Wavelength dependence of linear polarization in the

第50卷第1期 Vol.50No.l红外与激光工程Infrared and Laser Engineering2021年1月Jan. 2021超表面透镜的宽带消色差成像（特邀）莫昊燃1’2,纪子韬\郑义栋\梁文耀\虞华康\李志远1(1.华南理工大学物理与光电学院，广东广州510641;2.广东晶启激光科技有限公司，广东东莞523808)摘要：超透镜是一种由二维亚波长阵列结构表面所设计的透镜，其对光场中振幅、相位和偏振的调控能力较灵活，同时具有低损耗、易集成、超轻薄等优点，近些年引起了科研人员广泛的研究兴趣。

然而在大多数情况下，针对特定波长设计的超透镜会遭受较大的色差，从而限制了其在多波长或宽带应 用中的成像作用。

超透镜因其二维平面结构引入了新的自由度，在对色差的消除上体现了新的潜力。

文中报道了多种不同的消色差超透镜设计及其消色差调控机理，并对现有的消色差超透镜从调制波段 类型进行了分类，如对离散波长的和对连续波长的消色差超表面透镜，后者又可从工作模式上分类为透射型和反射型，最后介绍了超透镜阵列在成像上的应用以及其在大景深宽带消色差器件上的前景。

关键词：超表面；超透镜；消色差聚焦透镜中图分类号：0436 文献标志码：A DOI：10.3788/IRLA20211005Broadband achromatic imaging with metalens {Invited)Mo Haoran1’2,Ji Zitao1，Zheng Yidong1，Liang Wenyao1，Yu Huakang1，Li Zhiyuan1(1. School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641, China;2. Guangdong Full-spectra Laser Technology Co., Ltd, Dongguan 523808, China)Abstract:Metalens,the specific type of lens designed with the surfaces mading of two dimensional array at the subwavelength scale,has shown great flexibilities to control the light field,including the arbitrary modulation abilities of amplitude,phase and polarization at the subwavelength scale.Moreover,the metalens possesses the unique advantages of low loss,integratable and conformable design and ultrathin,therefore attracts immense attentions in recent years.However,in most cases,the metalens designed for a specific wavelength may penetrate through the large chromatic aberration,which limits their usefulness in multi-wavelength or broadband applications.On the other hand,the metalens has renewed new degrees of freedom due to its two-dimensional planar structure,which has the potential in the elimination of chromatic aberration.Some different typical achromatic metalens designs and their achromatic modulation mechanism were reviewed,the existing achromatic metalens were classified from the types of modulated light bands,such as the achromatic matelens for discrete and continuous wavelength respectively,and the latter can be classified as transmissive and reflective from the working mode.Finally,the application of metalenses array in imaging and their prospect of broadband achromatic devices of large depth of field were introduced.Key words:metasurfaces;metalens;achromatic focusing lens收稿日期:2020-11 -14;修订日期:2020-12-29基金项目:国家重点研发计划（2018YFA0306200);国家自然科学基金（11974119, 12074127, 11504114);广州市科技计划项目(201904010105);中央高校基本科研业务费专项资金(2019ZZ50);华南理工大学教研教改项目（x2wl-Yl 190281)20211005-1第1期红外与激光工程第50卷0引言透镜是光学应用的基本元件，在数码相机、激 光、光学传感、安防、车载等各个领域都有着广泛的 应用。

1, in the crystal diffraction, can use the visible light? The relationship between the diffraction intensity and the diffraction intensity of the high index crystal clusters is higher than that of the low index crystal clusters.2, try to prove that the face centered cubic lattice is body centered cubic; cubic lattice is face centered cubic.3, covalent binding, two electron atom cloud overlap attraction, and close to the atomic, electronic clouds overlap will produce enormous repulsion. How to explain it.4, one-dimensional atomic chain, positive and negative ion distance is a, and the Madelung constant.5, what is the difference between a long wavelength optical wave and long wave acoustic branches in nature? From the experimental curve, a high density of lattice wave modes. Long acoustical waves can lead to macroscopic polarization of ionic crystals.6, the atomic mass of M, spacing a, restoring force constants for simple one-dimensional lattice B, the frequency of the wave, and for(1) the total energy of the wave,(2) the average total energy of each atom.7, tight binding model, the inner layer of electrons can be compared with the outer band, which is wide, why?8, the known one-dimensional lattice of electrons can beIn the formula, a is the lattice constant, and M is the mass of the electron.(1) band width,(2) the average speed of electrons,(3) effective mass of electrons at the top and bottom of the band1.1 in crystallography, the cell is selected according to what properties of crystal?[answer]In crystallography, the cell selection principle is to consider the periodic and crystal structure considering macroscopic crystal symmetry.Six what is the crystal system of the 1.2 corners of the compact and a unit cell containing a few atoms?[answer]Six angle stacking six angle system, a cell (parallelepiped) contains two atoms.1.3 in the crystal diffraction, why not use visible light?[answer]The magnitude of the distance between the atoms in crystal meters to the atomic lattice became diffractive grating, wavelength Ying Xiaoyu meters. But the wavelength of visible light was 7.6?4.0 meters, is 1000 times the distance between the atoms in crystal. Therefore, in crystal diffraction, can not use visible light.2.1 covalent binding, two electron atom cloud overlap attraction, and close to the atomic, electronic clouds overlap will produce enormous repulsion. How do you explain it?[answer]Covalent binding, the formation of covalent bond pairing of electrons, they spin in the opposite direction, the two electron electron clouds overlap makes the energy of the system is reduced, stable structure. But when atoms near, inside the atom filled shell electron electron clouds overlap, quantum states of the same electronic produced enormous repulsion, the energy of the system increases rapidly.2.2 why many metals are dense structures?[answer]Metal binding by principle of minimum energy constraints and atoms and a total of electron cloud of the Coulomb energy should as far as possible low (absolute value as much as possible). Atomic more compact, atom and a total of electron cloud on the more closely, Coulomb energy is low. So, many metal structure for stacking structure.3.1 what is the normal vibration mode? Whether the normal vibration wave number, wave number or vibration mode number is the same thing?[answer]The vibration of the vibration frequency of the vibration of the resonant vibration of neglect to discuss in order to make the problem is simplified and can seize the main contradiction in the analysis of lattice vibrations, the inter atomic interaction in a Taylor series in the non linearapproximation called harmonic approximation. In the harmonic approximation, by N atoms of crystal lattice vibration, equivalent 3N independent harmonic oscillator. Each sub model called normal vibration mode, which corresponds to all the atoms in the model, it is the lattice vibrational modes in the most simple basic vibration mode. Atoms, or said lattice vibration wave is usually a normal vibrational modes of linear superposition.Normal vibration number, lattice, or the number of lattice vibration mode number is one thing, this number is equal to all the atoms in a crystal and the number of degrees of freedom, which is equal to 3N.What is the difference between the 3.2 long branch of optical lattice waves and long wave acoustic branches in nature?[answer]Characteristics of long wavelength optical lattice is within each cell in different atoms relative vibration, vibration frequency is high, it contains all of the lattice vibrations of the highest frequency of vibration mode. Long acoustic branches of lattice is characterized in that the original cells of different atomic no relative displacement, the original cells do movement as a whole, the vibration frequency is low, it contains the lattice vibration frequency of the lowest mode of vibration, wave velocity is a constant. Any crystal there are acoustic branches of lattice, but simple lattice (non lattices) crystal optical lattice does not exist.3.3 the temperature must be, the number of phonons of an optical wave is much, or the number of phonons in the acoustic wave.[answer]The frequency of the wave (average) phonon number.Because the frequency of the optical wave is higher than the frequency of the acoustic wave, (), (), so in the temperature of a certain case, the number of phonons of an optical wave is less than the number of phonons of acoustic wave.3.4 long acoustical waves can lead to macroscopic polarization of ionic crystals?[answer]Long wavelength optical lattice so can lead to macroscopic polarization of ionic crystals, the root is long optical lattice wave makes the original cell in different atoms (positive and negative ions) produced a relative displacement. Is the characteristics of long wavelength acoustical lattice waves, primitive cell in all atom has no relative displacement. So long wavelength acousticallattice waves cannot lead to macroscopic polarization of ionic crystals.3.5 do you think there is a strong infrared absorption of the simple lattice?[answer]Experiments have shown that ionic crystals can strongly absorb the far infrared light wave. The root of this phenomenon is in ionic crystals of long optical wave with far infrared electromagnetic field strongly coupled. Simple lattice does not exist in the optical wave, so simple lattice does not absorb far infrared light wave.3.6 what is the root cause of the deviation between the Einstein model and the experiment at low temperature?[answer]According to the definition of the Einstein temperature, Einstein model of lattice wave with a frequency of about, belonging to the optical frequency. But the optical lattice in the low temperature contribution to the heat capacity is very small, low temperature of heat capacity with large is mainly long wavelength acoustical lattice waves. That is to say Einstein did not test on account of its acoustic wave contribution to the heat capacity is Einstein model at low temperature and the deviation of the roots.3.7 in very low temperatures, the Debye model agrees well with the experiment and why?[answer]At very low temperature, not only the optical wave to stimulate and phonon energies are larger for the short wavelength acoustical lattice waves have not been excited, get excited just phonon energy is small long wavelength acoustical lattice waves. Long wavelength acoustical lattice waves elastic wave. Debye model only considering the elastic wave to the heat capacity contribution. Because of this, at very low temperatures, the Debye model and fact consistent, natural and experimental match.4.2 what is the characteristic of the electron in the boundary of the Brillouin zone?[answer]Electronic energy band depends on the direction of the wave vector, in either direction, on the boundary of the Brillouin zone, nearly free electron band usually appear on the band gap. If the electronic boundary and reciprocal lattice vector orthogonal, the width of the band gap is periodic potential field of pay in the Fourier series coefficients.On the boundary of the Brillouin zone, the slope is zero in the direction perpendicular to theboundary of the Brillouin zone, that is, the energy of the electron is orthogonal to the boundary of the Brillouin zone.4.3 when the wave vector of the electron falls on the boundary of the Brillouin zone, how can the effective mass of the electron differ from the real quality?[answer]In addition to the external force of the electron in the crystal, and the lattice interaction, an external force is F, the force of the lattice on the electron is Fl, and the acceleration of the electron is.But the specific form of Fl is difficult to learn. To make the formula does not contain Fl, but also to maintain the identity of the left and right, then only.Group M and m and obviously, the lattice of electronic effect is weak, the effective mass m * real quality difference is smaller and smaller. On the contrary, the lattice of electronic effect is strong, effective mass m * real quality difference is bigger and bigger. When the electron wave vector falls in the Brillouin zone boundary, and the Brillouin zone boundary parallel to the crystal surface for electron scattering effect of the strongest. The crystal surface reflection direction, the lattice scattering wave phase same superposition formed a strong reflection wave. Because in the Brillouin zone boundary of the electronic and lattice effect is very strong, so the effective mass and the real quality have significant difference4.4 electronicWhat is the physical meaning of the effective mass?[answer]Still from the point of view of energy. The change of electron energy.It can be seen from the above formula, the effective mass of the electron can be changed to when the energy of the electron is obtained from the external field and the energy is transferred to the crystal lattice.,The average velocity of electrons is a constant, or the external force is equal to the force of the lattice, and the direction is opposite.4.5 tight binding model, the inner layer of the band and the outer band can be compared, which one is wide? Why?[answer]Taking the s state electron as an example, it is shown that the width of the electronic energy band of the tight binding model depends on the size of the integral, and the integration of the 5.9.Lies in and adjacent grid points of the overlapping degree. The tight binding model, of the inner electrons and small stack extent, of the outer electrons and the overlapping degree high. Therefore, under the tight binding model, the inner electrons of the band and the outer electrons of the band compared, outer layer of the electronic band.4.6, what is the physical meaning of the energy surface in the boundary of the Brillouin zone and the interface between the interface and the interface?[answer]The electron wave vector k into parallel to the boundary of the Brillouin zone of component and vertical to the Brillouin zone boundary K component stilbene. The average velocity of electronsobtain,.Can surface in the Brillouin zone boundary and interface vertical intersection, in the Brillouin zone boundary constant = vertical to interface component of the velocity is zero. Vertical interface component of the velocity is zero, lattice of electrons to produce a Bragg reflection results. In the perpendicular to the interface to, the incident electron sub wave and the lattice of reflection wave interference into a standing wave.5.1 a simple lattice of a simple energy level contains a few electrons?[answer]Design lattice is composed of n Lattice composition, a can with n different wave vector state, hold 2n electronics. Due to electronic energy band is the even function of the wave vector, so the energy (2n). Visible on a level contains four electrons.5.2 the energy band of the intrinsic semiconductor and the difference between the energy bandand the insulator?[answer]At low temperatures, an intrinsic semiconductor can and insulator band structure is the same. But the intrinsic band gap semiconductor with narrow, band gap width usually in 2 EV below. Due to the narrow band gap, the band gap semiconductor sign full of top electronic can, with the aid of thermal excitation, transitions to the forbidden band above with the bottom, make full of dissatisfaction with, empty belt is not empty, two are of conductive contributions.6.1 how do you understand the absolute zero degree and the average kinetic energy of the electrons in the room temperature is very close to this point?[answer]Not change is only get far away from the free electron theory considering the electron kinetic energy. In the absolute zero, metal free (price) electronics, distributed in the Fermi level and below level, that is distributed in a Fermi sphere. At room temperature, the Fermi sphere Fermi surface is occupied by electrons. These electrons from the lattice wave energy is not enough to make the transition to the Fermi surface near or outside the state to state transition of the Fermi surface in the vicinity of a few electrons, and the vast majority of electron energy state. That is to say, room temperature electron average kinetic energy and absolute zero degrees when the average kinetic energy must be very similar.6.2 why temperature, Fermi energy decreases?[answer]When, half quantum state is occupied by electrons of energy is the Fermi level. Elevated temperature, energy of electrons near the Fermi surface obtained from the lattice is bigger, more outside the transition to the Fermi surface of the electronic, the original half quantum state is occupied by electrons energy level electrons less than half, half quantum state is occupied by electrons of energy must be reduced. That is to say, elevated temperature, Fermi energy decreases.6.5 why the concentration of valence electron is higher, the electric conductivity is higher?[answer]Conductance is measure of the metal through flow capacity. Through flow capacity is determined in unit time through the cross-sectional area of the electron number (see question 18). But not all of the valence electrons of conductive contribute, conductive contribution is of electrons near the Fermi surface. The more the greater the Fermi sphere, the conductive contribute to the number of electrons. A Fermi sphere depends on Fermi radius.The electron concentration of n is higher, the greater the number of electron Fermi sphere, contribute to conducting more of the conductivity of the metal is higher.6.6 magnetic field and electric field, which field to the electron distribution function influence big? Why?[answer]Magnetic field and electric field, electric field on the electron distribution function. Because of the effect of magnetic field on the electron is the Lorentz force, Lorentz force only change direction of electron flow, and no electronic acting. That is to say, when the only magnetic field, the valence electrons in nonmagnetic metal distribution function does not change. But in electric and magnetic fields exist at the same time, due to the formation of additional Hall electric field, magnetic field of non magnetic metal electron distribution function emerged. But compared with the electric field, magnetic field on electron distribution function is much weaker.1 covalent binding, two atom electron clouds overlap to produce attractive, while the atoms are close to the electron cloud overlap will produce tremendous repulsive force, how to explain?Covalent binding, the formation of covalent bond pairing of electrons, they spin in the opposite direction, the two electron electron cloud over stack which leads to the reduction of the energy of the system, stable structure, but when atoms near, overlapping atoms within the full shell electron cloud of electrons, quantum states of the same electronic produced enormous repulsion, making the energy of the system increases rapidly.2 explain the phenomenon that a neutral atom absorbs an electron.When a neutral atom absorption an electron into the negative ion, the electronic stability into the atomic shells, the electrons and nuclei of the Coulomb attract to absolute value must be greater than it can with the exclusion of other electronic. But the Coulomb attraction between the electron and the nucleus can be a negative value. That is, when the neutral atom absorbs an electron into the negative ion, the energy of the ion is less than the energy of the neutral atom. Therefore, a neutral atom absorbs an electron.3 why many metals are dense structures?Metal collection by principle of minimum energy constraints and atoms and a total of electron cloud of the Coulomb energy should as far as possible low (absolute value as much as possible). The more compact the atom is, the more compact the atom is and the electronic cloud of electrons, and the lower the Coulomb energy, so it has a dense structure.4 do you think that the elastic strength of the solid is mainly determined by the exclusion effect or the attraction?As shown in the figure, less than R0 in the vicinity of the force curve is steeper, when applying a certain force, solid deformation is small, the slope of the curve near the force determines the elastic properties of solids, and near the force curve slope depends in the repulsive force. Therefore, the elastic strength of the solid is mainly determined by the rejection.5 Einstein model: it is assumed that all atoms vibrate at the same frequencySuccess: by selecting the appropriate Einstein temperature, in the larger temperature range, the results of theoretical calculation and the experimental results are quite good. And the heat capacity tends to zero as the temperature decreases.Deficiency: the temperature is very low, the heat capacity is reduced by the temperature of the index, and the experimental results show that: the heat capacity by the three party to reduce the temperature.The reason: Einstein ignored the difference of the wave frequency.In Debye model the elastic continuum wave wave represents, Bravais lattice is treated as a continuous isotropic medium.Success: the Debye model approximate calculation results of temperature is lower than.Reason: This is because the temperature is very low, the main only long acoustic wave lattice wave excitation, the lattice as continuum elastic wave is appropriate.6 how to explain the conductivity and non conductivity of the material?The material contains a large number of electrons, some of which are conductive, some not. The full band contains a large number of electrons, and the distribution of the electrons in the Brillouin zone is symmetrical, because the contribution of the electrons in the K state to the current is mutually offset. In the non full band, the probability that the K state and the -K state are occupied by the electrons is the same in the absence of the external field. The distribution of the electrons in the Brillouin zone is symmetrical, and does not show theThe symmetry of the distribution of the current, when there is an external field, are destroyed, and some K states have no -K states. On the conductor, there is a part of the tape, in the role of the external field that produces the macroscopic current, to the non conductor, either full of the belt, or is completely empty, so will not produce the current.7 the energy band of the intrinsic semiconductor and the difference between the energy band and the insulator?At low temperature, the band structure of the energy band of the intrinsic semiconductor is the same as that of the insulator. But the sign of the semiconductor band gap narrower, the band width is usually in two electron volts, due to the narrow band gap, the band gap semiconductor sign full of top electronic can, with the aid of thermal excitation, above the band gap transition to empty the bottom of the band, making full of dissatisfaction with empty, both of the conductive contributions.1 ion crystal characteristics: an ion of the nearest neighbor ions for the opposite sex ion; ion crystal, the coordination number of up to 8.The stability of the combination of 2 ionic crystals: poor conductivity, high melting point, high hardness and low coefficient of expansion.Two the 3 basic characteristics of the covalent bond: saturation and orientation; the strength of the covalent bond depends on the degree of the formation of the two electron orbitals of the covalent bond.4 near free electron approximation models: electrons in metals are subject to (the action of the periodic potential field) and the assumption (the fluctuation of the potential field is smaller).Two energy is close to and interacts with each other, and the result is that the energy level is higher than that of the original one (energy increase), and the lower energy state (energy decrease) of the 5 states.6 band gap and (band number) as well as (periodic potential field fluctuations).6 a simple lattice of a simple energy level contains a few electrons?The lattice is composed of N lattice points, then a can with N different wave vector state, can accommodate 2N electronics. Because the energy band of the electron is even function of the wave vector, the energy level is N/2, so the energy level is 4 electrons.7. The tight binding approximation method of thought: electronic in an atom near the (lattice), mainly by the atomic potential field effect, and other atomic potential role as a perturbation, the crystal electron wave function approximation as atomic orbital wave function of a linear combination of, to the relationship between the atoms and the crystal of the electronic band. In the tight binding approximation, the interaction between different atoms is considered.8 what is the characteristic of the electron in the boundary of the Brillouin zone?The energy band of the electron depends on the direction of Yu Bo vector. In either direction, the band gap of the energy band of the near free electrons can be generally appeared on the boundary of the Brillouin zone. If the boundary of the electron is perpendicular to the inverse lattice vector Kn, the width of the forbidden band is E=2|V (Kn), and the V (Kn) is the coefficientof the Fourier series of the periodic potential field. On the boundary of the Brillouin zone, the slope of the equal energy surface in the direction perpendicular to the boundary of the Brillouin zone is zero, that is, the equal energy surface of the electron and the boundary of the Brillouin zone are orthogonal.9 when the wave vector of the electron falls on the boundary of the Brillouin zone, why is the effective mass of the electron with the true quality?In addition to the effect of the external force, the electron in the crystal is also interacting with the lattice. The force of the lattice is F, the electron acceleration is a= (+Fl F) /m, but the specific form of Fl is hard to know. To make the formula does not contain Fl, but also to maintain the identity of the left and right, then only a=F/m*, obviously, the role of the lattice of electrons is weaker, the difference between the effective quality of m* and the real quality of M is smaller. In contrast, the stronger the effect of the lattice on the electron, the greater the difference between the effective mass m* and the real quality m. When the wave vector of the electron falls on the boundary of the Brillouin zone, the scattering of the crystal plane parallel to the boundary of the Brillouin zone is stronger than that of the electron. In the reflection direction of the crystal plane, the scattered wave phase of each lattice point is the same, and the strong reflection wave is formed. Because of the strong interaction between the electron and the lattice on the boundary of the Brillouin zone, there is a significant difference between the effective mass and the real quality.1. The thermal expansion of the reasons: if the vibration is strictly harmonic, there is no thermal expansion and the actual thermal expansion between atoms of non harmonic caused by the action of.Reasons for heat conduction: the contribution of electrons to the conduction of heat is not considered, and the heat conduction in the crystal is mainly depended on phonon. Solid in the presence of temperature gradient, the phonon gas density distribution is not uniform, relationship between mean number of phonon Sui temperature, Bose distribution. Simple harmonic approximation is the result of different lattice is completely independent of, there is no interaction between the different phonon, similar to that of an ideal gas. Actually harmonic function make different lattice wave exists between certain coupling, thereby ensuring the different lattice can exchange energy between, achieve statistical equilibrium.2 what is the normal vibration mode? Whether the normal vibration wave number, wave number or vibration mode number is the same thing?In order to make the problem both simplified and seize the main contradiction, in the analysis discussed the lattice vibration, interatomic mutual force of Taylor series in the non linear term ignored approximation known as harmonic approximation. In the harmonic approximation, the lattice vibration is composed of N atoms in the crystal, can be equivalent to the vibration of 3N independent harmonic oscillators. The vibrational mode of each harmonic oscillator is called a normal mode, which corresponds to all the atoms in the mode of vibration, which is the simplestand most basic vibration mode of the lattice vibration mode. Atomic vibration, vibration or vibration is usually linear superposition of the 3N normal vibration mode. The three is one thing, the number is equal to the sum of the degrees of freedom of all atoms in the crystal, that is equal to 3N.3 long wavelength optical acoustic wave and long wave branch Berger essentially what is the difference?The characteristics of long wavelength optical lattice is within each cell in different atoms relative vibration, vibration frequency is high, it contains all of the lattice vibrations of the highest frequency of vibration mode. Long acoustic branches of lattice is characterized in that the original cells of different atomic no relative displacement, the original cells do movement as a whole, vibration frequency is low, it contains the lattice vibration frequency of the lowest mode of vibration, wave velocity is a constant. Are there any crystal lattice wave acoustic branch, but there is no simple crystal lattice wave optical branch.4 long acoustical waves can lead to macroscopic polarization of ionic crystals?Long wavelength optical lattice so can lead to macroscopic polarization of ionic crystals, the root is long optical lattice wave makes the original cell in different atoms (positive and negative ions) produced a relative displacement. The characteristics of acoustic wave is long, in the cells of all atoms have no relative displacement. Therefore, long acoustical waves can not lead to macroscopic polarization of ionic crystals.5 do you think there is a strong infrared absorption of the simple lattice?Experiments have confirmed that the ion crystal can strongly absorb far infrared light. The root of this phenomenon is that the long optical transverse wave energy in the ion crystal is strongly coupled with the far infrared electromagnetic field. There is no optical wave in the simple lattice, so the simple lattice will not absorb the far infrared light wave.6 what is the root cause of the deviation between the Einstein model and the experiment at low temperature?According to the definition of the Einstein temperature, Einstein model of lattice wave frequency is approximately 10 13 times square Hz, which belongs to the optical branch frequency, but the optical lattice in the low temperature contribution to the heat capacity is very small, low temperature contribution to the heat capacity of is mainly long wavelength acoustical lattice waves. It is said that Einstein did not consider the contribution of acoustic wave to the heat capacity is the root of it in low temperature and experimental errors.7 Debye in very cold model experiments. Why?At very low temperature, not only the optical wave to stimulate and phonon energies are larger。

Nov.2020Vol.37No.S Transactions of Nanjing University of Aeronautics and AstronauticsFBS Effect and Temperature Dependence in Trench⁃AssistedMultimode FiberZHANG Zelin1，2，LU Yuangang1，2*，XIE Youwen1，2，HUANG Jian1，2，ZHOU Lang1，2 1.Key Laboratory of Space Photoelectric Detection and Perception of Ministry of Industry and Information Technology，College of Astronautics，Nanjing University of Aeronautics and Astronautics，Nanjing211106，P.R.China；2.College of Science，Nanjing University of Aeronautics and Astronautics，Nanjing211106，P.R.China（Received13July2020；revised10September2020；accepted12September2020）Abstract:We propose the trench-assisted multimode fiber（TA-OM4）as a novel sensing fiber in forward Brillouin scattering（FBS）-based temperature sensor，due to its higher temperature sensitivity，better bending resistance and lower propagation loss，compared with the single mode fiber（SMF）and other sensing fibers.The FBS effect and acousto-optic interaction in TA-OM4are the first time to be demonstrated and characterized at1550nm theoretically and experimentally.A2.0km long TA-OM4is put into an oven to measure its temperature sensitivity，which can reach up to80.3kHz/℃，exceeding53%of SMF（52.4kHz/℃）.The simulated and experimental results verify that the TA-OM4may be a good candidate as the sensing fiber for the FBS-based temperature sensor.Key words：forward Brillouin scattering；acousto-optic interaction；optic-fiber sensor；temperature sensitivity；multimode fiberCLC number：TN29Document code：A Article ID：1005‐1120（2020）S‐0095‐070IntroductionStimulated Brillouin scattering（SBS）in opti‐cal fiber is a phenomenon caused by the interaction between a light wave and an acoustic wave，which is widely studied and employed in the field of distrib‐uted sensing［1-2］.Backward Brillouin scattering in‐duces high frequency shifts around10GHz which can be utilized in Brillouin optical time-domain sen‐sors and Brillouin laser.However，the forward Brill‐ouin scattering（FBS）have much lower frequency shift of several hundreds of mega Hertz，which can be used in several applications，such as temperature sensing，opto-mechanical chemical sensors，optical frequency comb and opto-mechanical laser［3-6］.Recently，the temperature sensors based on FBS have been proposed using the silica single mode fiber（SMF），high nonlinear fiber（HNLF）and photonics crystal fiber（PCF）［7-9］.However，the lower temperature sensitivity of SMF may limit its measurement pared with SMF，al‐though the HNLF and PCF have slightly lager tem‐perature sensitivities，their disadvantages of bad bending resistance，high cost and large propagation loss which are5.4dB/km of PCF and0.76dB/km of HNLF，respectively，can compromise their sens‐ing performance for future FBS-based temperature sensors in complex engineering application［8-9］.For‐tunately，the trench-assisted multimode fiber（TA-OM4），due to its low propagation loss（0.24dB/ km）which is similar to that of SMF（0.20dB/ km），excellent bending resistance and high back‐ward stimulated Brillouin scattering（BSBS）and modulation instability（MI）threshold，has been a good candidate as the sensing fiber in BSBS-based temperature sensors［10］.However，the characteristic of FBS process in TA-OM4at1550nm and its ap‐plications in FBS-based temperature sensors have*Corresponding author，E-mail address：*************.cn.How to cite this article:ZHANG Zelin，LU Yuangang，XIE Youwen，et al.FBS effect and temperature dependence in trench‐assisted multimode fiber［J］.Transactions of Nanjing University of Aeronautics and Astronautics，2020,37(S)：95‐101. http：///10.16356/j.1005‐1120.2020.S.012Vol.37 Transactions of Nanjing University of Aeronautics and Astronauticsnot been reported.In this paper，we theoretically and experimen‐tally investigate the acousto-optic interaction causedby FBS and FBS spectrum in TA-OM4.Further‐more，we have found that the largest strain coeffi‐cient in TA-OM4is about4.0kHz/με，which is sosmall that the frequency shift of FBS is not sensitiveto make acceptable strain measurement.Therefore，we only focus on its temperature dependence ofFBS in this pared with the temperatureresponse of FBS in SMF，we experimentally mea‐sure the FBS temperature response of TA-OM4.The highest temperature dependence of TA-OM4islinear with a coefficient of80.3kHz/℃，which is53%larger than that of SMF（52.4kHz/℃）.Thesimulated and experimental results show that theTA-OM4may be a good candidate as the sensing fi‐ber in FBS-based temperature sensors.1FBS Resonances in TA⁃OM41.1Theoretical description of FBS in optical fi⁃berThe acoustic modes responsible for FBS are ra‐dial dilatational modes（R0，m）and mixed torsional-radial modes（TR2，m）.The FBS is a typical opto-acoustic interaction，which can be described as thecoupling amplitude equations between optical fieldE（r，z，t）and acoustic wave for the displacementvector U（r，z，t）［11］∂2E ∂z2-n2effc2∂2E∂t2=1ε0c2∂2P NL∂t2(1)∂2U∂z2+Γ∂U∂t+V s2∇×(∇×U)-V l2∇(∇∙U)=Fρ(2) where P NL is the total nonlinear polarization，c the light velocity in vacuum，n eff the effective refractive index，ε0the vacuum permittivity，V l the longitudi‐nal acoustic velocity of the fiber，ρ0the density of fused silica，V s shear sound velocity of the fiber，andΓthe acoustic damping parameter.F=ε0[12γ12∇()E∙E+γ44(E∙∇)E]is the elec‐trostrictive driving term，andγ12andγ44are both the elements of the electrostrictive tensor for fused sili‐ca.By employing the finite element analysis（FEA）method and solving Eq.（1），we obtain the optical field E（r）.Moreover，by solving Eq.（2）with the appropriate boundary conditions，we difine the nor‐malized displacement distribution U m（r）in terms of Bessel functions J n（z），where n is the order of Bes‐sel functions.By usingρm(r)=-ρ0∇U m(r)，we obtain the density vibration caused by FBS.For the radial dilatational R0，m modes，the boundary condition corresponding to the free fiber surface can be written as(1-α2)J0(y)-α2J2(y)=0(3) whereαis the ratio between shear sound velocity and longitudinal acoustic velocity，and y m the m th zero of Eq.（3）.Furthermore，the central frequency of the m th acoustic mode can be expressed asf m=y m V lπd(4) where d is the cladding diameter of optical fiber.Similar to the Kerr effect in fiber，the opto-me‐chanical coefficient can be used to quantify the opto-acoustic interaction caused by FBS，which can be expressed as［6，12-13］γ(m)OM=k02πn2neff cρ0Q(m)E Q(m)pΓm f m(5) whereΓm is the linewidth of the m th resonant peak induced by FBS.The Q(m)E and Q(m)p are the elec‐trostrictive overlap and photo-elastic overlap，which determines the efficiency of stimulation of acoustic modes and describes the modification of the effec‐tive index by acoustic modes［13-14］，respectively.By solving Eqs.（1）—（5），the acoustic field distribu‐tion and FBS resonances can be obtained next.1.2Simulation and FBS spectrum in TA⁃OM4For TA-OM4，the diameters of the fiber core and cladding are50and125μm，respectively.The refractive index profile is given in Fig.1.The refrac‐tive index profile shows a quasi-quadratic distribu‐tion in the central region and has a trench-index pro‐file around the fiber core［10］.The three highest linear polarization（LP）modes are respectively LP01，96No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench-Assisted Multimode FiberLP11and LP21，and the corresponding intensity ratio of these three LP modes I01∶I11∶I21，is1∶0.14∶0.006. Considering the highest intensity ratio of LP01，the tiny coupling efficiency between LP01and other high-order modes and the single mode condition of most optical components［15］，it is enough to investigate the FBS process of TA-OM4corresponding to the fundamental mode LP01.By solving Eqs.（1）and（2），three excited acoustic modes are found and displayed in Fig.2. As it shown in Fig.2（a），taking R0，4mode as an example，the R0，m modes are the radial dilatational modes，which have the most efficient scattering ef‐ficiency and are independent of angular coordinate φ.Especially，the R0，m modes can induce refractive index changes so that the pure phase modulation will be also induced.Other acoustic modes are TR2，m acoustic modes，which are the mixed tor‐sional-radial modes.As it shown in Figs.2（b）and （c），different from R0，m modes，the TR2，m modes are doubly degenerated，which vary sinusoidally with angular coordinate2φ.Furthermore，the scat‐tering efficiency of TR2，m modes is much lower than that of R0，m modes.For the TR2，m（90°/0°）mode，its induced birefringent axes are parallel to the birefringent axes of TA-OM4，which does not induce the depolarized scattering but the polarized scattering and also cause pure phase modulation. For the TR2，m（45°/-45°）mode，the mode pat‐tern is rotated by45°.In this case pure phase modu‐lation will not occur，and the depolarized scattering is induced［16］.Fig.1Refractive index profile of TA-OM4and calculated three LP optical modes with the highestintensityFig.2Normalized transverse profile of acoustic modes excited by LP01optical mode in TA-OM497Vol.37Transactions of Nanjing University of Aeronautics and Astronautics Generally ，the overlap between optical modes and acoustic modes determines the shape of FBS resonances.Taking four acoustic modes （R 0，1to R 0，4）as examples ，the 2D mode profiles of longitu‐dinal optical fundamental mode LP 01and four acous‐tic modes are displayed in Fig.3.In order to experimentally investigate the FBS process in TA -OM4，we also measure the FBS spectrum by using a coherent detection ，which isshown in Fig.4.The light source （NKT Photonics ）is a 1550nm single -wavelength semiconductor la‐ser with linewidth 5kHz.The pump light propagat‐ing through the isolator （ISO ）is split into two branches by a 50/50coupler.The upper branch used as the pump light is amplified by an erbium -doped fiber amplifier （EDFA ，Amonics ）.A narrow bandpass filter （BPF ，AOS Photonics ）with 3.5GHz bandwidth is used to eliminate the amplified spontaneous emission （ASE ）noise induced by ED‐FA.A variable attenuator （VA ）is utilized to adjust the input power level to protect fiber components.The pump light is launched into 2.0km long TA -OM4（YOFC ）to obtain the FBS signal which beats with the reference light.Finally ，a 1.6GHz bandwidth photodetector （PD ，Thorlabs PDB480）is utilized to detect the beat signal ，which is ana‐lyzed by an electrical spectrum analyzer （ESA ，Tektronix RSA5126B ）and used to obtain the FBS spectrum.In our experiment ，the incident light power is 11.2mW.The measured FBS spectrum is shown in Fig.5.The measured FBS spectrum includes two parts.One part is from the R 0，m modes and the other is from the TR 2，m modes.However ，due to the ran‐dom change of polarization states along the TA -OM4，the FBS intensities induced by TR 2，m modes are much lower than those of R 0，m modes.As it shown in Fig.5，we can find that the fourth resonant peak with the highest intensity locates at 173.1MHz.By solving Eq.（5），we obtain the calculated opto -mechanical coefficient of R 0，4mode as 5.25（W∙km ）-1，which is slightly higher than that of SMF 5（W ∙km ）-1［6］.In Fig.6，two adjacent resonant peaksgenerated by R 0，m modes have equivalent frequency interval of 47.5MHz ，which can be verified by solv‐ing Eq.（4）.It is obvious that ，whatever resonant peaks intensity and frequency shift ，the calculated and experimental results are in good agreement.The largest difference of normalized intensity be‐tween calculated and experimental results are less than 5%，which are from the error of the estimated fiberparameters.Fig.32-D profiles of optical mode LP 01and acoustic modes R 0,1to R0,4Fig.4Experimental setup of measuring the FBS spectrum of TA -OM4Fig.5The measured FBS spectrum of TA -OM498No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench -Assisted Multimode Fiber 2TemperatureResponse inTA⁃OM4In order to evaluate whether the TA -OM4can be used as the novel sensing fiber in FBS -based tem ‐perature sensors ，we put both TA -OM4and SMF into an oven to measure their temperature sensitivi‐ties of R 0，m modes ，and results are shown in Fig.7.Seven different temperatures between -10℃to 50℃are measured with a temperatures step of 10℃.It is obvious that the temperature sensitivities increase linearly with an increase in m value of R 0，m modes ，whose trends are in accordance with that in Ref.［17］.The observed temperature coefficient of R 0，12in TA -OM4can reach 80.3kHz/℃，which is 53%larger than that of SMF （52.4kHz/℃）.Furthermore ，we also obtain the temperature sensitivities of spectral peaks corresponding to R 0，4（f 4=173.1MHz ）mode in TA -OM4and R 0，5（f 5=222.9MHz ）mode in SMF ，which exhibit the high‐est resonance intensity of all peaks.In Fig.8，the calibration temperature coefficient of TA -OM4（αTA‐OM4）can reach 31.9kHz/℃，which is much 41%larger than that of SMF （αSMF =22.6kHz/℃）.3ConclusionsFBS processes in TA -OM4are theoreticallyand experimentally investigated and the acousto -op‐tic interaction of TA -OM4at 1550nm are charac‐terized and demonstrated.We experimentally mea‐sure the FBS spectrum ，which is in good agreement with simulated results.The temperature sensitivities of R 0，m modes in TA -OM4are also measured ，which exceed 40%of SMF.The calculated and ex‐perimental results demonstrate that the TA -OM4could be a good sensing fiber in FBS -based tempera‐ture sensors ，with advantages of high temperature sensitivity ，good bending resistance and low propa‐gation loss.References［1］MATSUI T ，NAKAJIMA K ，YAMAMOTO F.Guided acoustic -wave brillouin scatteringcharacteris‐Fig.6Measured (green)and calculated (red)normal‐ized FBS resonant intensity in TA -OM4in‐duced by R 0,mmodesFig.7Measured temperature sensitivities of TA -OM4and SMF versus different R 0,m modes ，re‐spectivelyFig.8Temperature sensitivities of R 0,4mode in TA -OM4and R 0,5mode in SMF99Vol.37 Transactions of Nanjing University of Aeronautics and Astronauticstics of few-mode fiber［J］.Applied Optics，2015，54（19）：6093-6097.［2］BAO X，CHEN L.Recent progress in Brillouin scat‐tering based fiber sensors［J］.Sensors，2011，11（4）：4152-4187.［3］FU Y，FAN X，WANG B，et al.Discriminative mea‐surement of temperature and strain using stimulatedBrillouin scattering and guided acoustic-wave brillouinscattering［C］//2018Asia Communications and Photo‐nics Conference（ACPC）.Hangzhou：IEEE，2018：1-3.［4］CHOW D M，THEVENAZ L.Opto-acoustic chemi‐cal sensor based on forward stimulated Brillouin scat‐tering in optical fiber（Invited）［C］//Proceedings ofthe7th International Conference on Photonics（ICP）.［S.l.］：IEEE，2018：1-3.［5］BUTSCH A，KOEHLER J R，NOSKOV R E，et al.CW-pumped single-pass frequency comb genera‐tion by resonant optomechanical nonlinearity in dual-nanoweb fiber［J］.Optica，2014，1（3）：158-164.［6］LONDON Y，DIAMANDI H H，ZADOK A.Elec‐tro-opto-mechanical radio-frequency oscillator drivenby guided acoustic waves in standard single-mode fi‐ber［J］.APL Photonics，2017，2（4）：041303.［7］YAIR A，LONDON Y，ZADOK A.Scanning-free characterization of temperature dependence of forwardstimulated Brillouin scattering resonances［C］//Pro‐ceedings of the24th International Conference on Opti‐cal Fiber Sensors（ICOFS）.Curitlba：SPIE，2015：96345C.1-96345C.4.［8］HAYASHI N，SUZUJI K，SET S Y，et al.Temper‐ature coefficient of sideband frequency produced by po‐larized guided acoustic-wave Brillouin scattering inhighly nonlinear fibers［J］.Applied Physics Express，2017，10（9）：092501.1-092501.3.［9］CARRY E，BEUGNOT J C，STILLER B，et al.Temperature coefficient of the high-frequency guidedacoustic mode in a photonic crystal fiber［J］.AppliedOptics，2011，50（35）：6543-6547.［10］ZHANG Z L，LU Y G.Trench-assisted multimode fi‐ber used in Brillouin optical time domain sensors［J］.Optics Express，2019，27（8）：11396-11405.［11］KANG M S，BRENN R，RUSSELL R S J.All-opti‐cal control of gigahertz acoustic resonances by forwardstimulated inter-polarization scattering in a photoniccrystal fiber［J］.Physical Review Letters，2010，105（15）：153901.1-153901.4.［12］BUTSCH A，KANG M S，EUSER T G，et al.Op‐tomechanical nonlinearity in dual-nanoweb structuresuspended inside capillary fiber［J］.Physical ReviewLetters，2012，109（18）：183904.1-183904.5.［13］DIAMANDI H H，LONDON Y，ZADOK A.Opto-mechanical inter-core cross-talk in multi-core fi‐bers［J］.Optica，2017，4（3）：289.［14］BIRYUKOV A S，SUKHAREV M E，DIANOV E M.Excitation of sound waves upon propagation of la‐ser pulses in optical fibers［J］.Quantum Electronics，2002，32（9）：765-775.［15］XU Y，REN M，LU Y，et al.Multi-parameter sensor based on stimulated Brillouin scattering in inverse-para‐bolic graded-index fiber［J］.Optics Letters，2016，41（6）：1138-1141.［16］NISHIZAWA N，KUME S，MORI M，et al.Experi‐mental analysis of guided acoustic wave Brillouin scat‐tering in PANDA fibers［J］.Journal of the Optical So‐ciety of America B，1995，12（9）：1651-1655.［17］CHUN Y D，SHANG L H，JING L L，et al.Simul‐taneous measurement on strain and temperature viaguided acoustic-wave Brillouin scattering in singlemode fibers［J］.Acta Physica Sinica，2016，65（24）.240702.1-240702.7.Acknowledgements This work was supported in part by the National Natural Foundation of China（Nos.61875086，61377086），the Aerospace Science Foundation of China （No.2016ZD52042），and Nanjing University of Aeronautics and Astronautics Ph.D.short-term visiting scholar project （No.190901DF08）.Authors Mr.ZHANG Zelin is currently a Ph.D.candidate of Optical Engineering at the Department of Applied Phys‐ics，Nanjing University of Aeronantics and Astronautics （NUAA）.His research focuses on distributed fiber sensors and nonlinear fiber optics.Prof.LU Yuangang is currently a professor in College of As‐tronautics at NUAA.His research focuses on distributed fi‐ber sensors，image processing and technology of photoelec‐trical detection.Author contributions Mr.ZHANG Zelin contributed to simulation by doing experiment and writing the manuscript. Prof.LU Yuangang designed and guided the study，and gave key opinions on the core issues.Mr.XIE Youwen and Mr.HUANG Jian conducted some related works about the experiments.Ms.ZHOU Lang conducted some related works about the simulation.Competing interests The author declare no competing interests.（Production Editor：XIA Daojia）100No.S ZHANG Zelin,et al.FBS Effect and Temperature Dependence in Trench-Assisted Multimode Fiber101沟道型折射率多模光纤的前向布里渊散射效应及其温度响应张泽霖1，2，路元刚1，2，谢有文1，2，黄剑1，2，周朗1，2（1.空间光电探测与感知工业和信息化部重点实验室，南京航空航天大学航天学院，南京211106，中国；2.南京航空航天大学理学院，南京211106，中国）摘要：提出了沟道型折射率多模光纤（TA‐OM4）可作为一种新型传感光纤应用于基于前向布里渊散射（FBS）的温度传感器中。

Light Field Manipulation: A Revolution inOptics and Its ApplicationsIn the realm of optics, light field manipulation has emerged as a cutting-edge technology, promising unprecedented control over the propagation and interaction of light. This field, often referred to as "light field engineering" or "light field调控," involves the precise manipulation of the amplitude, phase, polarization, and wavelength of light, enabling the creation of novel optical phenomena and devices with unique functionalities.The concept of light field manipulation dates back to the early days of optics, but significant progress has been made in recent years due to advancements in nanotechnology, materials science, and computational methods. This has led to the development of a range of innovative optical devices and systems that have revolutionized various fields, including imaging, communications, and energy conversion. One of the most significant applications of light field manipulation is in the field of computational imaging. By precisely controlling the light field, researchers have been able to create novel imaging systems that offerunprecedented resolution, depth of field, and dynamic range. These systems, known as light field cameras or plenoptic cameras, capture not only the intensity of light but alsoits direction, enabling the reconstruction of the three-dimensional scene with unprecedented fidelity.Another important area where light field manipulation has found widespread application is in optical communications. By manipulating the phase and polarizationof light, researchers have been able to develop high-capacity optical fiber communication systems that can transmit information at unprecedented speeds and distances. These systems are critical for enabling the global internet and high-speed data networks.In addition to its applications in imaging and communications, light field manipulation is also finding uses in areas such as energy conversion and quantum information processing. By controlling the light field at the nanoscale, researchers have been able to developefficient solar cells and photodetectors that convert sunlight into electricity with unprecedented efficiency. Similarly, the precise control of light-matter interactionsusing light field manipulation offers the potential for novel quantum devices and algorithms that could revolutionize computing and information processing.The future of light field manipulation looks even more promising. With the continued development of advanced materials and nanotechnologies, as well as the increasing availability of powerful computational resources, we can expect to see even more innovative applications of light field manipulation in areas such as biomedicine, security, and defense.Overall, light field manipulation represents a significant leap forward in our ability to control and manipulate light. Its impact on optics and its applications is likely to be profound, enabling the creation of novel devices and systems with unprecedented capabilities and functionalities. As we continue to explore the frontiers of light field manipulation, we stand on the cusp of a new era in optics that will transform our world in ways we can only imagine.**光场调控：光学领域的革命及其应用**在光学领域，光场调控已经成为一项尖端技术，它承诺对光的传播和相互作用进行前所未有的控制。

laParticle size analysis-Laser diffraction methods(ISO-13320-1)IntroductionLaser diffraction methods are nowadays widely used for particle sizing in many different applications. The success of the technique is based on the tact that it can be applied to various kinds of particulate systems, is fast and can be automated and that a variety of commercial instruments is available. Nevertheless, the proper use of the instrument and the interpretation of the results require the necessary caution.Therefore, there is a need for establishing an international standard for particle size analysis by laser diffraction methods. Its purpose is to provide a methodology for adequate quality control in particle size analysis.Historically, the laser diffraction technique started by taking only scattering at small angles into consideration and, thus, has been known by the following names:-fraunhofer diffraction;-(near-) forward light scattering;-low-angle laser light scattering (LALLS).However, the technique has been broadened to include light scattering in a wider angular range and application of the Mie theory in addition to approximating theories such as Fraunhofer and anomalous diffraction.The laser diffraction technique is based on the phenomenon that particles scatter light in all directions with an intensity pattern that is dependent on particle size. All present instruments assume a spherical shape for the particle. Figure 1 illustrates the characteristics of single particle scattering patterns: alternation of high and low intensities, with patterns that extend for smaller particles to wider angles than for larger particles[2-7,10,15 in the bibliography].Within certain limits the scattering pattern of an ensemble of particles is identical to the sum of the individual scattering patterns of all particles present. By using an optical model to compute scattering for unit volumes of particles in selected size classes and a mathematical deconvolution procedure, a volumetric particle size distribution is calculated, the scattering pattern of which fits best with the measured pattern (see also annex A).A typical diffraction instrument consists of a light beam (usually a laser), a particulate dispersing device, a detector for measuring the scattering pattern and a computer for both control of the instrumentand calculation of the particle size distribution. Note that the laser diffraction technique cannot distinguish between scattering by single particles and scattering by clusters of primary particles forming an agglomerate or an aggregate. Usually, the resulting particle size for agglomerates is related to the cluster size, but sometimes the size of the primary particles is reflected in the particle size distribution as well. As most particulate samples contain agglomerates or aggregates and one is generally interested in the size distribution of the primary particles, the clusters are usually dispersed into primary particles before measurement.Historically, instruments only used scattering angles smaller than 14°,which limited the application to a lower size of about 1μm. The reason for this limitation is that smaller particles show most of their distinctive scattering at larger angles (see also annex Z).Many recent instruments allow measurement at larger scattering angles, some up to about 150°,for example through application of a converging beam, more or larger lenses, a second laser beam or more detectors. Thus smaller particles down to about μm can be sized. Some instruments incorporate additional information from scattering intensities and intensity differences at various wavelengths and polarization planes in order to improve the characterization of particle sizes in the submicrometre range.Particle size analysis – Laser diffraction methods-Part 1:General principles1 scopeThis part of ISO 13320 provides guidance on the measurement of size distributions of particles in any two-phase system, for example powders, sprays, aerosols, suspensions, emulsions and gas bubbles in liquids, through analysis of their angular light scattering patterns. It does not address the specific requirements of particle size measurement of specific products. This part of ISO13320 is applicable to particle sizes ranging from approximately μm to 3μm.For non-spherical particles, an equivalent-sphere size distribution is obtained because the technique uses the assumption of spherical particles in its optical model. The resulting particle size distribution may be different from those obtained by methods based on other physical principles . Sedimentation, sieving).3,terms, definitions and symbolsFor the purposes of this part of ISO 13320, the following terms, definitions and symbols apply.terms, definitionsabsorptionintroduction of intensity of a light beam traversing a medium through energy conversion in the mediumcoefficient of variation (变异系数)Noative measure(%) for precision: standard deviation divided by mean value of population and multiplied by 100 or normal distributions of data the median is equal to the meanrefractive index（Ｎｐ）Refractive index of a particle, consisting of a real and an imaginary (absorption) part.Np=n p-ik prelative refractive index （m）complex refractive index of a particle, relative to that the medium。