Nonlinear Mixing Process Research Articles

Topological protection of dual-polarization biphoton states in photonic crystals

Polarization control is a major issue in topological quantum optics that limits reliable generation and transmission of quantum states. This study presents what we believe to be a novel topological photonic crystal design that provides topological protection for biphoton pairs for both TE and TM polarization. By well-designed cell configurations within the lattice, two topological boundaries emerge that can accommodate TM and TE modes at the same time. By adjusting the dispersion curves, we can further design nonlinear four-wave mixing processes within the topological photonic crystals and provide theoretical explanations for the entanglement of the dual-polarization biphoton states. Numerical results confirm the robust transport of entangled photon pairs, even when subjected to sharp bending. Moreover, combining the dual-polarization topological photonic crystal with a polarization beam splitter enables the preparation of polarization-encoded maximally entangled states. Our work exhibits significant potential for applications in robust optical quantum information processing and quantum secure communication.

Nonlinear Formulation of Multicomponent Reactive Transport With Species‐Specific Dispersion Properties

AbstractThe modeling of reactive transport through porous media is a challenging numerical problem. Methods of solution have leveraged the stoichiometry of chemical reactions to address the transport of multiple aqueous species by expressing them in terms of an equivalent, linearly independent variable (component). This approach effectively decouples advection‐dispersion transport from the source terms associated with equilibrium reactions. A common assumption found in the literature is that all species disperse with the same transport coefficients. Recent experimental studies have discussed that this is not necessarily the case, particularly for transverse mixing, which is limited by the species‐specific molecular diffusion. This article presents a formulation of multicomponent reactive transport that takes into account the differences in dispersion coefficients. These differences lead to a nonlinear transport equation for the components, from where an expression for evaluating reaction rates is derived. It is demonstrated that this expression simplifies to the well‐known equations assuming the same dispersion for all species. Numerical simulations of a binary chemical system under diffusion‐ and advection‐dominated transport conditions are used to evaluate the influence that differential transport coefficients have upon the output of chemical reactions. Results indicate that differences in transport coefficients are particularly relevant when the chemical signature of the input solutions is not strongly dominated by one of the species in the component. Unexpectedly, this opens the possibility to mineral dissolution coexisting with precipitation during the mixing of two waters in equilibrium. This phenomenon can be explained by nonlinear mixing processes proportional to the differences in transport coefficients.

The Improved U-STFM: A Deep Learning-Based Nonlinear Spatial-Temporal Fusion Model for Land Surface Temperature Downscaling

The thermal band of a satellite platform enables the measurement of land surface temperature (LST), which captures the spatial-temporal distribution of energy exchange between the Earth and the atmosphere. LST plays a critical role in simulation models, enhancing our understanding of physical and biochemical processes in nature. However, the limitations in swath width and orbit altitude prevent a single sensor from providing LST data with both high spatial and high temporal resolution. To tackle this challenge, the unmixing-based spatiotemporal fusion model (STFM) offers a promising solution by integrating data from multiple sensors. In these models, the surface reflectance is decomposed from coarse pixels to fine pixels using the linear unmixing function combined with fractional coverage. However, when downsizing LST through STFM, the linear mixing hypothesis fails to adequately represent the nonlinear energy mixing process of LST. Additionally, the original weighting function is sensitive to noise, leading to unreliable predictions of the final LST due to small errors in the unmixing function. To overcome these issues, we selected the U-STFM as the baseline model and introduced an updated version called the nonlinear U-STFM. This new model incorporates two deep learning components: the Dynamic Net (DyNet) and the Chang Ratio Net (RatioNet). The utilization of these components enables easy training with a small dataset while maintaining a high generalization capability over time. The MODIS Terra daytime LST products were employed to downscale from 1000 m to 30 m, in comparison with the Landsat7 LST products. Our results demonstrate that the new model surpasses STARFM, ESTARFM, and the original U-STFM in terms of prediction accuracy and anti-noise capability. To further enhance other STFMs, these two deep-learning components can replace the linear unmixing and weighting functions with minor modifications. As a deep learning-based model, it can be pretrained and deployed for online prediction.

Cascaded four-wave mixing all-optical wavelength converter based on highly nonlinear fiber deposited graphene oxide

The all-optical wavelength conversion using cascaded four-wave mixing (FWM) phenomena with graphene oxide (GO) and a highly nonlinear fiber (HNLF) device is demonstrated experimentally. GO has a strong third-order nonlinear effect and is an excellent nonlinear optical material for nonlinear optical wavelength conversion. The group velocity matching of pump and signal, HNLF, and GO amplification promote the cascaded nonlinear frequency mixing process. From the experimental and analytical results, the maximum spacing between signal and pump is 21 nm, and specifically, the order of cascaded FWM light increases from order 1 to order 2 with increasing GO, and the first-order FWM conversion efficiency increases to a maximum of −14.5 dB. To the best of our knowledge, this is the first time that cascaded FWM-based all-optical wavelength conversion in HNLF–GO with wide wavelength selectivity is investigated with combined pump and signal light. Our findings not only provide an effective method for achieving all-optical wavelength conversion in cascaded FWM but also offer the possibility of fabricating high-performance nonlinear optical devices.

Intrinsic photomixing detector based on amorphous silicon for envelope mixing of optical signals

In this work, a promising device for direct optical envelope mixing, the Intrinsic Photomixing Detector (IPD) based on hydrogenated amorphous silicon, is reported. The IPD directly generates a photocurrent proportional to the nonlinear mixing of two optical modulation envelope functions. Experiments illustrate efficient mixing in the visible range at low light levels down to ϕ1 = 4.36 mW/cm2 (444 nm) and ϕ2 = 1.03 mW/cm2 (636 nm). Modulation frequencies exceeding the MHz range are demonstrated. Electro-optical simulations identify defect-induced electrical field screening within the absorber to cause the nonlinear mixing process, opening-up the opportunity to tailor devices toward application-specific requirements. The IPD functionality paves the way toward very simple but high-performance photodetectors for 3D imaging and ranging for direct optical convolutional sensors or for efficient optical logic gates. Using amorphous silicon provides a photodetector material base, which can easily be integrated on top of silicon electronics, enabling fill factors of up to 100%.

Few-femtosecond phase-sensitive detection of infrared electric fields with a third-order nonlinearity

Measuring an electric field waveform beyond radio frequencies is often accomplished via a second-order nonlinear interaction with a laser pulse shorter than half of the field’s oscillation period. However, synthesizing such a gate pulse is extremely challenging when sampling mid- (MIR) and near- (NIR) infrared transients. Here, we demonstrate an alternative approach: a third-order nonlinear interaction with a relatively long multi-cycle pulse directly retrieves an electric-field transient whose central frequency is 156 THz. A theoretical model, exploring the different nonlinear frequency mixing processes, accurately reproduces our results. Furthermore, we demonstrate a measurement of the real part of a sample’s dielectric function, information that is challenging to retrieve in time-resolved spectroscopy and is therefore often overlooked. Our method paves the way towards experimentally simple MIR-to-NIR time-resolved spectroscopy that simultaneously extracts the spectral amplitude and phase information, an important extension of optical pump-probe spectroscopy of, e.g., molecular vibrations and fundamental excitations in condensed-matter physics.

Parametric amplification based on intermodal four-wave mixing between different supermodes in coupled-core fibers.

Parametric amplifiers relying on the nonlinear four-wave mixing process are known for their signature symmetric gain spectrum, where signal and idler sidebands are generated on both sides of a powerful pump wave frequency. In this article we show analytically and numerically that parametric amplification in two identically coupled nonlinear waveguides can be designed in such a way that signals and idlers are naturally separated into two different supermodes, hence providing idler-free amplification for the supermode carrying signals. This phenomenon is based on the coupled-core fibers analogue of intermodal four wave-mixing occurring in a multimode fiber. The control parameter is the pump power asymmetry between the two waveguides, which leverages the frequency dependency of the coupling strength. Our findings pave the way for a novel class of parametric amplifiers and wavelength converters, based on coupled waveguides and dual-core fibers.

Wavefront shaping with nonlinear four-wave mixing

Wavefront manipulations have enabled wide applications across many interdisciplinary fields ranging from optics and microwaves to acoustics. However, the realizations of such functional surfaces heavily rely on micro/nanofabrication to define the structured surfaces, which are fixed and only work within a limited spectrum. To address these issues, previous attempts combining tunable materials like liquid crystal or phase-change ones onto the metasurfaces have permitted extra tunability and working spectra, however, these additional layers bring in inevitable loss and complicate the fabrication. Here we demonstrate a fabrication-free tunable flat slab using a nonlinear four-wave mixing process. By wavefront-shaping the pump onto the flat slab, we can successfully tune the effective nonlinear refraction angle of the emitting FWM beams according to the phase-matching condition. In this manner, a focusing and a defocusing nonlinear of FWM beam through the flat slab have been demonstrated with a converging and a diverging pump wavefronts, respectively. Furthermore, a beam steering scheme over a 20° angle has been realized through a non-degenerate four-wave mixing process by introducing a second pump. These features open up a door to manipulating light propagation in an all-optical manner, paving the way to more functional and tunable flat slab devices in the applications of imaging and all-optical information.

Ultrafast modulation of a high harmonic generation in a bulk ZnO single crystal.

Optical modulation of high harmonic generation (HHG) is of fundamental interest in science and technology, which can facilitate understanding of HHG generation mechanisms and expand the potential optoelectronic applications. However, the current established works have neither shown the advanced modulation performance nor provided a deep understanding of modulation mechanisms. In this work, taking wurtzite zinc oxide (ZnO) single crystal as a prototype, we have demonstrated an all-optical intensity modulation of high-order HHG with a response time of less than 0.2 ps and a depth of more than 95%, based on the pump-probe configuration with two different pumping wavelengths. Besides the achieved excellent modulation performance, we have also revealed that the modulation dynamics in ZnO single crystal highly depend on the excitation conditions. Specifically, the modulation dynamics with the near-bandgap or above-bandgap excitation are attributed to the non-equilibrium interband carrier relaxations, while for mid-gap excitation, the modulation dynamics are dominated by the nonlinear frequency mixing process. This work may enhance the current understanding of the HHG modulation mechanism and enlighten novel device designs.

Modulation Transfer Spectroscopy of a four-level ladder system in atomic rubidium

We demonstrate Modulation Transfer Spectroscopy for a four-level ladder-configuration system in atomic rubidium that probes Rydberg states. Three lasers at wavelengths of 780 nm (probe), 1529 nm (dressing), and ∼700 nm (coupling) drive the 5S1/2→5P3/2→4D3/2→nF5/2 excitation path, with the first two lasers independently frequency-locked to their respective atomic resonances. To observe modulation transfer that involves the uppermost step, we apply frequency sidebands to the coupling laser with an electro-optic modulator before overlapping all three beams in a rubidium vapor cell. Within the cell, the probe beam efficiently acquires sidebands at the modulation frequency through a nonlinear mixing process that occurs when the coupling beam is tuned to atomic resonance. The transmitted probe beam is focused onto a fast photodiode; the phase of the resulting beat note exhibits a derivative-like response. We demonstrate that this response can be obtained with relatively low laser powers and use it as an error signal to limit the relative frequency drift of the coupling laser to ∼30 kHz on the timescale of hours.

Low-Frequency Oscillations in Optical Measurements of Metal-Nanoparticle Vibrations.

Time-resolved optical measurements of vibrating metal nanoparticles have been used extensively to probe the ultrafast mechanical properties of the nanoparticles and of the surrounding liquid, but nearly all investigations so far have been limited to the linear regime. Here, we report the observation of a low-frequency oscillating signal in transient-absorption measurements of nanoparticles with octahedral gold cores and cubic silver shells; the signal appears at the difference of two mechanical vibrational frequencies in the particles, suggesting a nonlinear mixing process. We tentatively attribute this proposed mixing to a nonlinear coupling between a vibrational mode of the nanoparticle and its optical-frequency plasmon resonance. The optimization of this nonlinear transduction may enable high-efficiency opto-mechanical frequency mixing in the GHz-THz frequency regime.

A Characteristics Set Computation Model for Internal Wavenumber Spectra and Its Validation with MODIS Retrieved Parameters in the Sulu Sea and Celebes Sea

The quasi-linear or nonlinear interactions among different ocean motions dominate the system internal structure and appearance feature presented in spatial and temporal evolution. However, deficiency of the characteristics set computation model for internal wavenumber spectra proves to be a serious barrier to derive interaction mechanisms of internal waves with large or small scale ocean motions. In this study, a characteristics set computation model for internal wavenumber spectra is proposed for complicated offshore environments. The refraction of current shear instability, bottom topography and the reflection at surface and bottom are attentively considered in the complicated characteristics inlaid scheme. Model results are validated with MODIS retrieved internal wave parameters in the Sulu Sea and Celebes Sea. This original characteristics set computation model for internal wavenumber spectra can be used widely and can further improve the understandings of generation, dissipation, nonlinear wave-wave interaction and mixing process of internal waves.

Nonlinear Spectral Unmixing of Hyperspectral Imagery Based on Hapke Model and Relevance Vector Regression Algorithm

Abstract This paper put forward a nonlinear hyperspectral imagery unmixing method based on Hapke nonlinear spectral mixture model and the relevance vector regression. This paper presents a method of relevance vector regression algorithm for unmixing of hyperspectral images. The spectrum was mixed to train the relevance vector regression algorithm according to Hapke non-linear mixing model. This method made our training process coincident with the physical feature of non-linear spectral mixing process. The experiments of smiulated data and hyperspectral imagery are conducted to validate the methods. The smiulated data and hyperspectral image was used for accuracy assessment. Results show that relevance vector regression algorithm can provide better result as compared with linear spectral unmixing model and support vector regression method. And our method provides better result with relative less relevant vector. The proposed algorithm reduced computational complexity of the spectral unmixing problem.

Impact of Mode-Area Dispersion on Nonlinear Pulse Propagation in Gas-Filled Anti-Resonant Hollow-Core Fiber

We numerically investigate the effect of mode-area dispersion in a tubular-type anti-resonant hollow-core fiber by using a modified generalized nonlinear Schrödinger equation that takes into account the wavelength-dependent mode area in its nonlinear term. The pulse evolution dynamics with and without the effect of mode-area dispersion are compared and analyzed. We show that strong dispersion of the mode area in the proximity of the cladding wall thickness-induced resonances has a significant impact on the soliton pulse propagation, resulting in considerable changes in the conversion efficiencies in nonlinear frequency mixing processes. The differences become more prominent when the pump has higher energy and is nearer to a resonance. Hence, the mode-area dispersion must be accounted for when modeling such a case.

Fiber source of femtosecond pulses at 910–940 nm based on a Mamyshev pulse oscillator and wavelength conversion in a photonic crystal fiber

In this work, we present a fiber-based setup for femtosecond pulse generation at ∼ 910 − 940 n m wavelength. Pump pulses from a Mamyshev oscillator with center wavelength at 1036 nm 1 ps duration are amplified and coupled into a photonic crystal fiber forming a soliton at 1051 nm. Due to the nonlinear four-wave mixing process, soliton pulses are converted to 910–940 nm with a few hundred femtosecond pulses with energy up to 0.7 nJ. The proposed design utilizes features of the Mamyshev oscillator, enabling a robust way of generating femtosecond pulses at ∼ 910 − 940 n m .

Field quantization in quantum plasmas: Photon and plasmon charge and mass

AbstractWe study electromagnetic field quantization in isotropic quantum plasmas, thus connecting two distinct problems of quantum plasma physics. We include plasmons and transverse photon states. We show that field quantization in a plasma is equivalent to that of massive boson fields and discuss the qualitative differences with respect to standard quantization in a vacuum. We consider nonlinear effects and show that photon and plasmon charges can be associated with the ponderomotive force. We also discuss the conservation properties of these affective charges during nonlinear mixing processes. The existence of photon and plasmon charge and mass could be relevant to laboratory experiments and to astrophysics.

On the Explicit Function of Life within a Physical Universe

To describe the meaning of functionality in a universe before life evolved, existing etiological and systemic accounts of function are evaluated. Since the theory of function is only applicable in context with living beings and artifacts used by living beings and therefore cannot predict how a prebiotic form of functionality could evolve, a maintenance account for functionality is proposed. This account ascribes functionality to a structurally disposed property that increases the probability of maintenance or recurrence of the property in the surrounding selective environment. With the help of the maintenance account and a concept of physical information comprising kinetic and structural types of information, possible evolutionary processes preceding the evolution of life are explored. As important mechanisms in abiotic and prebiotic evolution, linear and non-linear mixing processes, as well as dynamics of solitary waves, are identified. Before the question of the meaning of life in prebiotic environments is renewed and an educated guess based on the elaborated arguments is made on the progress of evolution under the influencing impression of the living state, the evolution of functionality in different selective contexts is analyzed.

Exchange of optical vortices in symmetry-broken quantum systems

We investigate the interaction of laser pulses carrying orbital angular momentum (OAM) with a symmetry-broken ladder-type quantum coupling scheme involving three internal states. A weak probe beam acts on the lower leg of the ladder scheme, while a control beam of higher intensity drives the upper leg. In contrast to natural atoms, such a model with broken symmetry allows generating a sum-frequency signal beam between the most upper and lower quantum states, forming a cyclic closed-loop configuration of light-matter interaction. We propose situations for the efficient transfer of optical vortices to the generated signal beam via a nonlinear three-wave mixing process. It is demonstrated that the exchange process can occur both in the electromagnetically induced transparency (EIT) and the Autler-Townes splitting (ATS) regimes. The transition between the EIT and ATS conversion schemes can smoothly happen by simply tuning the knob of the control field. It is shown that the ATS regime is considerably more favorable than the EIT to achieve maximum energy conversion efficiency between light beams carrying the OAM. The results may provide an applications-based perspective to the ongoing research centered on vortex conversion-based comparisons between the ATS and EIT.

Cross-phase modulational instability of circularly polarized helical Bloch modes carrying optical vortices in a chiral three-core photonic crystal fiber.

We report the first, to the best of our knowledge, observation of cross-phase modulational instability (XPMI) of circularly polarized helical Bloch modes carrying optical vortices in a twisted photonic crystal fiber with a three-fold symmetric core, formed by spinning the fiber preform during the draw. When the fiber is pumped by a superposition of left-circular polarization (LCP) and right-circular polarization (RCP) modes, a pair of orthogonal circularly polarized sidebands of opposite topological charge is generated. When, on the other hand, a pure LCP (or RCP) mode is launched, the XPMI gain is zero, and no sidebands are seen. This observation has not been seen before in any system and is unique to chiral structures with N-fold rotational symmetry. The polarization state and topological charge of the generated sidebands are measured. By decomposing the helical Bloch modes into their azimuthal harmonics, we are able to deduce the selection rules for the appearance of modulational instability sidebands. We showed that the four waves in the nonlinear mixing process must exhibit the same set of azimuthal harmonic orders.

Mixing Ince–Gaussian modes through sum-frequency generation

We present a nonlinear mixing study of Ince–Gaussian (IG) beams in non-collinear sum-frequency generation, completing the fundamental analysis of all three families of paraxial wave equation solutions under this nonlinear process. Through theoretical and experimental results, we consider the nonlinear mixing of even and odd IG modes, and transition between the paraxial modes by controlling the eccentricity parameter ϵ and helical IG modes possessing arbitrary orbital angular momentum. Additionally, the selection rule of IG modes in the nonlinear mixing processes is determined. This work is important for optical communications and quantum protocols.