The proposition of Bell inequality arises from the exploration of fundamental contradictions between quantum mechanics and classical physics. J. Bell sought to settle the ongoing debates among physicists such as A. Einstein, M. Born, and N. Bohr regarding quantum mechanics, particularly focusing on whether the hypothesis of local hidden variables could account for the physical properties of entangled states. If this hypothesis was valid, it would provide stronger support local realism in classical physics. To test this hypothesis, J. Bell proposed an inequality, known as Bell inequality, which provides an empirical method for verifying the non-classical characteristics of quantum theory.Bell inequality is of paramount importance. Firstly, in the exploration of fundamental physical laws, Bell inequality can be utilized to experimentally verify the non-classicality of quantum mechanics, deepening our understanding of the quantum world and advancing the further development of physics. Secondly, through a thorough investigation of Bell inequality, it is possible to develop more secure and efficient quantum communication technologies, as well as promote the development of fields such as quantum computing and quantum networks.However, explaining Bell inequality is not straightforward. This inequality involves basic concepts such as probability and measurement, employing assumptions like realism and locality that have been ingrained into foundational thinking through classical physics research. Moreover, its mathematical form and derivation process are relatively complex, requiring profound knowledge of mathematics and physics for comprehension. Therefore, establishing an intuitive understanding of Bell inequality can effectively facilitate its research and application.To facilitate a simpler and more intuitive understanding of Bell inequality, this paper provides a review on Bell inequality's intuitive explanation and research progress. This paper is organized as follows: The first part introduces the controversies facing quantum physics and the motivation behind the proposition of Bell inequality. In the second part, we introduce the mathematical form and physical significance of the Bell-CHSH inequality. Specifically, we introduce the concept of the Bell-CHSH inequality, derive the CHSH inequality for continuous hidden variables and discrete hidden variables, derive Bell inequality based on quantum mechanics theory using two specific examples: finding that the product states satisfy the CHSH inequality while the entangled states violate it.In the third part, we analyze why it is said that Bell inequality resolves the debate in quantum physics. We believes that Bell inequality does not solve the problem of whether quantum mechanics is complete, nor does it solve the issue of whether the Copenhagen interpretation is correct. Instead, it provides a criterion for judging whether hidden variable theories can accurately predict experimental phenomena while satisfying realism and locality. If this conclusion holds true, it suggests that further research could be conducted to determine what kind of hidden variables exist, potentially leading to a fundamental replacement of quantum mechanics as the foundational theory.In the fourth part, we introduce two Bell inequalities represented using Venn diagrams. Specifically, based on the assumptions of realism and locality, we use probability theory for inference, geometrically display two sets of Bell inequalities through Venn diagrams, and then introduce entangled states into the inequalities, verifying that entangled states violate Bell inequality.In the fifth part, we introduce the experimental research progress of Bell inequality, including the Wu-Shaknov experiment, Freedman-Clauser experiment, Aspect experiment, Zeilinger experiment, as well as recent experiments on closing detection loopholes, locality loopholes, and free choice loopholes. Finally, we introduce the experimental work of the authors on verifying Bell-CHSH inequality. The sixth part is the conclusion. This paper is expected to help readers gain an intuitive understanding of the important concept of Bell inequality.

Fiber channel is the best choice for metropolitan quantum information processing due to its advantages of high compatibility, low cost and not easy to be affected by environment. However, when the non-classical optical field is transmitted in the fiber, it will be affected by the extra noise, leading to decoherence, and thus the quantum properties will be reduced or disappeared. With the development of quantum information in long distance fiber, how to realize the non-classical light field in fiber channel transmission without the influence of extra noise has been paid more and more attention.In this paper, a four-fiber channel quantum error correction scheme is proposed theoretically. The quantum error correction of the quantum state in the fiber channel is realized by establishing the correlated noise channel, and the effective transmission of the squeezed state optical field in the fiber channel is completed.The influence of parameters such as the correlation degree of the optical fiber correlated noise channel, the optical fiber transmission distance and the power of the local oscillating light on the quantum error correction is analyzed theoretically. The numerical simulation of our scheme shows that, when the noise is ideally correlated, the extra noise can be completely removed, and the quantum characteristics of the squeezed state optical field will not disappear with the increase of transmission distance and the power of the local oscillator (LO) beam, so the quantum state is ideally protected. Even if the noise in the established correlation noise channel is only partially correlated, our error correction scheme still effectively reduces the extra noise and enhances the transmission distance of the non-classical optical field in the fiber channel. When the relative phase of the correlated noise is assumed to be /2, the transmission distance of the squeezed state light field with a squeezing degree of 10 dB in the fiber channel can be increased from 10 km to 30 km when the power of the LO is 0.2 mW. This study lays a foundation for the research of continuous variable fiber quantum information in metropolitan area.

ObjectiveIn quantum optics, (nature) atoms are orders of magnitude smaller than the wavelength of the light they interact with, which justifies the dipole approximation by allowing them to be viewed as point-like emitters. However, recent experiments extending the small (nature) atom platform to artificial 'giant' atomic systems built from superconducting circuits, represent a breakdown of the dipole approximation and have attracted significant attention. The waveguide quantum electrodynamics systems with giant atoms have emerged as a new promising platform for engineering transport of photons and single-photon routing. The system enables strong tunable atom-waveguide coupling and manifests multiple-point self-interference in the photon scattering spectra. Recently, a setup with chiral interfaces between giant atoms and waveguides is no longer challenging based on technological progress, in particular, the chiral coupling can also allow decoherence-free states, nonreciprocal photon transport, and tunable Markovianity. Few studies have also considered the unequal local phases at different coupling points for photon routing. Nevertheless, here we study the single-photon scattering problem by considering chiral local coupling phases.MethodWe consider the system Hamiltonian in real-space and linear dispersion relation. We solve the Schrdinger equation within the single-photon manifold by considering the -function potential effect of the atom at the coupling point, where an appropriate ansatz is used for the probability amplitudes of the system's state, and the transmission and reflection coefficients are found with the direction-dependent propagating phases. The effects induced by chiral phases in the scattering spectra are studied by engineering the local coupling phases and coupling strengths.Results and DiscussionsWe show that the transmission spectrum of an incident photon can transition from complete transmission to total reflection when the chiral phases satisfy specific conditions, regardless of the number of coupling points. In particular, the Lamb shifts vanishes at resonance, allowing for in situ control of the photon transport by varying the propagating phases. Moreover, when the internal atomic spontaneous emission is introduced, we show that perfect nonreciprocal photon scattering can be achieved by engineering the chiral local phases, in contrast to the non-Markovian retardation effect.ConclusionWe have studied the effect of chiral local coupling phases on single-photon scattering. By engineering the chiral phases, it is not only possible to flexibly control the single-photon scattering properties, but also to achieve perfect nonreciprocal photon scattering. The findings of this study indicate that the giant-atom-waveguide system with chiral local coupling phases is a promising candidate for realizing single-photon routers and has potential applications in quantum network engineering and quantum information processing.

ObjectiveOptical lattice clocks based on optical frequency transitions of neutral atoms have demonstrated excellent stability and uncertainty, which are one of the most promising candidates for the next generation of second replications. However, the current limitation is that optical lattice clocks are still in the laboratory prototype stage and cannot operate autonomously for extended periods, making a continuous realization of a timescale impractical. Therefore, it is crucial to assess the impact of this limited availability on the generated time scale.MethodThis paper studies how to build a time scale with an intermittently operating optical lattice clock, based on simulations. A simulation approach is employed to construct a time scale composed of a continuously operating active hydrogen maser and an intermittent 87Sr optical lattice clock, utilizing Kalman filter algorithm for steering. The hydrogen maser serves as a flywheel clock to ensure the continuity of the time scale, while the 87Sr optical lattice clock acts as the frequency reference. The Kalman filter algorithm, widely employed for estimating the frequency and frequency drift of the free-running time scale in relation to the optical clock, is a prominent method used for steering the frequency and frequency drift of the time scale based on such estimates. The selection of key parameters in the Kalman filter algorithm is discussed in detail. Additionally, the study investigates the influence of various operational strategies for optical lattice clocks. This is done by considering several different scenarios for the availability of the optical lattice clock, such as the different uptime ratios (the optical lattice clock operating for 0.4 hours, 2 hours and 12 hours per day) and different operating interval with the same uptime ratio (the optical lattice clock operating for 2 hours per day, 4 hours per 2 days and 4 hours per 8 days).Results and DiscussionsOur findings reveal that the longer the optical lattice clocks operate, the better the frequency stability of time scales is. Moreover, the performance of the timescale can be improved by dividing the total uptime of the optical lattice clock into multiple sub-periods, while keeping the overall uptime the same. More frequent measurements and steering effectively reduce the Dick effect in the steering process. The simulation result shows that 8.3% uptime ratio of the OLC, the root-mean-square (RMS) of the time errors is less than 0.8 ns after 30 days, while the frequency stability of the time scale reaches 4×10−17 at 30 days.ConclusionThis paper presents a novel approach for building a time scale with an intermittently operating optical lattice clock. We establish a frequency difference model to prove the feasibility of frequency steering in theory, calculate the key parameters in the Kalman filter algorithm and find out the rules to be followed in choosing the steering strength and steering frequency. This research should be useful for applying the proposed scheme to other combinations of optical frequency standards and flywheels, and promote the development of optical clock technologies.

ObjectiveAs the primary tool for high-precision phase measurement, optical phase sensing has an important application in fields such as target tracking and phased-array radar. Currently, phase sensing primarily relies on distributed quantum sensing protocols to achieve high-precision phase measurement across multiple sensing nodes. Research indicates that utilizing entangled state networks can further improve phase estimation accuracy, reaching measurement sensitivities beyond the shotnoise limit. However, as the number of sensing nodes increases, system losses also increase, leading to a decrease in the precision of optical phase sensing. This becomes a major factor constraining the practical application of quantum sensing. To investigate the potential application of optical phase sensing with fewer nodes, exploration of the angle of arrival (AoA) in dual-node optical sensing is conducted.MethodThis paper presents an AoA estimation protocol based on phase squeezed states. AoA estimation is transformed into a phase difference estimation problem between two sensing nodes. By deriving the phase difference between two sensing nodes under the beam splitter model, it is found that the measurement accuracy of phase difference is not only limited by the squeezing degree of the phase squeezed state, but also related to the vacuum fluctuations introduced by the beam splitter network. To explore the application of AoA in dual-node optical sensing, an experimental setup for AoA estimation based on phase squeezed states is constructed. The preparation of phase squeezed state is carried out using an optical parametric oscillator (OPO). The OPO adopts a single-resonator structure, allowing the 532 nm pump light to pass through the cavity twice and the 1 064 nm fundamental light to resonate inside the cavity. To achieve stable output of phase squeezed state, the OPO should operate in an amplification state. Therefore, the Pound-Drever-Hall (PDH) locking technique is employed to lock the relative phase between the seed light and the pump light. In order to realize dual-node optical phase sensing, a variable beam splitter is used to split the squeezed state light into two sensing nodes, resulting in entanglement between the two sensing nodes. By controlling the splitting ratio between the two sensing nodes, the response characteristics of the entanglement degree of the dual sensing nodes with respect to the reflectance R of the variable beam splitter are investigated.Results and DiscussionsTo maximize the quantum enhancement advantage of phase squeezed states in AoA estimation, the entanglement degree of the dual sensing nodes is measured with the reflectance R varied. The results indicate that when R is 0.5, the quantum entanglement properties between the two sensing nodes are maximized. As R deviates from 0.5, the entanglement decreases due to the vacuum fluctuations introduced by the beam splitter. To validate the feasibility of phase estimation based on phase squeezed states, the optical phase shift is measured for different modulation phases. The results demonstrate a sinusoidal trend in the phase shift as the modulation phase varies from 0 to 2, consistent with theoretical predictions. Furthermore, compared to classical protocols, the noise fluctuations in phase difference estimation based on phase squeezed states exhibit a significant reduction, highlighting the quantum enhancement advantage of arrival angle estimation protocols based on non-classical states.ConclusionThis paper proposes an AoA estimation protocol based on entangled state optical fields. A continuous solid-state laser source with a central wavelength of 1 064 nm, an optical parametric oscillator, and a variable beam splitter are used to prepare entangled state optical fields with a maximum entanglement of (6.1±0.2) dB. By controlling the optical phase of the sensing nodes, precise scanning of the 0～2 phase for two sensing nodes is achieved, enabling AoA estimation beyond the shot noise limit. Compared to classical protocols, this protocol can suppress the fluctuations of noise in AoA estimation to at least 5.9 dB below the shot noise baseline, increasing the accuracy of AoA estimation by over 74.1%. This protocol is expected to improve the precision of phase estimation beyond the shot noise limit, providing a theoretical and experimental basis for higher-precision spatial positioning and quantum ranging technologies.

ObjectiveThe continuous variable quantum key distribution protocol has drawn much attention because of its easy preparation of light source, higher detection efficiency than single photon detector and good compatibility with passive optical communication networks. The measurement device-independent protocol effectively eliminates all known or unknown side-channel attacks in the detection side. However, the initial experiment that encodes information on the amplitude and phase quadratures using coherent or squeezed states, indicated a relatively complexity compared to the unidimensional modulation. The unidimensional continuous variable quantum key distribution protocol has the characteristics of simple modulation process, low cost-effectiveness, and less consumption of random numbers. Realization condition of unidimensional modulation protocol is more convenient than that of two-dimensional Gaussian modulation. For the purpose of simplifying the system and reducing experimental complexity, a novel protocol is proposed, achieving relatively higher security key rate and longer distances.MethodThis paper introduces unidimensional continuous-variable measurement-device-independent quantum key distribution using squeezed states and the security performance of the proposed scheme is comprehensively analyzed including both symmetric and asymmetric transmission distances. For the convenience of analyzing the security of protocol, an entanglement-based (EB) scheme is proposed to provide a comprehensive proof. Based on the measurement device-independent protocol, general coherent state preparation is expanded to the squeezed state. Taking into account the realistic conditions, a detailed comparison investigates the impact of introducing light source noise and detection noise on the protocol's security performance. Furthermore, the impact of squeezing parameter on the performance of the protocol is explored for both asymmetric and symmetric distances. The performance of the protocol is also investigated under the eavesdropper's one mode attack and two mode attack.Results and DiscussionsOur simulation results reveal the existence of optimal modulation variances and squeezing parameters at different transmission distances. These results provide a theoretical framework for achieving optimal secure key rates and secure transmission distances in experimental implementations, thereby facilitating the practical realization of the proposed scheme. Based on these results, we can achieve relatively higher secure key rate by selecting the appropriate parameter for adapting different application scenarios. This could pave the way for greater cost-effectiveness and a simpler way to implement the protocol in the future. As theoretical analysis mentioned about imperfect source and detectors, it may be insufficient to guarantee the realistic implement. It is possible that these imperfections can be compensated by optical phase-sensitive amplifiers.ConclusionThis paper presents a protocol for unidimensional continuous-variable measurement-device-independent quantum key distribution using squeezed state. By adjusting the modulation variance and squeezed parameter, we can achieve more efficient and longer transmission distances while ensuring the actual security performance of the system. This research also clarifies that the influencing mechanism of source noise and detected noise on the performance of the protocol. We can selectively tune the modulation variance and squeezed parameter towards different application scenarios.

As a special type of quantum correlation stands between quantum entanglement and Bell nonlocality in the hierarchy of quantum correlations, quantum steering is usually described as that one party, Alice, can steer the state of a distant party, Bob, by local measurements on Alice. There are situations where Alice can steer Bob's state but Bob cannot steer Alice's state, or vice versa, which are referred to as one-way steering. Continuous variable entanglement plays an important role in quantum information processing. In general, the quantum fluctuations of the two quadrature components of the continuous variable entangled state are symmetric. We will refer to this as unbiased entanglement. Gaussian biased entangled state is an easily produced special asymmetric quantum entangled state, where the quantum noises of amplitude and phase quadratures are asymmetric, and it has been applied in the field of quantum information. However, the quantum steering properties of Gaussian biased entangled state remains unknown. In this paper, we analyze quantum steering of the bipartite and tripartite Gaussian biased entangled states and the transmission properties of them in noisy channels, and compare the results with quantum steering of Gaussian unbiased entangled states. We generate the bipartite and tripartite biased entangled states by coupling a phase-squeezed state and vacuum states on an optical beam splitter network. Then, we distribute one of the entangled states through noisy channels. The quantum steering of the bipartite and tripartite Gaussian biased entangled states is analyzed theoretically by reconstructing their covariance matrixes, respectively. The results show that, compared with Gaussian unbiased entangled states, the quantum steering regions of biased entangled states are more sensitive to channel noise. And the quantum steering direction of biased entangled states is easier to reverse by changing the amplitude of channel noise. This paper provides a reference for realizing quantum information processing based on quantum steering of biased Gaussian entangled states.

The time-domain balanced homodyne detector (TBHD) can be used to detect the quadratures of the pulsed optical signal directly, and it is a crucial component of the continuous variable quantum key distribution (CVQKD) system. At the receiver side of the CVQKD system, the recovery of clock signal and the monitoring of local oscillator (LO) power is realized using fiber optic couplers, photodetectors and power meters usually. The fiber optical couplers not only reduce the LO power but also introduce security vulnerability. To simplify the structure of the receiver side, reduce the cost and increase the security of CVQKD system, we design and experimentally realize a new type TBHD with clock recovery and power monitoring functions. The detector makes full use of the photoelectron current generated by the cascaded photodiode. It can not only measure the quadratures of the pulsed optical signal, but also monitor the LO power in real-time and generate the clock signal with the same frequency as the LO beam. In experiment, a common mode rejection ratio of 75 dB could be obtained, and a maximum signal-to-noise ratio of 13.50 dB could be measured at a repetition rate of 1 MHz. At the same time, the clock signals with the same frequency as the LO beam were generated, and the output voltage value scales with the LO power was measured. A good linear relationship between the output voltages and the LO powers was obtained. The fitting slope or gain is 2.52×10−7 V/photon, and the sum of residual error squares is 2.51×10−4 V2. Then the output voltage can be used to predict the LO power and the corresponding shot noise variance without using a fiber optical coupler and power meter. The new type TBHD can significantly reduce the complexity and cost of the receiver side of CVQKD system. At the same time, it effectively avoids the security vulnerability due to the varying ratio of the fiber optical coupler and enhance the actual security of the system.

In trace gas detection based on laser absorption spectroscopy, the overlap of different gas absorption spectra affects the extraction of the characteristics of the absorption spectrum, which consequently introduce the error of the deduced concentration. In this paper, a trace gas detector by the combination of a multipass cell and direct absorption spectroscopy is present. BP neural network model and PLS model are utilized, respectively, to restrict the spectral overlap. In order to simplify the training progress, simulated spectral models have been used as training set. The laser frequency are calibrated with the help of the transmission peaks of an F-P cavity and then introduced into the simulation model. As a result, the accuracy of the simulation has been improved. Then, the measured data is acted as test set. The linearity of the system's response to the concentration is greater than 0.99, and the relative error is less than 0.21%. Finally, the influence of etalon noise to the two algorithm has been analyzed and the result shows the concentration error with PLS model is less than 4.4×10-7, which is more than five times that by BP neural network.

ObjectiveQuantum interference radar (QIR) is a promising technology that has been widely developed in modern warfare and civil fields. QIR is information transmission through quantum signals, and quantum signals are greatly disturbed by the transmission environment, so the detection efficiency will also be affected. When detecting photon transmission through the rainfall region, phase delay will occur, resulting in attenuation of quantum signal strength and energy reduction, and thus reducing the accuracy of QIR detection, such as ice crystal particles, tropospheric water clouds, raindrop particles, etc. However, until now, the effect of rainfall on QIR performance has not been studied. Therefore, it is very important to analyze the influence of light scattering characteristics of raindrop particles on QIR detection performance under different rainfall intensity.MethodsAfter linear superposition, raindrop particles of different sizes can still be regarded as spherical particles, similar to equivalent spheres. Firstly, the light scattering characteristics of raindrop particles are analyzed based on Mie scattering theory and Gamma distribution spectrum function. Secondly, according to the scattering characteristics, the energy attenuation of photons passing through the rainfall region is analyzed, and the relationship model between rainfall intensity and link attenuation and transmission distance is established. According to the parity operator detection method, the relationship between rainfall intensity and sensitivity and resolution is studied and analyzed for different pulse photon number and different emission wavelength, and simulation experiments are carried out.Results and DiscussionsThe extinction coefficient increases gradually with the increase of rainfall intensity (Fig. 3). Photon energy decreases with the increase of transmission distance, and the greater the rainfall intensity, the more obvious the photon energy attenuation trend (Fig. 4). Link attenuation increases with the increase of rainfall intensity and transmission distance (Fig. 5). The number of pulse photons has a great influence on the sensitivity and resolution of QIR. With the same number of photons, the sensitivity of QIR decreases with the increase of rainfall intensity; with the increase of photon number, the sensitivity of QIR increases with the increase of photon number when the influence of rainfall is small (Fig. 6). At the same photon number, the resolution of QIR decreases with the increase of rainfall intensity (Fig. 7); at the same incident wavelength, the resolution decreases with the increase of rainfall intensity, but the influence of wavelength on the resolution is not obvious (Fig. 8). In general, selecting the appropriate wavelength and increasing the number of pulse photons can effectively improve the performance of QIR detection.

ObjectiveThe cold atomic absorption imaging technique converts the spatial distribution of ultracold erbium atoms into digital images to extract spatial distribution features, temperature, density, and other information by comparing the light intensity distribution with and without atoms, so a better imaging quality is important for studying the long-range dipole-dipole interaction of ultracold erbium atoms. In practical measurements, the light interference and mechanical vibrations of the imaging system usually cause fringe patterns, limiting the accuracy of imaging and the ability to extract physical parameters. In addition to hardware measures such as using an excellent anti-reflection coating and optimizing the optical path to reduce interference, utilizing algorithms for fringe denoising possesses broader reliability and practicality.MethodThis paper utilizes Principal Component Analysis (PCA) as a powerful statistical tool for analyzing large experimental datasets, specifically for fringe removal in absorption imaging of ultracold erbium atoms. Our approach incorporates spatial shifting of the image to broaden the basis, effectively addressing the common mismatches between absorption and reference images due to mechanical vibrations within the imaging system. Masking operations were employed to eliminate the influence of atomic clouds. Ultimately, an ideal reference image with the same fringe patterns for the absorption image was reconstructed to suppress the fringe patterns caused by light field difference. In order to facilitate operations, we have designed and developed software based on PCA for ultracold erbium atom absorption imaging using the Matlab App Designer.Results and DiscussionsThis study demonstrates an algorithm that efficiently removes fringe patterns in absorption imaging of ultracold erbium atoms. By utilizing this algorithm, we have successfully reduced the noise level to approximately 1/2 of the theoretical limit achieved by traditional methods. Additionally, our approach corrects pixel value differences arising from fluctuations in probe beam power over time, improving the accuracy of extracted temperature and spatial distribution information.ConclusionThis paper applies a denoising algorithm based on Principal Component Analysis to address the fringe noise issue in absorption imaging of ultracold erbium atoms. By using principal component analysis to decompose the extended reference image set and reconstruct an ideal reference image with the same fringe patterns for the absorption image, we effectively suppress the unwanted fringe patterns in the atomic spatial distribution. The quantitative analysis shows that this method suppresses the noise to the quantum limit shot noise level, and the extraction of the ultracold atomic temperature is more accurate after denoising. Based on this, a denoising software for ultracold erbium atom absorption imaging was designed and developed using the Matlab App Designer.

The propagation of intense femtosecond laser pulses in air involves many linear and nonlinear effects, such as diffraction, dispersion, Kerr self-focusing, multiphoton ionization, etc. When the Kerr self-focusing effect and the plasma defocusing effect reach a dynamic equilibrium, a high-intensity "optical filament" is generated. The properties of filamentation have attracted significant attention owing to many interesting phenomena, such as conical emission, third-order harmonic generation, and supercontinuum (SC) radiation. Specifically, the SC spectra induced by filaments undergo a significant extension covering a wide range from the UV to the mid-IR and attracts considerable interest for its potential application in remote sensing detection of atmospheric pollution. Therefore, it is of great significance to explore the propagation of filament and the characteristics of mid-infrared spectral in complex atmospheric environments.Based on the (3D+1) dimensional nonlinear Schrdinger (NLS) equation, the transmission characteristics of femtosecond pulses in air are described. Firstly, under the slowly varying envelope approximation, we use the evolution of the cylindrically symmetric linearly polarized laser electric field along the propagation axis z to describe the propagation dynamics of femtosecond laser pulses in air. Secondly, the time Fourier transform and the spatial Crank-Nicholson difference scheme are used to numerically solve the coupling equation. Finally, by adjusting the laser pulse input parameters (such as input power, waist width and pulse width) and the focal length of the lens, the filaments are generated by intense femtosecond laser pulses at different heights within 1 km from the ground.In this paper, using atmospheric stratification model and numerically analyzing that pressure, beam waist width, pulse width and attenuation of scattering medium influence on the transmission of the filamentation and the characteristics of supercontinuum spectrum. The results show that: Small changes in pressure lead to significant changes in the characteristics of optical filaments (starting position, length, stability, energy flux, and axial intensity time distribution), which directly affect the characteristics of the supercontinuum spectrum excited by plasma filaments; With the increase of waist width and pulse width, the starting point of the filaments is closer and closer to the ground. Then, by analyzing the intensity spectra, the effects of beam waist width and pulse width on mid-infrared spectra are further discussed. It is found that the mid-infrared spectral intensity decreases with the increase of beam waist width under the same focal length. As the filaments are produced farther from the ground, the intensity of the mid-infrared spectrum becomes stronger. At the same time, the spectrum excited by plasma filaments can cover the whole wavelength range of visible light, and the redshift wavelength can extend to 5 m; Although the scattering medium causes exponential attenuation of laser energy, especially when the laser beam reaches an altitude of about 500 m, this attenuation has a more significant effect on the characteristics of the optical filaments. However, with appropriate initial parameters, the attenuation has a minimal impact on the mid-infrared spectrum intensity within the supercontinuum spectrum. Therefore, it is extremely important to regulate these parameters, and this study provides an important theoretical basis for detecting the composition of atmospheric pollutants by using mid-infrared spectroscopy at different altitudes in the upper air.

ObjectiveHigh-order effects in optical fibers, such as third-order dispersion and fifth-order nonlinear effects, are common influencing factors in practical optical fiber transmission, significantly impacting the transmission and characteristics of optical solitons. Through systematic mathematical modeling and analysis, this study aims to reveal the impact of these high-order effects on the dynamic behavior of vector solitons and to explore the characteristics and behaviors of vector solitons. By providing theoretical foundations and experimental guidance for the application of optical solitons in fiber transmission, this research can further expand the transmission capacity of optical communication and provide essential support for the construction of future high-capacity, long-distance communication networks.MethodBased on the coupled nonlinear Schrdinger equation (NLS), this study employs an analytical approach - the variational method, to investigate the dynamic characteristics of bright and dark vector solitons in birefringent optical fibers considering third-order dispersion and fifth-order nonlinear effects. The variational method is used to derive the evolution equations for the parameters of the two types of solitons, and the impact of third-order dispersion and fifth-order nonlinearity on soliton transmission and interaction is analyzed through graphical representations.Results and DiscussionsThis study examines the dynamic characteristics of the orthogonal polarization components of bright and dark vector solitons in birefringent optical fibers considering high-order effects such as third-order dispersion and fifth-order nonlinearity. The findings are as follows: In terms of transmission characteristics, both types of vector solitons in birefringent optical fibers exhibit properties of maintaining constant amplitude and conserving energy. Positive third-order dispersion reduces the rate of change of the center position of bright solitons with transmission distance, while negative third-order dispersion increases this rate for bright solitons and has the opposite effect on the center position of dark vector solitons. Fifth-order nonlinearity does not affect the transmission speed and center position of solitons. Regarding the interaction between soliton components, fifth-order nonlinearity has no direct relationship with the interaction between the polarization components of vector solitons. Positive third-order dispersion can either enhance or weaken the effective interaction between solitons, depending on the specific range of its values, while negative third-order dispersion always enhances the interaction between solitons. Additionally, in the absence of third-order dispersion, polarization components of vector solitons that are very close to each other consistently repel each other during transmission in birefringent optical fibers. The stronger the soliton amplitude, the stronger the internal interaction, which is detrimental to the stable transmission of vector solitons.ConclusionThe research findings indicate that third-order dispersion and fifth-order nonlinearity do not affect the amplitude of vector solitons, which remains constant during transmission. Positive third-order dispersion reduces the rate of change of the center position of bright solitons with transmission distance, whereas for dark solitons, the effect is reversed. The rate of change in phase with transmission distance is linearly related to the values of the third-order dispersion coefficient and the fifth-order nonlinearity coefficient, while fifth-order nonlinearity does not affect the transmission speed and center position of solitons. Additionally, positive third-order dispersion can either enhance or weaken the interaction between soliton components, while negative third-order dispersion always enhances their interaction. In the absence of third-order dispersion, polarization components of solitons that are very close to each other consistently repel each other during transmission, with stronger amplitudes leading to stronger interactions, which are detrimental to the stable transmission of solitons; fifth-order nonlinearity has no direct effect on the interaction between soliton components. These results contribute to a deeper understanding of the dynamic behavior of vector solitons in birefringent optical fibers and provide important references for the design and optimization of optical fiber communication systems and transmission.