Realization of double uniform line self-focusing of elliptical Airyprime beams.

Double line self-focusing characteristics of elliptical Airyprime beams (EAPBs) with different elliptical vertical-axis factor ß are investigated by varying the main ring radius r0. Overly large or small r0 results in the inhomogeneous distribution of light intensity at one linear focus of the double line self-focusing. Only when r0 is appropriate and ß is within a certain range, can double uniform line self-focusing happen to the EAPB. Moreover, the self-focusing ability of the second line self-focusing is weaken than that of the first line self-focusing. Under the premise of our selected values of beam parameters, the EAPB can achieve double uniform line self-focusing when r0 = 0.3 mm and ß = 0.58∼0.71. The focal length of the first line self-focusing, the lengths of double linear focus, and the self-focusing abilities of the double uniform line self-focusing can be regulated by varying ß within the range of 0.58∼0.71. If ß is smaller than 0.58 or larger than 0.71, it will lead to nonuniform line self-focusing. An explanation of the physical mechanism behind the double uniform line self-focusing of the EAPB is proposed. Finally, the experimental measurements of the line self-focusing of the EAPB confirm the validity of the above conclusions. This research provides a new solution on how to generate double uniform line self-focusing and new insights into the practical application of elliptical self-focusing beams.

Realization of a circularly transformed Airyprime beam with powerful autofocusing ability.

The reported autofocusing ability of a ring Airyprime beam array reaches up to 8632.40, while the strongest autofocusing ability of a circular Airyprime beam (CAPB) is only 1822.49. How can the autofocusing ability of a single beam reach the autofocusing ability of a beam array? To achieve this goal, a circularly transformed Airyprime beam (CTAPB) is introduced by following two steps. First, a circular equation transformation on the two transverse coordinates in the electric field expression of a propagating Airyprime beam is performed. Then, the electric field expression of a propagating Airyprime beam is integrated over the angle. The intensity profile of a CTAPB on the initial plane changes significantly with varying the primary ring radius r0. With increasing r0, therefore, the autofocusing ability of a CTAPB undergoes a process of first increasing and then decreasing, while the focal length always increases. A CTAPB exhibits more powerful autofocusing ability than a CAPB. The maximum autofocusing ability of a CTAPB can reach up to 8634.76, which is 4.74 times that of a CAPB, while the corresponding focal length is 95.11% of a CAPB. A CTAPB on the initial plane can be approximately characterized by a ring Airyprime beam array with sufficient number of Airyprime beams. Due to the better symmetry, a CTAPB has a slightly stronger autofocusing ability than a ring Airyprime beam array and almost the same focal length as a ring Airyprime beam array. The CTAPB is also experimentally generated, and the experimental results indicate that the CTAPB has powerful autofocusing ability. As a replacement of a CAPB and a ring Airyprime beam array, this introduced CTAPB can be applied to the scenes which involve abruptly autofocusing effect.

Effects of low concentration of gallic acid on the growth and microcystin production of Microcystis aeruginosa.

Gallic acid (GA) is an allelochemical that has been utilized in high concentrations for the management of harmful algal blooms (HABs). However, there is limited knowledge regarding its impact on the growth of M. aeruginosa as the GA concentration transitions from high to low during the HABs control process. This study has revealed that as the GA concentration decreases (from 10 mg/L to 0.001 µg/L), a dose-response relationship becomes apparent in the growth of M. aeruginosa and microcystin production, characterized by high-dose inhibition and low-dose stimulation. Notably, at the concentration of 0.1 µg/L GA, the most significant growth-promoting effect on both growth and MCs synthesis was observed. The growth rate and maximum cell density were increased by 1.09 and 1.16 times, respectively, compared to those of the control group. Additionally, the contents of MCs synthesis saw a remarkable increase, up by 1.85 times. Furthermore, lower GA concentrations stimulated the viability of cyanobacterial cells, resulting in substantially higher levels of reactive oxygen species (ROS) and chlorophyll-a (Chl a) compared to other concentrations. Most importantly, the expression of genes governing MCs synthesis was significantly upregulated, which appears to be the primary driver behind the significantly higher MCs levels compared to other conditions. The ecological risk quotient (RQ) value of 0.1 µg/L GA was the highest of all experimental groups, which was approximately 30 times higher than that of the control, indicating moderate risk. Therefore, it is essential to pay attention to the effect of M. aeruginosa growth, metabolism and water ecological risk under the process of reducing GA concentration after dosing during the HABs control process.

Applications of optical property measurement for quality evaluation of agri-food products: a review.

Spectroscopic techniques coupled with chemometric approaches have been widely used for quality evaluation of agricultural and food (agri-food) products due to the nondestructive, simple, fast, and easy characters. However, these techniques face the issues or challenges of relatively weak robustness, generalizability, and applicability in modeling and prediction because they measure the aggregate amount of light interaction with tissues, resulting in the combined effect of absorption and scattering of photons. Optical property measurement could separate absorption from scattering, providing new insights into more reliable prediction performance in quality evaluation, which is attracting increasing attention. In this review, a brief overview of the currently popular measurement techniques, in terms of light transfer principles and data analysis algorithms, is first presented. Then, the emphases are put on the recent advances of these techniques for measuring optical properties of agri-food products since 2000. Corresponding applications on qualitative and quantitative analyses of quality evaluation, as well as light transfer simulations within tissues, were reviewed. Furthermore, the leading groups working on optical property measurement worldwide are highlighted, which is the first summary to the best of our knowledge. Finally, challenges for optical property measurement are discussed, and some viewpoints on future research directions are also given.

HighlightsEmerging techniques for measuring optical properties are briefly introducedQualitative analyses of maturity evaluation and defect detection are reviewedQuantitative analyses of attribute prediction and microstructure estimation are presentedLight transfer simulations based on optical properties are comprehensively discussedLeading groups are summarized for the first time, to the best of our knowledgeChallenges and prospects for optical property measurement are given.

Key to an extension or shortening of focal length in the enhancement of autofocusing ability of a circular Airyprime beam caused by a linear chirp factor.

Researchers are puzzled whether the enhancement of the abruptly autofocusing ability caused by a linear chirp factor is accompanied by the shortening or the extension of the focal length. In this Letter, a circular Airyprime beam is chosen as the research object to reveal this mystery. Extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability depends on the exponential decay factor a and the dimensionless radius of the primary ring. When a is small enough, there exists a critical value for the dimensionless radius. If the dimensionless radius is greater than the critical value, the focal length is shortened in the enhancement of the abruptly autofocusing ability. If the dimensionless radius is less than the critical value, the focal length is extended in the enhancement of the abruptly autofocusing ability. As a increases, the critical value for the dimensionless radius decreases until it reaches zero. The physical mechanism of extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability is elucidated.

Analysis of Light Penetration Depth in Apple Tissues by Depth-Resolved Spatial-Frequency Domain Imaging.

Spatial-frequency domain imaging (SFDI) has been developed as an emerging modality for detecting early-stage bruises of fruits, such as apples, due to its unique advantage of a depth-resolved imaging feature. This paper presents theoretical and experimental analyses to determine the light penetration depth in apple tissues under spatially modulated illumination. Simulation and practical experiments were then carried out to explore the maximum light penetration depths in 'Golden Delicious' apples. Then, apple experiments for early-stage bruise detection using the estimated reduced scattering coefficient mapping were conducted to validate the results of light penetration depths. The results showed that the simulations produced comparable or a little larger light penetration depth in apple tissues (~2.2 mm) than the practical experiment (~1.8 mm or ~2.3 mm). Apple peel further decreased the light penetration depth due to the high absorption properties of pigment contents. Apple bruises located beneath the surface peel with the depth of about 0-1.2 mm could be effectively detected by the SFDI technique. This study, to our knowledge, made the first effort to investigate the light penetration depth in apple tissues by SFDI, which would provide useful information for enhanced detection of early-stage apple bruising by selecting the appropriate spatial frequency.

Investigation of the effect of chirped factors on the interference enhancement effect of an Airyprime beam propagating in free space.

The first-order and the second-order chirped factors are imposed on the Airyprime beam, and the analytical expression of the chirped Airyprime beam propagating in free space is derived. The phenomenon that the peak light intensity on observation plane other than initial plane is greater than that on initial plane is defined as the interference enhancement effect, which is caused by the coherent superposition of the chirped Airyprime and the chirped Airy-related modes. The effects of the first-order and the second-order chirped factors on the interference enhancement effect are theoretically investigated, respectively. The first-order chirped factor only affects the transverse coordinates where the maximum light intensity appears. The strength of interference enhancement effect of the chirped Airyprime beam with any negative second-order chirped factor must be stronger than that of the conventional Airyprime beam. However, the improvement of the strength of interference enhancement effect caused by the negative second-order chirped factor is realized at the expense of shortening the position where the maximum light intensity appears and the range of interference enhancement effect. The chirped Airyprime beam is also experimentally generated, and the effects of the first-order and the second-order chirped factors on the interference enhancement effect are experimentally confirmed. This study provides a scheme to improve the strength of interference enhancement effect by controlling the second-order chirped factor. Compared with traditional intensity enhancement methods such as using lens focusing, our scheme is flexible and easy to implement. This research is beneficial to the practical applications such as spatial optical communication and laser processing.

Simultaneously enhancing autofocusing ability and extending focal length for a ring Airyprime beam array by a linear chirp.

It is of great significance to solve the problem that improving autofocusing ability is always at the cost of shortening focal length. By introducing a linear chirp into a ring Airyprime beam array, an optimization scheme to simultaneously achieve the enhancement of autofocusing ability and the extension of focal length is proposed. The autofocusing ability can be enhanced by up to 72.28%, and the corresponding focal length is extended by 34.81%. The focal length can be extended by 110.28% at most, and the corresponding autofocusing ability is improved by 48.59%. To verify the feasibility of this scheme, we have carried out an experiment for the generation of a ring Airyprime beam array with a linear chirp, and the experimental results for autofocusing ability and focal length are in good agreement with theoretical results. Our findings have potential applications in many aspects, such as free space optical communication.

Effect of chirped factors on the abrupt autofocusing ability of a chirped circular Airyprime beam.

Recently, a new type of abruptly autofocusing beam called circular Airyprime beam (CAPB) has been reported. Its abrupt autofocusing ability has been proven to be approximately seven times that of a circular Airy beam under the same conditions. Further improving the abrupt autofocusing ability of the CAPB without changing the beam parameters is a concern in optical research. In this study, we investigated the effect of introducing first- and second-order chirped factors on the abrupt autofocusing ability of the CAPB. When the positive first-order chirped factor was below the saturated chirped value, the abrupt autofocusing ability of the chirped CAPB was stronger and the focus position was smaller compared with those of the conventional CAPB. Regarding the abrupt autofocusing ability, there was an optimal value for the first-order chirped factor. At the optimal value, the abrupt autofocusing ability of the chirped CAPB was the strongest. On the other hand, a positive second-order chirped factor promoted the abrupt autofocusing ability of the CAPB and shortened the focus position. The introduction of such value was more effective than the introduction of a positive first-order chirped factor in promoting abrupt autofocusing of the CAPB. The abrupt autofocusing ability of the CAPB was further improved by combining the optimal first-order chirped factor and a positive second-order chirped factor. Finally, the chirped CAPB was experimentally generated, and the corresponding abrupt autofocusing behaviors were measured, validating the theoretical results. Overall, we provide an approach for improving abruptly autofocusing CAPBs.

A Nano Refractive Index Sensing Structure for Monitoring Hemoglobin Concentration in Human Body.

This paper proposes a nanosensor structure consisting of a metal-insulator-metal (MIM) waveguide with a rectangular root and a double-ring (SRRDR) with a rectangular cavity. In this paper, the cause and internal mechanism of Fano resonance are investigated by the finite element method (FEM), and the transport characteristics are optimized by changing various parameters of the structure. The results show that the structure can achieve double Fano resonance. Due to the destructive disturbance between the wideband mode of the inverted rectangle on the bus waveguide and the narrowband mode of the SRRDR, the output spectrum of the system shows an obvious asymmetric Fano diagram, and the structural parameters of the sensor have a great influence on the Fano resonance. By changing the sensitive parameters, the optimal sensitivity of the refractive index nanosensor is 2280 nm/RIU, and the coefficient of excellence (FOM) is 76.7. In addition, the proposed high-sensitivity nanosensor will be used to detect hemoglobin concentration in blood, which has positive applications for biosensors and has great potential for future nanosensing and optical integration systems.

Generation of finite energy Airyprime beams by Airy transformation.

In this paper, the lone generation of a new kind of beam named finite energy Airyprime (FEA) beam through the Airy transformation of the coherent superposition of four different elegant Hermite-Gaussian modes is reported for the first time. Analytical expressions of the centroid, the r.m.s beam width, the divergence angle, and the beam propagation factor of the FEA beam are derived in the output plane of Airy transformation, respectively. The effects of the Airy control parameters on the intensity distribution, the centroid, the r.m.s beam width, and the beam propagation factor are examined in detail through numerical examples. Unlike the Airy beam, the FEA beam upon free space propagation will be associated with an additional Airy mode, and the beam pattern of the FEA beams propagating in free space will evolve into a solid beam spot with two tails along two transverse directions, as well as the the intensity of main lobe of the FEA beam decays much slowly during free space propagation. Further, an experiment setup is established to generate the FEA beam via Airy transformation of four mixed elegant Hermite-Gaussian modes. The propagation characteristics such as the intensity distribution, the r.m.s beam width and the beam propagation factor are measured. The experimental results agree well with the theoretical predictions. Our study affords an effective and novel approach to generate the FEA beam, and is beneficial to expand the potential application of the FEA beam.

Interference enhancement effect in a single Airyprime beam propagating in free space.

An analytical expression of a single Airyprime beam propagating in free space is derived. Upon propagation in free space, a single Airyprime beam in arbitrary transverse direction is the coherent superposition of the Airyprime and the Airy-related modes, which results in the interference enhancement effect under the appropriate condition. The Airy-related mode is the conventional propagating Airy mode with an additional π/2 phase shift and a weight coefficient of half the normalized propagation distance. Due to the peak light intensity in the initial plane being set to be 1, the strength of interference enhancement effect is characterized by the maximum light intensity. The maximum light intensity of a single Airyprime beam propagating in free space is independent of the scaling factor and is only decided by the exponential decay factor. When the exponential decay factor is above the saturated value, the interference enhancement effect disappears. When the exponential decay factor decreases from the saturated value, the maximum light intensity of a single propagating Airyprime beam increases, and the position of maximum light intensity is getting farther away. With the increase of the scaling factor, the position of maximum light intensity of a single propagating Airyprime beam is extended. The intensity distribution and the transverse Poynting vector of a single propagating Airyprime beam are demonstrated in different observation planes of free space. The flow direction of transverse energy flux effectively supports the interference enhancement effect of a single propagating Airyprime beam. The Airyprime beam is experimentally generated, and the interference enhancement effect is experimentally confirmed. The interference enhancement effect is conducive to the practical application of a single Airyprime beam.

Abruptly autofocusing of generalized circular Airy derivative beams.

In this paper, we introduce a novel kind of abrupt autofocusing beams namely the generalized circular Airy derivative beams (CADBs) as an extension of circular Airy beam (CAB). The propagation dynamics of the CADBs is examined theoretically. Our results show that the CADBs exhibit stronger autofocusing ability than the CAB under the same condition. The physical mechanism of the abruptly autofocusing of the CADBs is interpreted by mimicking the Fresnel zone plate lens. Here, the abruptly autofocusing ability is described by a ratio K = Ifm/I0m where Ifm and I0m correspond to the maximum intensities in the focal and the source planes, respectively. As an example, the K-value of the circular Airyprime beam (CAPB, the first-order Airy derivative beam) is about 7 times of that of the CAB. In addition, the CAPB have narrower FWHM (full width at half maxima) in the focus position than the CAB, and the focal spot size of the CAPB is smaller than that of the CAB. Furthermore, we establish an optical system involving a phase-only spatial light modulator to generate the CAPB and measure its autofocusing characteristics experimentally. The measured K-value is about 9.4 percentage error between theory and experiment owing to the imperfection generation of the CAPB. The proposed generalized CADBs will find applications in biomedical treatment, optical manipulation and so on.

Dependence of autofocusing ability of a ring Airyprime beams array on the number of beamlets.

A ring Airyprime beams (RAPB) array, which consists of N evenly displaced Airyprime beamlets in the initial plane, is first introduced, to the best of our knowledge, in this Letter. Here, we focus on the effect of the number of beamlets N on the autofocusing ability of the RAPB array. With the given beam parameters, an optimal number of beamlets, which is the minimum number of beamlets to realize the saturated autofocusing ability, is selected. The focal spot size of the RAPB array remains unchanged before the number of beamlets reaches the optimal number of beamlets. More importantly, the saturated autofocusing ability of the RAPB array is stronger than that of the corresponding circular Airyprime beam. The physical mechanism of the saturated autofocusing ability of the RAPB array is interpreted by simulating the Fresnel zone plate lens. The influence of the number of beamlets on the autofocusing ability of the ring Airy beams (RAB) array under the same beam parameters with the RAPB array is also presented for comparison. Our findings are beneficial for the design and application of the ring beams array.

Transformation of a Hermite-Gaussian beam by an Airy transform optical system.

Analytical expression of the Airy transform of an arbitrary Hermite-Gaussian beam is derived. The optical field in the x-direction of the Airy transform of Hermite-Gaussian beams with transverse mode number m is the sum of the zero-order derivative to mth-order derivative of the Airy function with different weight coefficients. The analytical expressions of the centre of gravity and the beam spot size of an arbitrary Hermite-Gaussian beam passing through an Airy transform optical system are also presented, which are very concise. Because the Airy transform of a Hermite-Gaussian beam has the same evolution law in the two transverse directions, only the effects of the control parameter α and the transverse mode number m on the normalized intensity distribution, the centre of gravity, and the beam spot size in the x-direction are theoretically investigated, respectively. The Airy transform of Hermite-Gaussian beams is also realized in the experiment. The influence of the control parameters on the normalized intensity distribution, the centre of gravity, and the beam spot size is experimentally investigated, respectively. The experimental results are consistent with the theoretical simulation results. When Hermite-Gaussian beams pass through an Airy transform optical system, the number of lobes may change, and the importance of lobes with the same status in the input plane may become different. By using the Airy transform of Hermite-Gaussian beams, the practical applications of Hermite-Gaussian beams can be extended.

Airy transform of Laguerre-Gaussian beams.

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG01, LG02, LG11, and LG12 modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG01, LG02, LG11, and LG12 modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and ß on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and ß decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and ß, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.

Fullerene-intercalated graphene nanocontainers for gas storage and sustained release.

Molecular dynamics simulations are performed to investigate the storage capacity and sustained release of nitrogen (N2) in the graphene-based nanocontainers. Sandwiched graphene-fullerene composites (SGFC) composed of two parallel graphene sheets and intercalated fullerenes are constructed. The simulation results show that the mass density of N2 at the first layer is extremely high, due to the strong adsorption ability of graphene sheets. And N2 molecules at this adsorbed layer are thermodynamically stable. Furthermore, we analyze the storage efficiency of SGFC. In general, the gravimetric and volumetric capacities decrease with the increasing number of intercalated fullerenes. On the contrary, the stability of SGFC is enhanced by more intercalated fullerenes. We therefore make a compromise and propose that 1 fullerene per 5 nm2 graphene to build a SGFC, which is much effective to storage N2. We also verify the reversibility that N2 can sustainably release from the SGFC. Our results may provide insights into the design of graphene-based nanocomposites for gas storage and sustained release with excellent structural stability and high storage capacity. Graphical abstract.

Beam propagation factor and kurtosis parameter of hollow vortex Gaussian beams: an alternative method.

Based on the second-order moments, an analytical and concise expression of the beam propagation factor of a hollow vortex Gaussian beam has been derived, which is applicable for an arbitrary topological charge $m$m. The beam propagation factor is determined by the beam order $n$n and the topological charge $m$m. With increasing the topological charge $m$m, the beam propagation factor increases. However, the effect of the beam order $n$n on the beam propagation factor is associated with the topological charge $m$m. By using the transformation formula of higher-order intensity moments, an analytical expression of the kurtosis parameter of a hollow vortex Gaussian beam passing through a paraxial and real $ABCD$ABCD optical system has been presented. The kurtosis parameter is determined by the beam order $n$n, the topological charge $m$m, and the position of observation plane $ \eta $η. The influence of the beam order $n$n on the kurtosis parameter is related with the topological charge $m$m and the position parameter $ \eta $η. When the beam order $n$n is larger than 1, the kurtosis parameter in different observation $\eta$η-planes decreases and tends to a stable value with increasing the topological charge $m$m. When $m = \pm {2}n$m=±2n, the kurtosis parameter is independent of the position parameter $ \eta $η and keeps unvaried during the beam propagation. Regardless of the values of $n$n and $m$m, the kurtosis parameter must tend to a saturated value or a stable value as the position parameter $ \eta $η increases to a sufficiently large value. This research is beneficial to the practical application of a hollow vortex Gaussian beam.

Non-paraxial propagation of a circular Lorentz-Gauss vortex beam.

The optical field of a circular Lorentz-Gauss vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integrals. The expression of the longitudinal component of the angular momentum density of a circular Lorentz-Gauss vortex beam is also presented. The normalized intensity, the three components of intensity, and the longitudinal angular momentum density of a circular Lorentz-Gauss vortex beam are demonstrated in the reference plane, respectively. The effects of linearly polarized angle, topological charge, and Lorentzian width parameter on the intensity, the three components of intensity, and the longitudinal angular momentum density are analyzed, respectively. The normalized intensity and the longitudinal angular momentum density of a paraxial circular Lorentz-Gauss vortex beam are also shown in the same reference plane. The missing longitudinal component of the optical field will result in deficient patterns of the intensity and the longitudinal angular momentum density. In terms of the longitudinal angular momentum density, the longitudinal component of a circular Lorentz-Gauss vortex beam cannot be neglected under the condition that the Lorentzian width parameter and the Gaussian waist are of the order of the optical wavelength.

Circular Lorentz-Gauss beams.

A circular Lorentz-Gauss beam is introduced. The analytical optical field of the circular Lorentz-Gauss beam passing through a paraxial ABCD optical system is derived. Based on the second- and higher-order moments of the light intensity, the analytical beam propagation factor of a circular Lorentz-Gauss beam and the analytical kurtosis parameter of a circular Lorentz-Gauss beam passing through a paraxial ABCD optical system have also been derived. The properties of the circular Lorentz-Gauss beam propagating in free space are demonstrated. The normalized intensity distribution, the beam half width, the beam waist, the divergence, the beam propagation factor, and the kurtosis parameter of the circular Lorentz-Gauss beam are compared with those of the corresponding Lorentz-Gauss beam, respectively. The main difference between the circular Lorentz-Gauss and the Lorentz-Gauss beams is their different peripheries. The circular Lorentz-Gauss beam has better symmetry than the Lorentz-Gauss beam. The beam propagation factor of the circular Lorentz-Gauss beam is always slightly larger than that of the Lorentz-Gauss beam. Therefore, the circular Lorentz-Gauss beam is the enrichment and supplement of the existing Lorentz-Gauss beam.