavity field. The simulations allow for separation of coherent and incoherent Pauli-blocking and Coulomb interaction terms within the ${\ensuremath{\chi}}^{(3)}$-limit, and a direct comparison of each feature in one-quantum rephasing and zero-quantum spectra.

Nonlinear Schrödinger Kernel for Hardware Acceleration of Machine Learning

Alternative machine learning approaches that have extremely low latency and can work with only a small training dataset are needed for applications where the insatiable demands of deep learning methods for computing power and large training data cannot be met. Here we report a new optical accelerator for AI that exploits femtosecond pulses for both data acquisition and computing enabling classification at short time scales for fast optical imaging, sensing, and metrology without increasing data dimensions. Modulation of data onto the spectrum of femtosecond optical pulses followed by projection into a new space using nonlinear optics reduces the latency in the nonlinear classification of certain data by orders of magnitude. This Femtocomputing approach is validated by the classification of various datasets, including brain intracranial pressure, cancer cell imaging, spoken digit recognition, and the classic exclusive OR benchmark for nonlinear operation. The concept is demonstrated by seeding the nonlinear effect that is responsible for many fascinating natural phenomena, such as optical rogue waves. Stimulation of nonlinear optical interactions with spectrally modulated data transforms the data such that a computationally-light linear algorithm can learn a nonlinear decision boundary that separates the data into the correct classes. Since the optical kernel is not trained, its performance is inevitably data-dependent. Quantitative comparison with a popular numerical kernel offers insights into how this physical technique accelerates inference. Single-shot operation is demonstrated using time stretch data acquisition.

Study on weakening optical soliton interaction in nonlinear optics

Study on weakening optical soliton interaction in nonlinear optics

Phase-matching condition in rotatory nonlinear optics

Polarization rotation of light beams, such as optical activity and Faraday rotation, is a natural effect that generates the rotation of the polarized direction of light and some undiscovered characteristics in nonlinear optics. In our previous study, we theoretically investigated the second-harmonic generation process in rotatory nonlinear optics and found an unprecedented phase-matching condition. Here, the optical phase-matching condition in the second-harmonic generation with rotatory polarization is theoretically analyzed and associated with the angular rotation-induced phases of mixing waves, which goes beyond the previous theoretical analysis. Moreover, the Pancharatnam-Berry topological phase was found to be periodically generated and could be employed to compensate for the mismatched phase during nonlinear optical interaction. Possible experimental schemes were proposed and discussed. This work provides not only a universal and flexible (quasi-) phase-matching condition for the rotatory nonlinear optics existing in most nonlinear optical media but may also inspire the development of modern photonics.

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell’s law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light–matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

Stability of multi-hump localized solutions in the Holstein model for linear acoustic and soft nonlinear optical interactions

We consider the energy/electron transport problem along a lattice holding linear acoustic and soft cubic non-dispersive interactions in the long wave limit for Holstein’s approach. It is found that the model equations, consisting of the coupling between the linear Schrödinger and a nonlinear Klein–Gordon equations, support one- and two-hump solutions of the first and second kind. We derive these multi-humped solutions by using a compatible reduction of the equations of motion and by means of an adaptation of the direct method, both in the traveling frame. Remarkably, the solution profiles for the mechanical deformation recall the one and two soliton solutions of the Korteweg–de Vries equation. Then, based on the Fourier collocation method, we perform a numerical linear stability analysis of these solutions at the steady state to find the parameters regime for stability. Additionally, we are able to implement the Vakhitov–Kolokolov criterion to get the bifurcation value for the one-hump solution both of the first and second kind. We show that the two-hump solutions are linearly unstable.

Second Harmonic Generation in Lithiated Silicon Nanowires: Derivations and Computational Methods

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will be determined whether the medium in which SHG is conveyed is non-centrosymmetric or whether the medium is inversion symmetric where SHG as a part of the second-order nonlinear optical phenomenon does not exist. It will be demonstrated that the main interaction that determines SHG is multiphoton absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as the background that generates coherent states for electrons and photons that transverse the length of the silicon nanowire. The matrix elements of the Hamiltonian which represents the energy of the system will be used to calculate the probability density of second-order nonlinear optical interactions which includes collectively SHG, sum-frequency generation (SFG) and difference-frequency generation (DFG). As a result, it will be seen that at varies concentrations of lithium ions (Li+) within the crystallized silicon (c-Si) matrix the second-order nonlinear optical process has probabilities substantial enough to create second harmonic generation that could possibly be used for such applications as second harmonic imaging microscopy.