Intensity-dependent Refractive Index Research Articles

Optically tunable scattering using epsilon-near-zero-enabled nonlinear nanoantennas

Optical nanoantennas provide extraordinary capabilities in controlling light at subwavelength scale. It attracts increasing interest that how to achieve tunable nanoantennas for flexible and multifunctional miniaturized optical applications. Here, a sandwich-type nonlinear nanoantenna with a thin layer of epsilon-near-zero (ENZ) material is proposed to dynamically tune the far-field scattering via an all-optical approach. By synthetically combining the varying dependence of four fundamental Mie modes on refractive index and giant intensity-dependent refractive index change caused by nonlinear optical effect in ENZ material, the far-field scattering of the proposed nonlinear nanoantenna can be dynamically tuned from bidirectional to transverse or unidirectional scattering by readily controlling the intensity of incident light. We believe that the proposed all-optical nonlinear optical nanoantennas will motivate more promising applications of all-optical light modulation for photonic devices.

Influence of nonlinear semiconductor layer on optical properties in one-dimensional photonic crystals

In this paper, an attempt has been made to investigate a one-dimensional photonic crystal containing N-doped germanium semiconductor as a nonlinear defect layer with an intensity-dependent refractive index, silica (SiO2) and zinc selenide (ZnSe) as crystal cells. Bistability of the TE polarization of the transmission spectrum due to the nonlinear property of the defect layer is investigated by the transfer matrix method (TMM). The refractive index of the germanium nonlinear semiconductor layer is simultaneously depending on the doping density and the intensity of the irradiated light. The changes in both factors are investigated. The impact on the transmission spectrum of the bistability threshold due to the change in the thickness of the defect layer, the thickness of other layers of crystal cells, and the angle of incident light are investigated. The nonlinear effect caused by light intensity as well as doped density effect on the germanium nonlinear semiconductor medium is used simultaneously. As a result, the nonlinear effect caused by the light intensity to create bistability is more than the doping density.

Enhanced Femtosecond Nonlinearities and Multiphoton Absorptions in Discrete Bands of Porphyrins.

Optical nonlinearities of discrete absorption energy levels of one of the typical heterocyclic aromatic molecules, free-base porphyrins, have been probed over a broad spectral region (400-1600 nm) utilizing intense femtosecond pulses. A wide range of strong one- and multiphoton-induced nonlinear absorptions of both the blue-end Soret (B) band (au → b1g) and red-end orbital mixing split quasi-allowed Q-bands (Qx(0,0; 0,1), Qy(0,0; 0,1), au → eg) are critically probed and reported. During the resonant excitation within B- (400 nm) and Q-bands (600-750 nm), the nonlinear absorption has become predominant by the saturation of absorption (SA) of the one-photon absorption (1PA) process due to ground-state bleaching. At nonresonant wavelengths, it is dominated by the reverse saturation of absorption (RSA), involving various nonlinear processes of two-, three-, and four-photon (2PA, 3PA, and 4PA) absorptions, either to B- or Q-bands (1100-1600 nm). The laser intensity-dependent nonresonant (2PA, 800 nm) excitations for the prominent B-band show a distinct cross-over from SA to RSA, contributed by the excited-state absorption (ESA) utilizing a three-photon induced (3PA) process, whereas resonant (1PA, 400 nm) excitation reveals a systematic strong SA process. Both wavelength- and intensity-dependent nonlinear refractive index studies exhibit positive electronic Kerr-based self-focusing effects, with prominent contributions of nonlinear absorption and higher-order effects. The spectrally discrete, highly intense laser probing of individual energy bands and the consequent variety of nonlinearities can be broadly generalized for many free-base porphyrins and metalloporphyrins. The present studies provide a strong foundation and new insight into the broad categories of macrocycles, such as porphyrins and phthalocyanines, for myriad applications in nonlinear optics and bio/optophotonics.

Nonlinear waves in a composite optical structure containing a dielectric layer between a photorefractive crystal and a medium with an exponential index profile

Three-layered asymmetric structure with different optical properties of the layers is considered. The structure consist of a photorefractive crystal with diffusion nonlinearity and very weak dark intensity, which is separated by optically linear dielectric layer from medium with spatially distributed refractive index according with an exponential profile. The paper objective is a theoretical analysis of wave disturbances arising from the introduction of a dielectric waveguide layer between photorefractive and graded-index media. Waves of new four kinds are described theoretically by exact solutions to the wave equation with spatial inhomogeneous and intensity-dependent refractive index. The waves differ from each other in the distribution profile and the range of existence. Waves with both oscillating and non-oscillating field profiles inside the dielectric layer are obtained. It is found that the dielectric layer significantly affects the main characteristics of the field distribution in the waveguide structure in the direction transverse to the layers. It is shown controlling the values of the characteristics of the layers allows selecting the required field profile, which can be used to suppress oscillations or increase the field intensity in certain regions of a layered structure.

Dynamic Tunable Deflection of Radiation Based on Epsilon-Near-Zero Material

Epsilon-near-zero nanoantennas can be used to tune the far-field radiation pattern due to their exceptionally large intensity-dependent refractive index. In this study, we propose a hybrid optical antenna based on indium tin oxide (ITO) to enable optical tuning of the deflection of radiation, specifically a hybrid structure antenna of ITO and dielectric material, which makes the deflection angle changes 17∘ as incident intensities increase. Moreover, by employing an array of ITO or hybrid nanodisks, we can enhance the unidirectionality of the radiation pattern, resulting in a needle-like shape with an angular beam width α< 8∘ of the main lobe. The deflection angle of the radiation pattern response with the needle-like lobe paves the way for further studies and applications in beam steering and optical modulation where dynamic control of the nanoantennas is highly desirable.

Theoretical investigation on the linear and nonlinear optical properties of DAPSH crystal

The linear polarizability, first and second hyperpolarizabilities of the asymmetric unit of DAPSH crystal are studied and compared with available experimental results. The polarization effects are included using an iterative polarization procedure, which ensures the convergence of the dipole moment of DAPSH embedded within a polarization field generated by the surrounding asymmetric units whose atomic sites are considered as point charges. We estimate macroscopic susceptibilities from the results of the polarized asymmetric units in the unit cell, considering the significant contribution of the electrostatic interactions in crystal packing. The results show that the influence of the polarization effects leads to a marked decrease of the first hyperpolarizability, compared with the respective isolated counterpart, which improves the concordance with the experiment. There is a minor influence of polarization effects on the second hyperpolarizability but our estimated result for the third-order susceptibility, related to the NLO process of the intensity dependent refractive index, is significant as compared with the results for other organic crystals, such as chalcone-derivatives. In addition, supermolecule calculations are conducted for explicit dimers in presence of the electrostatic embedding to illustrate the role played by the electrostatic interactions in the hyperpolarizabilities of the DAPSH crystal.

All-optical polarization tuning based on an intensity-dependent nonlinear metasurface

Active control of light polarization at the nanoscale is essential for integrated photonic devices. Here, an all-optical approach is proposed to tune the polarization state of near-infrared light using a nonlinear metasurface. Based on the large intensity-dependent refractive index change of epsilon-near-zero (ENZ) materials, a phase difference between two orthogonal electric fields at ENZ wavelength can be continuously tuned in a range larger than 0.61π by varying the incident light power. The polarization state of the reflected light can thus be actively tuned from linear to circular state via an all-optical approach. Notably, abundant polarization states can be obtained by altering the polarization angle of incident light. The proposed all-optical approach is promising for tunable photonic functionalities of practical applications.

Understanding the conditions for the optimum nonlinear refraction of epsilon-near-zero films based on transparent conducting oxides.

Transparent Conducting Oxides (TCOs) exhibit a large and ultrafast intensity-dependent refractive index in their Epsilon-Near-Zero (ENZ) spectral region, which depends dramatically on the material properties and measurement arrangement conditions. Therefore, attempts to optimize the nonlinear response of ENZ TCOs usually involve extensive nonlinear optical measurements. In this work, we show that significant experimental work can be avoided by carrying out an analysis of the material's linear optical response. The analysis accounts for the impact of thickness-dependent material parameters on the absorption and field intensity enhancement under different measurement conditions and estimates the incidence angle required for achieving the maximum nonlinear response for a given TCO film. We perform measurements of angle-dependent and intensity-dependent nonlinear transmittance for Indium-Zirconium Oxide (IZrO) thin films with different thicknesses and demonstrate a good agreement between the experiment and theory. Our results also indicate that the film thickness and the excitation angle of incidence can be adjusted simultaneously to optimize the nonlinear optical response, allowing a flexible design of TCO-based highly nonlinear optical devices.

Predicting nonlinear optical scattering with physics-driven neural networks

Deep neural networks trained on physical losses are emerging as promising surrogates for nonlinear numerical solvers. These tools can predict solutions to Maxwell’s equations and compute gradients of output fields with respect to the material and geometrical properties in millisecond times which makes them attractive for inverse design or inverse scattering applications. Here we develop a tunable version of MaxwellNet with respect to incident power, a physics driven neural network able to compute light scattering from inhomogenous media with a size comparable with the incident wavelength in the presence of the optical Kerr effect. MaxwellNet maps the relation between the refractive index and scattered field through a convolutional neural network. We introduce here extra fully connected layers to dynamically adjust the convolutional kernels to take into account the intensity-dependent refractive index of the material. Finally, we provide an example of how this network can be used for the topology optimization of microlenses that is robust to perturbations due to self-focusing.

Optical isolators based on nonreciprocal four-wave mixing

In this work we propose and theoretically characterize optical isolators consisting of an all-dielectric and non-magnetic resonator featuring an intensity-dependent refractive index and a strong coherent field propagating in a single direction. Such devices can be straightforwardly realized in state-of-the-art integrated photonics platforms. The mechanism underlying optical isolation is based on the breaking of optical reciprocity induced by the asymmetric action of four-wave mixing processes coupling a strong propagating pump field with co-propagating signal/idler modes but not with reverse-propagating ones. Taking advantage of a close analogy with fluids of light, our proposed isolation mechanism is physically understood in terms of the Bogoliubov dispersion of collective excitations on top of the strong pump beam. A few most relevant set-ups realizing our proposal are specifically investigated, such as a coherently illuminated passive ring resonator and unidirectionally lasing ring or Taiji resonators.

Simulations of Structure and Morphology in Photoreactive Polymer Blends under Multibeam Irradiation

We present a theoretical study of the organization of photoreactive polymer blends under irradiation by multiple arrays of intersecting optical beams. In a simulated medium possessing an integrated intensity-dependent refractive index, optical beams undergo self-focusing and reduced divergence. A corresponding intensity-dependent increase in molecular weight induces polymer blend instability and consequent phase separation, whereby the medium can evolve into an intersecting waveguide lattice structure, comprising high refractive index cylindrical cores and a surrounding low refractive index medium (cladding). We conduct simulations for two propagation angles and a range of thermodynamic, kinetic, and polymer blend parameters to establish correlations to structure and morphology. We show that spatially correlated structures, namely, those that have a similar intersecting three-dimensional (3D) pattern as the arrays of intersecting optical beams, are achieved via a balance between the competitive processes of photopolymerization rate and phase separation dynamics. A greater intersection angle of the optical beams leads to higher correlations between structures and the optical beam pattern and a wider parameter space that achieves correlated structures. This work demonstrates the potential to employ complex propagating light patterns to create 3D organized structures in multicomponent photoreactive soft systems.

Structure-dependent optical nonlinearity of indium tin oxide

We use post-deposition vacuum annealing of epsilon-near-zero (ENZ) indium tin oxide (ITO) nanolayers in order to modify their structural properties and enhance the third-order optical nonlinear response around the ENZ wavelength. We find that room temperature magnetron sputtering deposition results in polycrystalline thin films with an intrinsic tensile strain and a ⟨110⟩ fiber axis preferentially oriented normal to the substrate. Moreover, we demonstrate that post-deposition vacuum annealing treatments produce a secondary anisotropic phase characterized by compressive strain that increases with the annealing temperature. Finally, we use the Z-scan optical technique to accurately measure the complex nonlinear susceptibility χ(3) and the intensity-dependent refractive index change Δn for samples with different structural properties despite featuring similar ENZ wavelengths. Our intensity-dependent analysis demonstrates that an enhancement of the optical nonlinearity can be achieved by tuning the structure of ENZ nanolayers with values as large as χR(3)=(5.2 ± 0.3)×10−17m2/V2. This study unveils the importance of structural control and secondary phase formation in ITO nanolayers with ENZ optical dispersion properties for the engineering of integrated highly nonlinear devices and metamaterials that are compatible with the scalable silicon photonics platform.

Growth and characterization of barium bis para-nitrophenolate para-nitrophenol tetrahydrate single crystal for NLO applications

Single crystals of barium bis para-nitrophenolate para-nitrophenol tetrahydrate (BBPNT) was grown using slow evaporation technique with the crystal dimensions of 15 × 10 × 6 mm3. The structure of the BBPNT crystal was examined by X-ray diffraction and the functional groups present in the compound were identified using FTIR spectrum. The optical and electrical properties were characterized by UV–Vis spectrum and dielectric studies respectively. Thermal properties of the grown crystal were investigated by using thermo-gravimetric (TG) and differential thermal analyses (DTA). The mechanical behavior of the grown crystal was studied using Vickers microhardness test. Using the Kurtz-Perry powder method, the second-harmonic generation efficiency was found to be 15.75 times greater than to that of KDP. Third-order nonlinear response was studied using Z-scan technique with a He-Ne laser (632.8 nm) and NLO parameters such as intensity dependent refractive index, nonlinear absorption coefficient and third-order susceptibility were also estimated. In the PL spectra, a broad band observed at 525 nm suggests its applications for fabricating green laser and new tunable laser system. The laser damage threshold value of BBPNT was found to be 5.09 GW/cm2 using an Nd: YAG laser.

Ultrafast-nonlinear ultraviolet pulse modulation in an AlInGaN polariton waveguide operating up to room temperature

Ultrafast nonlinear photonics enables a host of applications in advanced on-chip spectroscopy and information processing. These rely on a strong intensity dependent (nonlinear) refractive index capable of modulating optical pulses on sub-picosecond timescales and on length scales suitable for integrated photonics. Currently there is no platform that can provide this for the UV spectral range where broadband spectra generated by nonlinear modulation can pave the way to new on-chip ultrafast (bio-) chemical spectroscopy devices. We demonstrate the giant nonlinearity of UV hybrid light-matter states (exciton-polaritons) up to room temperature in an AlInGaN waveguide. We experimentally measure ultrafast nonlinear spectral broadening of UV pulses in a compact 100 μm long device and deduce a nonlinearity 1000 times that in common UV nonlinear materials and comparable to non-UV polariton devices. Our demonstration promises to underpin a new generation of integrated UV nonlinear light sources for advanced spectroscopy and measurement.

Nonlinearity-Induced Reciprocity Breaking in a Single Nonmagnetic Taiji Resonator

We report on the demonstration of an effective, nonlinearity-induced non-reciprocal behavior in a single non-magnetic multi-mode Taiji resonator. Non-reciprocity is achieved by a combination of an intensity-dependent refractive index and of a broken spatial reflection symmetry. Continuous wave power dependent transmission experiments show non-reciprocity and a direction-dependent optical bistability loop. These can be explained in terms of the unidirectional mode coupling that causes an asymmetric power enhancement in the resonator. The observations are quantitatively reproduced by a numerical finite-element theory and physically explained by an analytical coupled-mode theory. This nonlinear Taiji resonator has the potential of being the building block of large arrays where to study topological and/or non-Hermitian physics. This represents an important step towards the miniaturization of nonreciprocal elements for photonic integrated networks.

Study on Changes in Spatial Self-Phase Modulation Pattern of Graphene Dispersion

Changes in spatial self-phase modulation (SSPM) patterns have been studied when a laser beam passes through graphene dispersions and graphene dispersed gel. Interference rings are formed due to spatial self-phase modulation, which is induced by the change of the intensity dependent refractive index of graphene dispersions. The interference pattern of SSPM is found to be distorted rapidly for the graphene dispersions, while no distortion for the graphene dispersed gel. Experimental results show that thermal convection effect plays a dominant role for the distortion of the SSPM pattern. The distorted extent and area of the SSPM pattern depend on the speed and direction of convection in the graphene dispersions. Theoretical analyses have been given for the reason of the SSPM pattern distortion. Convection can effectively change the spatial symmetry distribution of polarized graphene sheets and non-linear refractive index in the beam cross section, thus making the interference rings distortion based on the spatial self - phase modulation.

From anisotropy of dielectric tensors to birefringence: a quantum mechanics approach

The way quantum mechanical ab initio computer codes allow to compute, through perturbation theory (the so-called SC-CP, self-consistent coupled-perturbed scheme), many properties resulting from the interaction of the electric field with a crystalline system is illustrated. The polarizability, which leads to the dielectric tensors as well as to the refractive indices and to the birefringence of materials, is the simplest on this list. Higher order tensors, like the first and second hyperpolarizabilities, can be obtained as well with the CRYSTAL code here used. These properties, resulting from the Taylor expansion of the total energy of the solid as a function of the electric field, belong to a large family of phenomena generated by combining in different ways the frequencies of the fields. Second-harmonic generation (SHG), Pockels effect, intensity-dependent refractive index (IDRI), and other quantities now accessible to experiment can be computed at a relatively low cost and with high accuracy.

Absorptive loss and band non-parabolicity as a physical origin of large nonlinearity in epsilon-near-zero materials

For decades, nonlinear optics has been used to control the frequency and propagation of light in unique ways enabling a wide range of applications such as ultrafast lasing, sub-wavelength imaging, and novel sensing methods. Through this, a key thread of research in the field has always been the development of new and improved nonlinear materials to empower these applications. Recently, epsilon-near-zero (ENZ) materials have emerged as a potential platform to enhanced nonlinear interactions, bolstered in large part due to the extreme refractive index tuning (Δn∼ 0.1 - 1) of sub-micron thick films that has been demonstrated in literature. Despite this experimental success, the theory has lagged and is needed to guide future experimental efforts. Here, we construct a theoretical framework for the intensity-dependent refractive index of the most popular ENZ materials, heavily doped semiconductors. We demonstrate that the nonlinearity when excited below bandgap, is due to the modification of the effective mass of the electron sea which produces a shift in the plasma frequency. We discuss trends and trade-offs in the optimization of excitation conditions and material choice (such material loss, band structure, and index dispersion), and provide a figure of merit through which the performance of future materials may be evaluated. By illuminating the framework of the nonlinearity, we hope to propel future applications in this growing field.

Optical Kerr Nonlinearity of Disordered All-Dielectric Resonant High Index Metasurfaces with Negative Refraction

The optical Kerr effect of material with negative refraction is estimated for the first time. This is done via three-dimensional finite-difference time-domain (FDTD) simulations of disordered bidisperse metasurfaces consisting of high index (GaP) spheres at the wavelength of 532~nm. The metasurfaces comprise spherical particles randomly arranged on plane having two sizes close to the magnetic and electric dipole Mie resonances. The real part of the effective nonlinear refractive index of the metasurfaces is computed in the vicinity of the Mie resonances where the metasurface possesses the negative index of refraction. The optical Kerr nonlinearity has a peak under the condition for the negative refraction. Intensity-dependent refractive index of the bidisperse metasurfaces is studied through concentration transition to the negative refraction state. It is shown that the nonlinear Kerr coefficient of the monolayer metasurface has maximum when the effective linear refractive index is close to zero.

Ultrafast Nano-scale Optical Switching in a Plasmonic Interferometer with Enhanced Tunability

An all-optical switch based on plasmonic metal–insulator–metal (MIM) waveguides and the Mach–Zehnder (MZ) interferometer is designed. In order to realize an all-optical and active switch, a nonlinear material with intensity-dependent refractive index is introduced in one arm. Other than studying a typical MZ structure, we also investigate the asymmetric case where unequal thicknesses and distances for MZ arms are proposed. The finite element method (FEM) with a refined triangle mesh is employed for simulations. Results for ON and OFF states are provided with or without employing the pump field. Investigation of the geometrical dispersion reveals tunability of the structure for specific frequencies in the terahertz region. Finally, we show that introducing asymmetric arms provides better tunability in the designed ultrafast nano-scale switch and suggests its potential applications in integrated optical circuits.