Designation:E131–05Standard Terminology Relating toMolecular Spectroscopy1,2This standard is issued under thefixed designation E131;the number immediately following the designation indicates the year of original adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.A superscript epsilon(e)indicates an editorial change since the last revision or reapproval.1.Referenced Documents1.1ASTM Standards:3E135Terminology Relating to Analytical Chemistry for Metals,Ores,and Related MaterialsE168Practices for General Techniques of Infrared Quanti-tative AnalysisE204Practices for Identification of Material by Infrared Absorption Spectroscopy,Using the ASTM Coded Band and Chemical Classification IndexE284Terminology of AppearanceE386Practice for Data Presentation Relating to High-Resolution Nuclear Resonance(NMR)SpectroscopyE456Terminology Relating to Quality and Statistics1.2Other Documents:4ISO Guide30–1981(E)Terms and definitions used in connections with reference materials2.Terminologyabsorbance,A—the logarithm to the base10of the recip-rocal of the transmittance,(T).A5log10~1/T!52log10T(1)D ISCUSSION—In practice the observed transmittance must be substi-tuted for T.Absorbance expresses the excess absorption over that of a specified reference or standard.It is implied that compensation has been effected for reflectance losses,solvent absorption losses,and refractive effects,if present,and that attenuation by scattering is small compared with attenuation by absorption.Apparent deviations from the absorption laws(see absorptivity)are due to inability to measure exactly the true transmittance or to know the exact concentration of an absorbing substance.absorption band—a region of the absorption spectrum in which the absorbance passes through a maximum. absorption coefficient,a—a measure of absorption of radiant energy from an incident beam as it traverses an absorbing medium according to Bouguer’s law,P/P o=e−a b.D ISCUSSION—In IRS,a is a measure of the rate of absorption ofenergy from the evanescent wave.absorption parameter,a—the relative reflection loss per reflection that results from the absorption of radiant energy at a reflecting surface:a=1−R,and R=the reflected fraction of incident radiant power.absorption spectrum—a plot,or other representation,of absorbance,or any function of absorbance,against wave-length,or any function of wavelength.absorptivity,a—the absorbance divided by the product of the concentration of the substance and the sample pathlength, a=A/bc.The units of b and c shall be specified.D ISCUSSION—1—The recommended unit for b is the centimetre.Therecommended unit for c is kilogram per cubic metre.Equivalent units are g/dm3,g/L,or mg/cm3.D ISCUSSION—2—The equivalent IUPAC term is“specific absorptioncoefficient.”absorptivity,molar,e—the product of the absorptivity,a,and the molecular weight of the substance.D ISCUSSION—The equivalent IUPAC term is“molar absorption coef-ficient.”acceptance angle,n—for an opticalfiber,the maximum angle, measured from the longitudinal axis or centerline of thefiber to an incident ray,within which the ray will be accepted for transmission along thefiber by total internal reflection.D ISCUSSION—If the incidence angle exceeds the acceptance angle,optical power in the incident ray will be coupled into leaky modes or rays,or lost by scattering,diffusion,or absorption in the cladding.Fora cladded step-indexfiber in the air,the sine of the acceptance angle isgiven by the square root of the difference of the squares of the refractive indexes of thefiber core and the cladding,that is,by the relation as follows:sin A5=n122n22(2) where A is the acceptance angle and n1and n2are the refractive indexes of the core and cladding,respectively.If the refractive index is a function1This terminology is under the jurisdiction of ASTM Committee E13onMolecular Spectroscopy and Chromatography and is the direct responsibility ofSubcommittee E13.94on Terminology.Current edition approved Sept.1,2005.Published September2005.Originallyapproved st previous edition approved in2002as E131–02.2For other definitions relating to nuclear magnetic resonance,see Practice E386.3For referenced ASTM standards,visit the ASTM website,,orcontact ASTM Customer Service at service@.For Annual Book of ASTMStandards volume information,refer to the standard’s Document Summary page onthe ASTM website.4Available from American National Standards Institute(ANSI),25W.43rd St.,4th Floor,New York,NY10036.Copyright©ASTM International,100Barr Harbor Drive,PO Box C700,West Conshohocken,PA19428-2959,United States.of distance from the center of the core,as in the case of graded index fibers,then the acceptance angle depends on the distance from the core center.The acceptance angle is maximum at the center,and zero at the core-cladding boundary.At any radius,r,the sine of the acceptance angle of a graded indexfiber is defined in compliance with that of a step-index fiber as follows:sin A r5=n122n22(3)where Ar is the acceptance angle at a point on the entrance face at adistance,r,from the center,nr is the refractive index of the core at aradius,r,and n2is the refractive index of the cladding.In air,sin A andsin Ar are the numerical apertures.Unless otherwise stated,acceptanceangles and numerical apertures forfiber optics are those for the center of the endface of thefiber,that is,where the refractive index,and hence the numerical aperture,is the highest.accuracy—the closeness of agreement between an observed value and an accepted reference value(See Terminology E456).D ISCUSSION—The term accuracy,when applied to a set of observedvalues,will be a combination of a random component and a common systematic error or bias component.Since in routine use,random components and bias components cannot be completely separated,the reported“accuracy”must be interpreted as a combination of these two components.activefiber optic chemical sensor,n—afiber optic chemical sensor in which a transduction mechanism other than the intrinsic spectroscopic properties of the analyte is used to modulate the optical signal.D ISCUSSION—Examples include a pH sensor composed of a chemicalindicator substance whose color changes with pH,and an oxygen sensor coupled to an opticalfiber bearing a chemical indicator whose fluorescence intensity depends on oxygen concentration. aliasing—the appearance of features at wavenumbers other than their true value caused by using a sampling frequency less than twice the highest modulation frequency in the interferogram;also known as“folding.”analytical curve—the graphical representation of a relation between some function of radiant power and the concentra-tion or mass of the substance emitting or absorbing it. analytical wavelength—any wavelength at which an absor-bance measurement is made for the purpose of the determi-nation of a constituent of a sample.angle of incidence,u—the angle between an incident radiant beam and a perpendicular to the interface between two media.anti-Stokes line(band)—a Raman line(band)that has a frequency higher than that of the incident monochromatic beam.aperture of an IRE,A8—that portion of the IRE surface that can be utilized to conduct light into the IRE at the desired angle of incidence.apodization—modification of the ILS function by multiplying the interferogram by a weighting function the magnitude of which varies with retardation.D ISCUSSION—This term should strictly be used with reference to aweighting function whose magnitude is greatest at the centerburst and decreases with retardation.attenuated total reflection(ATR)—reflection that occurs when an absorbing coupling mechanism acts in the process of total internal reflection to make the reflectance less than unity.D ISCUSSION—In this process,if an absorbing sample is placed incontact with the reflecting surface,the reflectance for total internal reflection will be attenuated to some value between zero and unity(O <R<1)in regions of the spectrum where absorption of the radiant power can take place.attenuation index,k—a measure of the absorption of radiant energy by an absorbing material.k is related to the absorp-tion coefficient by:n k=a c o/4pn,where c o=the speed of light in vacuo,n=the frequency of radiant energy,and n=the refractive index of the absorbing medium. background—apparent absorption caused by anything other than the substance for which the analysis is being made. baseline—any line drawn on an absorption spectrum to estab-lish a reference point representing a function of the radiant power incident on a sample at a given wavelength.basic NMR frequency,n0—the frequency,measured in hertz (Hz),of the oscillating magneticfield applied to induce transitions between nuclear magnetic energy levels. bathochromic shift,n—change of a spectral band to longer wavelength(lower frequency)because of structural modifi-cations or environmental influence;also known as“red shift.”beamsplitter—a semireflecting device used to create,and often to recombine,spatially separate beams.D ISCUSSION—Beamsplitters are often made by depositing afilm of ahigh refractive index material onto aflat transmitting substrate with an identical compensator plate being held on the other side of thefilm. beamsplitter efficiency—the product4RT,where R is the reflectance and T is the transmittance of the beamsplitter. Beer’s law—the absorbance of a homogeneous sample con-taining an absorbing substance is directly proportional to the concentration of the absorbing substance.See also absorp-tivity.bias—a systematic error that contributes to the difference between a population mean of the measurements or test results and an accepted or reference value(see Terminology E456).D ISCUSSION—Bias is determined by the following equation:bias5e¯51n(i51n e i(4)where:n=the number of observations for which the accuracy is determined,e i=the difference between a measured value of a propertyand its accepted reference value,ande¯=the mean value of all the e i.Bouguer’s law—the absorbance of a homogeneous sample is directly proportional to the thickness of the sample in the opticalpath.D ISCUSSION—Bouguer’s law is sometimes also known as Lambert’slaw.boxcar truncation—identical effective weighting of all points in the measured interferogram prior to the Fourier transform; all points outside of the range of the measured interferogram take a value of zero.buffer—infiber optics,seefiber optic buffer.bulk reflection—reflection in which radiant energy is returned exclusively from within the specimen.D ISCUSSION—Bulk reflection may be diffuse or specular. centerburst—the region of greatest amplitude in an interfero-gram.D ISCUSSION—For unchirped or only slightly chirped interferograms,this region includes the“zero path difference point”and the“zero retardation point.”certified reference material,n—a reference material,the composition or properties of which are certified by a recognized standardizing agency or group.D ISCUSSION—A certified reference material produced by the NationalInstitute of Standards and Technology(NIST)is designated a Standard Reference Material(SRM).chemical shift(NMR),d—the defining equation for d is the following:d5Dnn R3106(5)where n R is the frequency with which the reference sub-stance is in resonance at the magneticfield used in the experiment and Dn is the frequency difference between the reference substance and the substance whose chemical shift is being determined,at constantfield.The sign of Dn is to be chosen such that shifts to the high frequency side of the reference shall be positive.D ISCUSSION—If the experiment is done at constant frequency(fieldsweep)the defining equation becomesd5Dnn R3S12Dnn RD3106(6)chirping—the process of dispersing the zero phase difference points for different wavelengths across the interferogram,so that the magnitude of the signal is reduced in the short region of the interferogram where all wavelengths would otherwise constructively interfere.clad—see cladding.cladding,n—of an opticalfiber,a layer of a optically transparent lower refractive index material in intimate con-tact with a core of higher refractive index material used to achieve total internal reflection.D ISCUSSION—The cladding confines electromagnetic waves to thecore,provides some protection to the core,and also transmits evanes-cent waves that usually are bound to waves in the core. concentration,c—the quantity of the substance contained in a unit quantity of sample.D ISCUSSION—For solution work,the recommended unit of concen-tration is grams of solute per litre of solution.core,n—of an opticalfiber,the center region of an optical waveguide through which radiant energy is transmitted.D ISCUSSION—In a dielectric waveguide such as an opticalfiber,therefractive index of the core must be higher than that of the cladding.Most of the radiant energy is confined to the core.correlation coefficient(r)—a measure of the strength of the linear relationship between X and Y,calculated by the equation:r xy5~(i51n X i Y i!~(i51n X i2!1/2~(i51n Y i2!1/2(7)where:n=the number of observations in X and Y.D ISCUSSION—Xiand Yiare any two mean corrected variables.For the simple linear regression only,r xy5R5~sign of b1!~R2!1/2(8)where:R2=the coefficient of multiple determination.critical angle,u c—the angle whose sine is equal to the relative refractive index for light striking an interface from the greater to the lesser refractive medium:u c=sin−1n21,where n21=the ratio of the refractive indices of the two media.D ISCUSSION—Total reflection occurs when light is reflected in themore refractive of two media from the interface between them at any angle of incidence exceeding the critical angle.depth of penetration,d p—in internal reflection spectroscopy, the distance into the less refractive medium at which the amplitude of the evanescent wave is e−1(that is,36.8%)of its value at the surface:d p5l12p~sin2u2h212!1/2(9)where:n21=n2/n1=refractive index of sample divided by that of the IRE;l1=l/n1=wavelength of radiant energy in the sample;and u=angle of incidence.derivative absorption spectrum—a plot of rate of change of absorbance or of any function of absorbance with respect to wavelength or any function of wavelength,against wave-length or any function of wavelength.difference absorption spectrum—a plot of the difference between two absorbances or between any function of two absorbances,against wavelength or any function of wave-length.diffuse reflection—reflection in which theflux is scattered in many directions by diffusion at or below the surface,(see Terminology E284).digitization—the conversion of an analog signal to digital values using an analog-to-digital converter“sampling”or “digital sampling.”digitization noise—the noise generated in an interferogram through the use of an analog-to-digital converter whose least significant bit represents a value comparable to,or greater than,the peak-to-peak noise level in the analog data. dilution factor—the ratio of the volume of a diluted solution to the volume of original solution containing thesamequantity of solute as the diluted solution.double modulation,n—a technique in which a modulated signal is further varied by a second means.D ISCUSSION—As an example,a spectrometer could generate a modu-lated signal while at the same time that signal is further varied by an external higher frequency modulator;on detection,the conventional spectrometric signal isfiltered out so that only the high frequency signal is recorded.double-pass internal reflection element—an internal reflec-tion element in which the radiant power transverses the length of the optical element twice,entering and leaving via the same end.effective pathlength(or effective thickness),d e—in internal reflection spectroscopy,the analog of the sample thickness in transmission spectroscopy that represents the distance of propagation of the evanescent wave within an absorbing sample in IRS.It is defined from the relationship:R=1−a d e,and is related to the absorption parameter by:a=a d e. evanescent wave—the standing wave that exists in the less refractive medium,normal to the reflecting surface of the IRE during internal reflection.extrinsicfiber optic chemical sensor,n—afiber optic chemi-cal sensor in which modulation of the optical signal is not effected through a change in the properties of thefiber itself.D ISCUSSION—Examples include a pH sensor composed of a chemicalindicator immobilized at the end of the opticalfiber,and a sensor based on Raman,fluorescence,infrared,visible,or other spectral information gathered in the acceptance cone of thefiber.far-infrared—pertaining to the infrared region of the electro-magnetic spectrum with wavelength range from approxi-mately25to1000µm(wavenumber range400to10cm-1). fast Fourier transform(FFT)—a method for speeding up the computation of a discrete FT by factoring the data into sparse matrices containing mostly zeroes.fiber optic buffer,n—material placed on or around a cladded opticalfiber to protect it from mechanical damage.D ISCUSSION—Mechanical damage can be caused by such things asmicrobends and macrobends formed during manufacture,spooling, subsequent handling,and pressure applied during use.Buffers may be bonded to the cladding and may also serve the purpose of preventing ambient energy from entering the core.fiber optic chemical sensor,n—afiber optic sensor that responds to a chemical stimulus.fiber optic sensor,n—a device that responds to an external stimulus and transmits through an opticalfiber a modulated optical signal,indicating one or more characteristics of the stimulus.D ISCUSSION—Examples include sensors which provide a suitablesignal or impulse to a meter.Such sensors might be found as the active elements in pH meters,strain gages,or pressure gages.fiber optics,n—the branch of science and technology devoted to the transmission of radiant energy throughfibers made of transparent materials.D ISCUSSION—Transparent materials include glass,fused silica,andplastic.Opticalfibers infiber optic cables may be used for data transmission,and for sensing,illumination,endoscopic,control,and display purposes,depending on their use in various geometric configu-rations,modes of excitation,and environmental conditions.Thefibers may be wound and bound in various shapes and distributions singly or in bundles.Bundles may be aligned or unaligned.Aligned bundles are often used to transmit and display images.filter—a substance that attenuates the radiant power reaching the detector in a definite manner with respect to spectral distribution.filter,neutral—afilter that attenuates the radiant power reaching the detector by the same factor at all wavelengths within a prescribed wavelength region.fixed-angle internal reflection element—an internal reflec-tion element which is designed to be operated at afixed angle of incidence.fluorescence—the emission of radiant energy from an atom, molecule,or ion resulting from absorption of a photon and a subsequent transition to the ground state without a change in total spin quantum number.D ISCUSSION—The initial andfinal states of the transition are usuallyboth singlet states.The average time interval between absorption and fluorescence is usually less than10−6s.folding—see aliasing.Fourier transform(FT)—the mathematical process used to convert an amplitude-time spectrum to an amplitude-frequency spectrum,or vice versa.D ISCUSSION—In FT-IR spectrometry,retardation is directly propor-tional to time;therefore the FT is commonly used to convert an amplitude-retardation spectrum to an amplitude-wavenumber spec-trum,and vice versa.Fourier transform infrared(FT-IR)spectrometry—a form of infrared spectrometry in which an interferogram is ob-tained;this interferogram is then subjected to a Fourier transform to obtain an amplitude-wavenumber(or wave-length)spectrum.D ISCUSSION—1—The abbreviation FTIR is not recommended.D ISCUSSION—2—When FT-IR spectrometers are interfaced withother instruments,a slash should be used to denote the interface;e.g.GC/FT-IR;HPLC/FT-IR,and the use of FT-IR should be explicit;i.e.FT-IR not IR.frequency,n—the number of cycles per unit time.D ISCUSSION—The recommended unit is the hertz(Hz)(one cycle persecond).frustrated total reflection(FTR)—the reflection which oc-curs when a nonabsorbing coupling mechanism acts in the process of total internal reflection to make the reflectance less than unity.D ISCUSSION—In the process the reflectance can vary continuouslybetween zero and unity if:(1)An optically transparent medium is within a fraction of a wavelength of the reflecting surface and its distance from the reflecting surface is changed,or(2)Both the angle of incidence and the refractive index of one of the media vary in an appropriate manner.In these cases part of the radiant power may be transmitted through the interface into the second medium without loss at the reflecting surface such that transmittance plus reflectance equals unity.It is possible,therefore to have this process taking place in some spectral regions even when a sample having absorption bands is placed in contact with the reflectingsurface.high-resolution NMR spectrometer—an NMR apparatus that is capable of producing,for a given isotope,line widths that are less than the majority of the chemical shifts and coupling constants for that isotope.D ISCUSSION—By this definition,a given spectrometer may be classedas a high-resolution instrument for isotopes with large chemical shifts, but may not be classed as a high-resolution instrument for isotopes with smaller chemical shifts.hole-burning,n—in luminescence,the photo-induced disap-pearance of a narrow segment within a broader absorption or emission band.D ISCUSSION—Holes are produced by the disappearance of resonantlyexcited molecules because of photochemical or photophysical pro-cesses.infrared—pertaining to the region of the electromagnetic spectrum with wavelength range from approximately0.78to 1000µm(wavenumber range12800to10cm-1). infrared spectroscopy—pertaining to spectroscopy in the infrared region of the electromagnetic spectrum.D ISCUSSION—1—Spectroscopy and other related terms are defined inTerminology E135.D ISCUSSION—2—Common applications of infrared spectroscopy arethe identification of materials and the quantitative analysis of materials (see,for example,Practices E204and Practices E168). instrument line shape(ILS)function—the FT of the function by which an interferogram is weighted.D ISCUSSION—This weighting may be performed optically,due to thefinite optical throughput,or digitally,through multiplication by an apodization function,or both.The ILS function is the profile of the spectrum of a monochromatic source producing a beam with the same throughput as the beam in the actual measurement being performed. instrument response time—the time required for an indicat-ing or detecting device to undergo a defined displacement following an abrupt change in the quantity being measured. integration period,p—the time,in seconds,required for the pen or other indicator to move98.6%of its maximum travel in response to a step function.D ISCUSSION—For instruments with afirst-order response,the integra-tion period will be approximately equal to four times the exponential time constant.It is equal to the period,classically defined,for a second order,critically damped response system.intercorrelation coefficient,(r XX)—a measure of the linear association between values of the same type of variable expressed as a correlation coefficient,(r).D ISCUSSION—The variables X and Y are replaced by Xj and Xkin theequation for the correlation coefficient,r.interferogram,I(d)—record of the modulated component of the interference signal measured as a function of retardation by the detector.D ISCUSSION—1—An alternate symbol is I(x).D ISCUSSION—2—The recommended symbol for the spectrum com-puted from I(d)is B(n).An alternate symbol is B(s). interferogram,double-sided—interferogram measured with approximately equal retardation on either side of the center-burst.interferogram,laser reference—sinusoidal interferogram of a laser source measured at the same time as the signal interferogram.D ISCUSSION—The zero crossings of this interferogram are used tocontrol sampling of the signal interferogram.It may also be noted that other effectively monochromatic sources can be used in place of the laser.interferogram,signal—interferogram of the beam of radiant energy whose spectrum is desired.interferogram,single-sided—interferogram in which sam-pling is initiated close to the centerburst and continues through that point to the maximum retardation desired. interferogram,white light—reference interferogram of a broadband light source measured at the same time as the signal interferogram and used to initiate data acquisition of consecutive scans for signal-averaging. interferometer—device used to divide a beam of radiant energy into two or more paths,generate an optical path difference between the beams,and recombine them in order to produce repetitive interference maxima and minima as the optical retardation is varied.interferometer,Genzel—interferometer in which the beam is focused in the plane of the beamsplitter and collimated before the moving mirror(s).interferometer,lamellar grating—interferometer in which the beam is reflected from two interleaved mirrors,one of which is stationary while the other is movable.D ISCUSSION—This type of interferometer is generally used only forfar infrared spectrometry.interferometer,Michelson—interferometer in which an ap-proximately collimated beam of radiant energy is divided into two paths by a beamsplitter;one beam is reflected from a movable mirror and the other from a stationary mirror,and they are then recombined at the beamsplitter. interferometer,rapid-scanning—interferometer in which the retardation is varied rapidly enough that the modulation frequencies in the interferogram are sufficiently high that the interferogram signal can be amplified directly without addi-tional modulation by an external chopper. interferometer,refractively scanned—interferometer in which the retardation between two beams is generated by the movement of a wedged optical element. interferometer,slow-scanning—interferometer in which the retardation is continuously varied,but so slowly that an external chopper is needed to modulate the beam at a frequency which is high enough for ac signal amplification. interferometer,stepped-scanning—interferometer in which the movable element is held stationary for the length of time required for signal integration and digitization of each sample point,and then translated to the next sample point. internal conversion,n—a transition between electronic states of the same total spin quantum number(multiplicity). internal,reflection attachment,IRA—the transfer optical system which supports the IRE,directs the energy of the radiant beam into the IRE,and then redirects the energy into the spectrometer or onto the detector.The IRA may bepartof an internal reflection spectrometer or it may be placed into the sampling space of a spectrometer.internal reflection element(IRE)—the transparent optical element used in internal reflection spectroscopy for estab-lishing the conditions necessary to obtain the internal reflec-tion spectra of materials.D ISCUSSION—Radiant power is propagated through it by means ofinternal reflection.The sample material is placed in contact with the reflecting surface or it may be the reflecting surface itself.If only a single reflection takes place from the internal reflection element the element is said to be a single reflection element;if more than one reflection takes place,the element is said to be a multiple reflection element.When the element has a recognized shape it is identified according to each shape,for example,internal reflection prism,internal reflection hemicylinder,internal reflection plate,internal reflection rod, internal reflectionfiber,etc.internal reflection spectroscopy(IRS)—the technique of recording optical spectra by placing a sample material in contact with a transparent medium of greater refractive index and measuring the reflectance(single or multiple)from the interface,generally at angles of incidence greater than the critical angle.intersystem crossing—-a transition between electronic states that differ in total spin quantum number(multiplicity).D ISCUSSION—Current experimental evidence indicates this process isnonradiative.intrinsicfiber optic chemical sensor,n—afiber optic chemi-cal sensor in which the modulation of the optical signal is effected through a change in the properties of the optical fiber itself,and such modulation occurs while the radiant energy is guided by the opticalfiber.irreversiblefiber optic chemical sensor,n—afiber optic chemical sensor that undergoes a permanent depletion or degradation of the transduction element as a result of the transduction process.D ISCUSSION—An example is a sensor based on an indicator that reactsirreversibly with the target analyte and that cannot be replenished after measurement.isoabsorptive point—a wavelength at which the absorptivities of two or more substances are equal.isosbestic point—the wavelength at which the absorptivities of two substances,one of which can be converted into the other,are equal.isostilbic point,n—in luminescence,the wavelength at which the intensity of emission of a sample does not change during a physical interaction or chemical reaction.level one(1)test,n—a simple series of measurements de-signed to provide quantitative data on various aspects of instrument performance and information on which to base the diagnosis of problems.level zero(0)test,n—a routine check of instrument perfor-mance,that can be done in a few minutes,designed to virtually detect significant changes in instrument perfor-mance and provide a database to determine instrument function over time.linear dispersion—the derivative,d x/d l,where x is the distance along the spectrum,in the plane of the exit slit,and l is the wavelength.lock signal(NMR)—the NMR signal used to control the field-frequency ratio of the spectrometer.It may or may not be the same as the reference signal. luminescence—the emission of radiant energy during a tran-sition from an excited electronic state of an atom,molecule, or ion to a lower electronic state.D ISCUSSION—1—The recommended unit for“sample pathlength”iscentimetres.This distance does not include the thickness of the walls of any absorption cell in which the specimen is contained.D ISCUSSION—2—In strict usage,a more appropriate term would be“specimen pathlength.”This is currently under advisement by E13. mid-infrared—pertaining to the infrared region of the elec-tromagnetic spectrum with wavelength range from approxi-mately2.5to25µm(wavenumber range4000to400cm-1). modulate,v—to vary a characteristic or parameter of an entity in accordance with a characteristic or parameter of another entity.modulation frequency,f v—the frequency,in Hz,at which radiant energy of a given wavenumber is modulated by a rapid-scanning interferometer.D ISCUSSION—1—This is given by the product of the wavenumber(cm−1)and the rate of change of retardation(cm·s−1).D ISCUSSION—2—An alternate symbol is fo.molar absorptivity,e—see absorptivity,molar. monochromator—a device or instrument that,with an appro-priate energy source,may be used to provide a continuous calibrated series of electromagnetic energy bands of deter-minable wavelength or frequency range.multiple correlation coefficient,(R)—the correlation,r yyˆ, between the accepted reference values,Y i,and the values determined using the calibration equation,Yˆi,equal to the square root of the coefficient of multiple determination,R2. near-infrared—pertaining to the infrared region of the elec-tromagnetic spectrum with wavelength range from approxi-mately0.78to2.5µm(wavenumber range12800to4000 cm-1).neutralfilter—seefilter,neutral.NMR absorption band;NMR band—a region of the spec-trum in which a detectable signal exists and passes through one or more maxima.NMR absorption line—a single transition or a set of degen-erate transitions is referred to as a line.NMR apparatus;NMR equipment—an instrument compris-ing a magnet,radio-frequency oscillator,sample holder,and a detector that is capable of producing an electrical signal suitable for display on a recorder or an oscilloscope,or which is suitable for input to a computer.nuclear magnetic resonance(NMR)spectroscopy—that form of spectroscopy concerned with radio-frequency-induced transitions between magnetic energy levels of atomic nuclei.numerical aperture(NA),n—the sine of one half of the vertex angle of the largest cone of meridional rays that can enter or leave an optical system or element,multiplied by the refractive index of the medium in which the cone is located.D ISCUSSION—Numerical aperture is generally measured with respectto an image point and will vary as that point is moved.For anoptical。
山东科学ＳＨＡＮＤＯＮＧＳＣＩＥＮＣＥ第３４卷第１期２０２１年２月出版Ｖｏｌ.３４Ｎｏ.１Ｆｅｂ.２０２１ＤＯＩ:１０.３９７６/ｊ.ｉｓｓｎ.１００２￣４０２６.２０２１.０１.００４ʌ新材料ɔ收稿日期:２０２０￣０９￣０３基金项目:滨州学院校级科研项目(ＢＺＸＹＬＧ１９２８)作者简介:李荣(１９８１ )ꎬ女ꎬ讲师ꎬ硕士ꎬ研究方向为电磁超材料特性ꎮＥ￣ｍａｉｌ:ｌｉｒｏｎｇ１９８１０８１０＠１６３.ｃｏｍ基于极化不敏感超材料的类电磁诱导透明特性研究李荣ꎬ郑文(滨州学院航空工程学院山东省航空材料与器件工程技术研究中心ꎬ山东滨州２５６６０３)摘要:设计了一种由４条金属直线和１个圆环构成的类电磁诱导透明超材料ꎬ当电磁波垂直入射到该超材料表面时ꎬ其具有水平极化和垂直极化不敏感特性ꎮ仿真了超材料的传输曲线特性ꎬ以及其表面电流分布特点ꎬ计算了相位传输曲线和群折射率ꎬ并对其介电常数传感特性进行了分析ꎮ计算所得群折射率最大值可达３８０ꎬ说明该超材料可用于制作慢光器件ꎮ用于制作传感器时ꎬ其ＤＦＯＭ值约为２０.１３ꎬ与前人所设计的传感器相比ꎬ具有较高的灵敏特性ꎮ研究结果表明ꎬ该超材料在制作慢光器件和传感器件方面具有一定的应用价值ꎮ关键词:类电磁诱导透明ꎻ超材料ꎻ极化不敏感ꎻ传感器ꎻ群折射率中图分类号:Ｏ４４１㊀㊀㊀文献标志码:Ａ㊀㊀㊀文章编号:１００２￣４０２６(２０２１)０１￣００２８￣０７开放科学(资源服务)标识码(ＯＳＩＤ):Ｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｔｈｅａｎａｌｏｇｏｆｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｉｎｃａｓｅｏｆａｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｓｅｎｓｉｔｉｖｅｍｅｔａｍａｔｅｒｉａｌＬＩＲｏｎｇꎬＺＨＥＮＧＷｅｎ(ＳｈａｎｄｏｎｇＥｎｇｉｎｅｅｒｉｎｇＲｅｓｅａｒｃｈＣｅｎｔｅｒｏｆＡｅｒｏｎａｕｔｉｃａｌＭａｔｅｒｉａｌｓａｎｄＤｅｖｉｃｅｓꎬＣｏｌｌｅｇｅｏｆＡｅｒｏｎａｕｔｉｃａｌＥｎｇｉｎｅｅｒｉｎｇꎬＢｉｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙꎬＢｉｎｚｈｏｕ２５６６０３ꎬＣｈｉｎａ)ＡｂｓｔｒａｃｔʒＩｎｔｈｉｓｓｔｕｄｙꎬａｎｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｔｍｅｔａｍａｔｅｒｉａｌｓｔｒｕｃｔｕｒｅｗｉｔｈｆｏｕｒｍｅｔａｌｌｉｎｅｓａｎｄａｒｉｎｇｉｓｐｒｏｐｏｓｅｄ.Ｉｔｅｘｈｉｂｉｔｓｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｈｏｒｉｚｏｎｔａｌａｎｄｖｅｒｔｉｃａｌｐｏｌａｒｉｚａｔｉｏｎｉｎｓｅｎｓｉｔｉｖｉｔｙｗｈｅｎｔｈｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｗａｖｅｉｓｐｅｒｐｅｎｄｉｃｕｌａｒｔｏｉｔｓｓｕｒｆａｃｅ.Ｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｔｈｅｍｅｔａｍａｔｅｒｉａｌｔｒａｎｓｍｉｓｓｉｏｎｃｕｒｖｅａｎｄｉｔｓｓｕｒｆａｃｅｃｕｒｒｅｎｔｄｉｓｔｒｉｂｕｔｉｏｎｈａｖｅｂｅｅｎｎｕｍｅｒｉｃａｌｌｙｃａｌｃｕｌａｔｅｄａｎｄｓｉｍｕｌａｔｅｄ.Ｆｕｒｔｈｅｒꎬｔｈｅｐｈａｓｅｐｒｏｐａｇａｔｉｏｎｃｕｒｖｅａｎｄｇｒｏｕｐｒｅｆｒａｃｔｉｖｅｉｎｄｅｘａｒｅｃａｌｃｕｌａｔｅｄａｎｄａｎａｌｙｚｅｄ.Ｔｈｅｍａｘｉｍｕｍｇｒｏｕｐｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｃａｎｒｅａｃｈｕｐｔｏ３８０ꎬｉｎｄｉｃａｔｉｎｇｔｈａｔｔｈｅｍｅｔａｍａｔｅｒｉａｌｃａｎｂｅｕｓｅｄｔｏｆａｂｒｉｃａｔｅｓｌｏｗｏｐｔｉｃａｌｄｅｖｉｃｅｓ.ＷｈｅｎｔｈｉｓｍｅｔａｍａｔｅｒｉａｌｉｓｕｓｅｄｔｏｍａｎｕｆａｃｔｕｒｅａｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｓｅｎｓｏｒꎬｔｈｅＤＦＯＭｖａｌｕｅｉｓａｐｐｒｏｘｉｍａｔｅｌｙ２０.１３ꎬｉｎｄｉｃａｔｉｎｇａｈｉｇｈｅｒｓｅｎｓｉｔｉｖｉｔｙｃｏｍｐａｒｅｄｗｉｔｈｔｈｏｓｅｏｆｔｈｅｅｘｉｓｔｉｎｇｓｅｎｓｏｒｓ.Ｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｍｅｔａｍａｔｅｒｉａｌｃａｎｂｅａｐｐｌｉｅｄｔｏｍａｎｕｆａｃｔｕｒｅｓｌｏｗｏｐｔｉｃａｌｄｅｖｉｃｅｓａｎｄｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｓｅｎｓｏｒｓ.Ｋｅｙｗｏｒｄｓʒａｎａｌｏｇｏｆｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙꎻｍｅｔａｍａｔｅｒｉａｌꎻｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｓｅｎｓｉｔｉｖｅꎻｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｓｅｎｓｏｒꎻｇｒｏｕｐｒｅｆｒａｃｔｉｖｅｉｎｄｅｘ第１期李荣ꎬ等:基于极化不敏感超材料的类电磁诱导透明特性研究㊀㊀电磁诱导透明(ｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙꎬＥＩＴ)是三维原子系统中的量子相消干涉现象ꎮ类电磁诱导透明(ａｎａｌｏｇｏｆｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙꎬＡ￣ＥＩＴ)ꎬ是利用人工电磁超材料模拟原子系统中的电磁诱导透明现象ꎬ其显著特点是在原本不透明的传输窗口产生了具有高Ｑ值和强色散性质的传输峰[１]ꎮ人工电磁超材料是具有特定几何结构的人造材料ꎬ可以与入射电磁波产生耦合效应ꎮ通过设计超材料的几何尺寸和结构ꎬ在电磁波的作用下ꎬ可以获得普通材料不能表现出来的特性ꎬ比如负折射率㊁完美吸波㊁慢光性质等等[２￣４]ꎮ超材料的类电磁诱导透明特性可以应用到量子存储㊁极化转换㊁光学开关㊁传感器等很多方面[５￣８]ꎮ孙雅茹等[９]设计了一种基于类电磁诱导透明的太赫兹波段的超材料传感器ꎬ该设备可用于生物化学领域的特异性传感检测ꎮＤｅｎｇ等[１０]设计了一种交叉极化转换器ꎬ该转换器可以将线极化波转换为交叉极化波ꎬ可应用于极化控制或滤波器设计ꎮＬｉｕ等[１１]设计了一种双层超材料结构ꎬ该超材料在工作频段具有两个传输透明窗口ꎬ可用于设计检测周围物质介电常数的传感器ꎮ近几年ꎬ基于固态等离子体㊁石墨烯等设计的可控电磁诱导透明超材料逐渐成为人们研究的热点ꎮ例如ꎬＫｏｎｇ等[１２]设计了一款由固态等离子体超材料和光子晶体组成的异质结构ꎬ通过调节固态等离子体的频率而不是改变超材料的几何结构ꎬ可以实现谐振频段的改变ꎬ该超材料结构可用于制作高灵敏度介电传感㊁光开关等器件ꎮＭｅｉ等[１３]提出了一种新型的耦合杂化石墨烯超材料结构ꎬ通过改变石墨烯的费米能级ꎬ可以在两个垂直极化方向上实现类电磁诱导透明的可调谐效应ꎮ以上研究所设计的超材料结构虽能达到一定的应用目的ꎬ但存在着几何单元电尺寸较大㊁几何结构复杂或性能指标较低等不足ꎮ鉴于此ꎬ本文设计了一款结构简单且几何单元电尺寸较小㊁性能指标较高的超材料结构ꎬ并对其类电磁诱导特性进行了较为深入的研究ꎮ图１㊀超材料结构示意图Ｆｉｇ.１㊀Ｓｃｈｅｍａｔｉｃｏｆｔｈｅｍｅｔａｍａｔｅｒｉａｌｕｎｉｔｃｅｌｌ１㊀结构设计超材料单元结构由４条金属线和１个圆环构成ꎬ如图１所示ꎮ４条金属线的长和宽均相等ꎬ圆环放置在４条金属线内部ꎬ整个结构具有中心对称性ꎮ几何参数具体为:ａ＝８.４ｍｍꎬｗ＝０.２ｍｍꎬｒ＝３.５ｍｍꎬｗ１＝０.５ｍｍꎮ金属线为铜材质ꎬ厚度为ｔ＝０.０３５ｍｍꎮ整个几何结构放置在边长ｂ＝１０ｍｍꎬ厚度ｔ１＝１ｍｍ的基板上ꎬ基板选用ＦＲ４ꎬ介电常数ε＝４.３ꎬ损耗角正切ｔａｎδ＝０.０２５ꎮ该单元结构在ｘ㊁ｙ方向呈周期性排列分布ꎮ利用ＣＳＴＭｉｃｒｏｗａｖｅＳｔｕｄｉｏ软件进行仿真ꎮ仿真设置平面电磁波垂直入射到超材料表面ꎬｘ方向为磁极化方向ꎬｙ方向为电极化方向ꎬＺ方向为开放边界ꎬｋ为电磁波失量ꎮ２㊀仿真结果和讨论２.１㊀４ＬＲｓ￣ＲＲ超材料结构构建若单元结构只有４条直线(称为４ＬＲｓ谐振器)时ꎬ电磁波垂直入射到该结构表面时ꎬ传输曲线在ｆ１＝１１.４ＧＨｚ处出现一个谐振谷ꎮ由于该结构具有中心对称性ꎬ在电磁波垂直入射时ꎬ满足极化不敏感特性ꎬ所以其水平极化的透射传输谱与垂直极化的透射传输谱完全重合ꎮ如图２所示ꎬ实线表示垂直极化的透射传输谱ꎬ点线表示水平极化的透射传输谱ꎮ图２中左下角的内插图表示４ＬＲｓ谐振器的单元结构ꎬ蓝色背景是ＦＲ４基板ꎮ若单元结构只有一个圆环(称为ＲＲ谐振器)时ꎬ电磁波垂直入射到该结构表面时ꎬ传输曲线在ｆ２＝９.９６ＧＨｚ处出现一个谐振谷ꎬ其透射传输谱与４ＬＲｓ谐振器类似ꎬ具有极化不敏感性ꎬ如图３所示ꎮ图３中左下角的内插图表示ＲＲ谐振器的单元结构ꎬ蓝色背景是ＦＲ４基板ꎮ９２山㊀东㊀科㊀学２０２１年图２㊀４ＬＲｓ的传输曲线Ｆｉｇ.２㊀Ｓｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｓｐｅｃｔｒａｆｏｒ４ＬＲｓ图３ＲＲ的传输曲线Ｆｉｇ.３㊀ＳｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｓｐｅｃｔｒａｆｏｒＲＲ㊀㊀类电磁诱导透明现象一般通过缺陷模式耦合或者明模式－暗模式耦合产生ꎮ缺陷模式指的是由于单元结构的对称性被打破而与入射电磁波产生耦合作用[１４]ꎮ明模式指的是由入射电磁波直接激发而产生谐振ꎬ暗模式指的是不能被入射电磁波直接激发ꎬ但可以通过与明模式的耦合进而被激发ꎬ并且明模式的Ｑ值小于暗模式的Ｑ值[１５]ꎮ由品质因数的定义Ｑ＝ｆ０/Δｆ(ｆ０是谐振频率ꎬΔｆ是曲线半高宽)[１６]ꎬ可得图２和图３的传输曲线的Ｑ值分别为２.３４和１.４７ꎬ即４ＬＲｓ谐振的Ｑ值大于ＲＲ谐振的Ｑ值ꎬ所以４ＬＲｓ谐振为暗模式ꎬ而ＲＲ谐振为明模式ꎮ若单元结构由４条直线和１个圆环(称为４ＬＲｓ￣ＲＲ谐振器)构成时ꎬ传输曲线在两个谐振谷之间出现了一个谐振峰(ｆ＝１０.５２ＧＨｚ)ꎬ表明此结构的超材料产生了类电磁诱导透明现象ꎮ该传输曲线同样具有极化不敏感特性ꎬ如图４所示ꎮ图４中左下角的内插图表示４ＬＲｓ￣ＲＲ谐振器的单元结构ꎬ蓝色背景是ＦＲ４基板ꎮ图４㊀４ＬＲｓ￣ＲＲ的传输曲线Ｆｉｇ.４㊀Ｓｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｓｐｅｃｔｒａｆｏｒ４ＬＲｓ￣ＲＲ图５给出了电磁波垂直入射时ꎬ极化角分别为０ʎ㊁９０ʎ㊁１８０ʎ㊁２７０ʎ时的水平极化透射传输谱ꎮ由图５可以看出ꎬ当极化角发生变化时ꎬ透射曲线没有发生明显的变化ꎬ充分证明了该结构具有极化不敏感的特性ꎮ由于水平极化入射电场与垂直极化入射电场相差９０ʎꎬ所以垂直极化透射谱与水平极化透射谱相同ꎮ极化不敏感透射谱的形成ꎬ与４ＬＲｓ￣ＲＲ结构单元的独特设置有关ꎮ在０ʎ㊁９０ʎ㊁１８０ʎ㊁２７０ʎ不同的极化角度下ꎬ圆环(ＲＲ)是相同的ꎬ４条直线(４ＬＲｓ)分别位于平行于ｘ轴或ｙ轴的方向ꎬ这使得４ＬＲｓ对平行极化和垂直极化入射电磁波的响应０３第１期李荣ꎬ等:基于极化不敏感超材料的类电磁诱导透明特性研究是相同的ꎮ因此ꎬ该超材料在０ʎ㊁９０ʎ㊁１８０ʎ㊁２７０ʎ等特定极化角度下均表现出极化不敏感特性ꎮ图５㊀极化角为０ʎ㊁９ʎ㊁１８０ʎ㊁２７０ʎ时的４ＬＲｓ￣ＲＲ透射传输谱(水平极化)Ｆｉｇ.５㊀Ｓｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｓｐｅｃｔｒａｆｏｒｐｏｌａｒｉｚａｔｉｏｎａｎｇｌｅｓｏｆ０ʎ㊁９ʎ㊁１８０ʎ㊁ａｎｄ２７０ʎ(ｘｐｏｌａｒｉｚａｔｉｏｎ)２.２㊀４ＬＲｓ￣ＲＲ超材料结构的表面电流为了进一步研究超材料产生的类电磁诱导透明现象的原因ꎬ本文仿真了４ＬＲｓ￣ＲＲ超材料结构的表面电流分布情况ꎮ当电磁波垂直入射到该超材料表面时ꎬ两个传输谷(ｆ３＝９.７９ＧＨｚꎬｆ４＝１１.３６ＧＨｚ)和一个传输峰(ｆ＝１０.５２ＧＨｚ)处的表面电流分布情况如图６所示ꎮ图６㊀电磁波垂直入射时的表面电流分布图Ｆｉｇ.６㊀Ｓｕｒｆａｃｅｃｕｒｒｅｎｔｄｉｓｔｒｉｂｕｔｉｏｎｓｏｆｔｈｅｍｅｔａｍａｔｅｒｉａｌｕｎｄｅｒａｐｅｒｐｅｎｄｉｃｕｌａｒｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｗａｖｅ图６(ａ)是垂直极化条件下传输谷ｆ３＝９.７９ＧＨｚ处的表面电流分布ꎬ此时表面电流主要分布在圆环左右两侧ꎬ４条直线上的表面电流被压制ꎮ这是由于此时入射电场方向沿ｙ方向ꎬ入射电磁波的低频部分与圆环结构产生谐振ꎬ导致在圆环左右两侧表面产生了感应电流ꎮ图６(ｃ)是垂直极化条件下传输谷ｆ４＝１１.３６ＧＨｚ处的表面电流分布ꎬ此时表面电流主要分布在４ＬＲｓ结构上且主要在左右两条直线上ꎬ圆环的表面电流几乎为零ꎮ这是因为此时入射电场方向沿ｙ方向ꎬ入射电磁波的高频部分与４ＬＲｓ结构的左右两条直线产生谐振ꎬ导致在这两条直线表面产生了感应电流ꎮ图６(ｂ)是垂直极化条件下传输峰ｆ＝１０.５２ＧＨｚ处的表面电流分布ꎬ此时表面电流在４ＬＲｓ结构以及圆环结构上都有表面电流分布ꎬ且电流强度比两个传输谷处的都要大ꎮ但是仔细观察可发现ꎬ在４ＬＲｓ结构的左右两条直线上表面电流的流动方向与圆环结构左右两侧的电流强度相当ꎬ但是流动方向相反ꎬ这导致４ＬＲｓ谐振器和ＲＲ谐振器发生破坏性干涉ꎬ并最终导致类电磁诱导透明现象的出现ꎮ１３山㊀东㊀科㊀学２０２１年图６(ｄ)~６(ｆ)为水平极化条件下传输谷ｆ３＝９.７９ＧＨｚꎬ传输峰ｆ＝１０.５２ＧＨｚ和传输谷ｆ４＝１１.３６ＧＨｚ处的表面电流分布情况ꎮ与上述分析相类似ꎬ由于水平极化条件下电磁波的电场部分主要沿ｘ方向ꎬ导致感应电流主要分布在圆环上下两侧或者４ＬＲｓ结构的上下两条直线的表面ꎮ另外ꎬ由于入射电磁波电场极化方向沿ｙ方向ꎬ传输曲线无论在波峰处ꎬ还是波谷处ꎬ超材料结构的表面电流分布均表现为左右对称ꎮ当电磁波垂直入射ꎬ且电场极化为水平极化时ꎬ表面电流则主要表现为上下对称ꎮ２.３㊀４ＬＲｓ￣ＲＲ超材料结构的传输相位、群时延和群折射率图７给出了电磁波垂直入射到所设计的超材料表面时的传输相位和群时延ꎬ其中虚线表示群时延ꎮ从图７中可以看出ꎬ两种极化条件下的传输相位曲线完全一致ꎬ再次证明了本文所设计的超材料结构具有水平极化和垂直极化的不敏感性ꎮ从图中还可看出ꎬ对应于电磁波频段９.７９~１１.３６ＧＨｚꎬ传输相位曲线发生了明显的陡峭变化ꎬ这说明在该频段内超材料出现了类电磁诱导透明现象ꎬ与图４所得结论相符合ꎮ另外ꎬ在产生类电磁诱导透明窗口的频段内ꎬ群时延最大值可达１.２ｎｓꎬ说明该超材料具有慢光效应ꎬ可用于设计慢光器件ꎮ图８表示群折射率随传输频率的变化曲线ꎬ由图８可知ꎬ群折射率最大值可达到３８０ꎬ同样说明该超材料具有慢光效应ꎮ该图还显示出电磁波垂直入射时ꎬ水平极化和垂直极化条件下的群折射率曲线完全一致ꎬ进一步证明了本文所设计的超材料结构具有水平极化和垂直极化的不敏感性ꎮ图７㊀电磁波垂直入射时的传输相位和群时延Ｆｉｇ.７㊀Ｓｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｐｈａｓｅａｎｄｇｒｏｕｐｄｅｌａｙｏｆｔｈｅｍｅｔａｍａｔｅｒｉａｌｕｎｄｅｒａｐｅｒｐｅｎｄｉｃｕｌａｒｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｗａｖｅ图８㊀群折射率随传输频率的变化Ｆｉｇ.８㊀Ｃｈａｒｇｅｏｆｓｉｍｕｌａｔｅｄｇｒｏｕｐｉｎｄｅｘｏｆｔｈｅｍｅｔａｍａｔｅｒｉａｌｗｉｔｈｔｒａｎｓｍｉｓｓｉｏｎｆｒｅｑｕｅｎｃｙ２３第１期李荣ꎬ等:基于极化不敏感超材料的类电磁诱导透明特性研究２.４㊀４ＬＲｓ￣ＲＲ超材料应用及评价由于所设计的超材料具有类电磁诱导透明特性ꎬ在传输透明窗口有一个较为尖锐的传输峰ꎬ我们尝试将该超材料用于设计传感器ꎮ图９表明ꎬ当超材料表面覆盖一层待测物时ꎬ如果待测物的介电常数发生变化ꎬ传输曲线的峰值所对应的电磁波频点也将发生变化ꎮ随着待测物介电常数的增大ꎬ传输峰将向频率变小的方向移动ꎬ即发生了红移现象ꎮ图９中实线表示电磁波垂直入射时电场方向为垂直极化方向ꎬ点线表示电磁波垂直入射时电场方向为水平极化方向ꎮ说明该超材料用于传感器时仍然具有水平极化和垂直极化不敏感特性ꎮ图１０是不同待测物的传输峰值所对应的频点与介电常数的关系图ꎮ从图１０中可以看出ꎬ当待测物的介电常数变大时ꎬ其传输峰值所对应的谐振频率将变小ꎬ且介电常数与频点之间满足线性关系ꎮ图９㊀不同待测物的传输曲线Ｆｉｇ.９㊀Ｓｉｍｕｌａｔｅｄｔｒａｎｓｍｉｓｓｉｏｎｓｐｅｃｔｒａｆｏｒｄｉｆｆｅｒｅｎｔｍｅｔａｍａｔｅｒｉａｌｓ图１０㊀不同待测物的传输峰值所对应的频点与介电常数的关系图Ｆｉｇ.１０㊀Ｔｈｅｆｒｅｑｕｅｎｃｙｐｏｉｎｔｏｆｔｈｅｔｒａｎｓｍｉｓｓｉｏｎｐｅａｋｗｉｔｈｄｉｆｆｅｒｅｎｔｐｅｒｍｉｔｔｉｖｉｔｙｖａｌｕｅｓ㊀㊀评价传感器性能的一个关键参数是ＤＦＯＭ值ꎬ是指单位折射率变化所引起的谐振峰频率平移量与谐振峰半高全宽的比值ꎬ即ＤＦＯＭ＝Δｆ/(Δｎ ＦＦＷＨＭ)ꎬ式中Δｆ表示谐振峰频率平移量ꎬΔｎ表示折射率变化量ꎬＦＦＷＨＭ表示谐振峰半高全宽[１７]ꎮ将折射率换算成介质的介电常数ꎬ由图１０线性关系图ꎬ可求得传感器的ＤＦＯＭ值约等于２０.１３ꎮ表１比较了不同超材料结构传感器的ＤＦＯＭ值[１８￣２２]ꎬ由表１可知ꎬ本文所设计的超材料传感器具有较高的ＤＦＯＭ值ꎬ其传感性能较好ꎮ表１㊀不同超材料结构传感器ＤＦＯＭ值比较Ｔａｂｌｅ１㊀Ｃｏｍｐａｒｉｓｏｎｍｅｔａｍａｔｅｒｉａｌｓｔｒｕｃｔｕｒｅｓ[１９]３.６６.１７[２０]６.０８.７３[２１]５.５１１.６６[２２]９.８９１３.４本文１０.５２０.１３３㊀结论设计了一种具有水平极化和垂直极化不敏感的超材料结构ꎬ其单元结构简单ꎬ且为单层平面结构ꎬ大大降低了加工成本和难度ꎮ通过分析表面电流分布特点㊁传输相位㊁群时延和群折射率ꎬ证实了该超材料具有３３４３山㊀东㊀科㊀学２０２１年类电磁诱导透明特性ꎮ基于该超材料还设计了一款具有较高灵敏性的传感器ꎮ由于所设计超材料具有较大的群折射率和较高的ＤＦＯＭ值ꎬ表明其在慢光器件㊁生物传感㊁环境测试等方面具有潜在应用价值ꎮ参考文献:[１]ＭＡＲＡＮＧＯＳＪＰ.Ｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙ[Ｍ]//ＥｎｃｙｃｌｏｐｅｄｉａｏｆＭｏｄｅｒｎＯｐｔｉｃｓ.Ａｍｓｔｅｒｄａｍ:Ｅｌｓｅｖｉｅｒꎬ２００５:３３９￣３４６.ＤＯＩ:１０.１０１６/ｂ９７８￣０￣１２￣８０９２８３￣５.００７５１￣５.[２]ＶＡＬＥＮＴＩＮＥＪꎬＺＨＡＮＧＳꎬＺＥＮＴＧＲＡＦＴꎬｅｔａｌ.Ｔｈｒｅｅ￣ｄｉｍｅｎｓｉｏｎａｌｏｐｔｉｃａｌｍｅｔａｍａｔｅｒｉａｌｗｉｔｈａｎｅｇａｔｉｖｅｒｅｆｒａｃｔｉｖｅｉｎｄｅｘ[Ｊ].Ｎａｔｕｒｅꎬ２００８ꎬ４５５(７２１１):３７６￣９.ＤＯＩ:１０.１０３８/ｎａｔｕｒｅ０７２４７.[３]ＣＨＥＮＨＳꎬＷＵＢＩꎬＺＨＡＮＧＢꎬｅｔａｌ.Ｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｗａｖｅｉｎｔｅｒａｃｔｉｏｎｓｗｉｔｈａｍｅｔａｍａｔｅｒｉａｌｃｌｏａｋ[Ｊ].ＰｈｙｓｉｃａｌＲｅｖｉｅｗＬｅｔｔｅｒｓꎬ２００７ꎬ９９(６):０６３９０３.ＤＯＩ:１０.１１０３/ＰｈｙｓＲｅｖＬｅｔｔ.９９.０６３９０３.[４]ＪＩＡＮＧＣꎬＬＩＵＨＸꎬＣＵＩＹＳꎬｅｔａｌ.Ｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙａｎｄｓｌｏｗｌｉｇｈｔｉｎｔｗｏ￣ｍｏｄｅｏｐｔｏｍｅｃｈａｎｉｃｓ[Ｊ].ＯｐｔｉｃｓＥｘｐｒｅｓｓꎬ２０１３ꎬ２１(１０):１２１６５￣１２１７３.ＤＯＩ:１０.１３６４/ＯＥ.２１.０１２１６５.[５]周强ꎬ刘金璐ꎬ谷远辉ꎬ等.量子保密通信用增益开关半导体脉冲激光器[Ｊ].中国激光ꎬ２０１６(５):２５￣３０.ＤＯＩ:１０.３７８８/ＣＪＬ２０１６４３.０５０２００５.ＺＨＯＵＱꎬＬＩＵＪＬꎬＧＵＹＨꎬｅｔａｌ.Ｇａｉｎ￣ｓｗｉｔｃｈｅｄｓｅｍｉｃｏｎｄｕｃｔｏｒｐｕｌｓｅｄｌａｓｅｒｆｏｒｑｕａｎｔｕｍｓｅｃｕｒｅｃｏｍｍｕｎｉｃａｔｉｏｎ[Ｊ].ＣｈｉｎｅｓｅＪｏｕｒｎａｌｏｆＬａｓｅｒｓꎬ２０１６(５):２５￣３０.ＤＯＩ:１０.３７８８/ＣＪＬ２０１６４３.０５０２００５.[６]ＺＨＡＮＧＹＰꎬＬＩＹꎬＣＡＯＹＹꎬｅｔａｌ.Ｇｒａｐｈｅｎｅｉｎｄｕｃｅｄｔｕｎａｂｌｅａｎｄｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｓｅｎｓｉｔｉｖｅｂｒｏａｄｂａｎｄｍｅｔａｍａｔｅｒｉａｌａｂｓｏｒｂｅｒ[Ｊ].ＯｐｔｉｃｓＣｏｍｍｕｎｉｃａｔｉｏｎｓꎬ２０１７ꎬ３８２:２８１￣２８７.ＤＯＩ:１０.１０１６/ｊ.ｏｐｔｃｏｍ.２０１６.０８.００３.[７]ＺＨＡＮＧＸＱꎬＬＩＱꎬＣＡＯＷꎬｅｔａｌ.Ｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｄｅｐｅｎｄｅｎｔｐｌａｓｍｏｎ￣ｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｉｎａｆｏｕｒｆｏｌｄｓｙｍｍｅｔｒｉｃｔｅｒａｈｅｒｔｚｍｅｔａｍａｔｅｒｉａｌ[Ｊ].ＩＥＥＥＪｏｕｒｎａｌｏｎＳｅｌｅｃｔｅｄＴｏｐｉｃｓｉｎＱｕａｎｔｕｍＥｌｅｃｔｒｏｎｉｃｓꎬ２０１３ꎬ１９(１):６０￣６６.[８]ＰＡＮＷꎬＹＡＮＹＪꎬＭＡＹꎬｅｔａｌ.Ａｔｅｒａｈｅｒｔｚｍｅｔａｍａｔｅｒｉａｌｂａｓｅｄｏｎｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｅｆｆｅｃｔａｎｄｉｔｓｓｅｎｓｉｎｇｐｅｒｆｏｒｍａｎｃｅ[Ｊ].ＯｐｔｉｃｓＣｏｍｍｕｎｉｃａｔｉｏｎｓꎬ２０１９ꎬ４３１:１１５￣１１９.ＤＯＩ:１０.１０１６/ｊ.ｏｐｔｃｏｍ.２０１８.０９.０１４.[９]孙雅茹ꎬ史同璐ꎬ刘建军ꎬ等.太赫兹超材料类ＥＩＴ谐振无标记生物传感[Ｊ].光学学报ꎬ２０１６ꎬ３６(３):２６１￣２６６.ＤＯＩ:１０.３７８８/ＡＯＳ２０１６３６.０３２８００１.ＳＵＮＹＲꎬＳＨＩＴＬꎬＬＩＵＪＪꎬｅｔａｌ.Ｔｅｒａｈｅｒｔｚｌａｂｅｌ￣ｆｒｅｅｂｉｏ￣ｓｅｎｓｉｎｇｗｉｔｈＥＩＴ￣ｌｉｋｅｍｅｔａｍａｔｅｒｉａｌｓ[Ｊ].ＡｃｔａＯｐｔｉｃＳｉｎｉｃａꎬ２０１６ꎬ３６(３):２６１￣２６６.ＤＯＩ:１０.３７８８/ＡＯＳ２０１６３６.０３２８００１.[１０]ＤＥＮＧＹＤꎬＳＯＮＧＺ.Ｍａｎｉｐｕｌａｔｉｎｇｐｏｌａｒｉｚａｔｉｏｎａｎｄｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｉｎａｓｗｉｔｃｈａｂｌｅｍｅｔａｍａｔｅｒｉａｌ[Ｊ].ＯｐｔｉｃａｌＭａｔｅｒｉａｌｓꎬ２０２０ꎬ１０５(５):１０９９７２.ＤＯＩ:１０.１０１６/ｊ.ｏｐｔｍａｔ.２０２０.１０９９７２.[１１]ＬＩＵＳＹꎬＸＵＺＸꎬＹＩＮＸＸꎬｅｔａｌ.Ａｎａｌｏｇｏｆｍｕｌｔｉｐｌｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｕｓｉｎｇｄｏｕｂｌｅ￣ｌａｙｅｒｅｄｍｅｔａｓｕｒｆａｃｅｓ[Ｊ].ＳｃｉｅｎｔｉｆｉｃＲｅｐｏｒｔｓꎬ２０２０ꎬ１０:８４６９.ＤＯＩ:１０.１０３８/ｓ４１５９８￣０２０￣６５４１８￣ｘ.[１２]ＫＯＮＧＸＫꎬＬＩＨＭꎬＢＩＡＮＢＲꎬｅｔａｌ.Ｍｉｃｒｏｗａｖｅｔｕｎｎｅｌｉｎｇｉｎｈｅｔｅｒｏｓｔｒｕｃｔｕｒｅｓｗｉｔｈｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙ￣ｌｉｋｅｍｅｔａｍａｔｅｒｉａｌｓｂａｓｅｄｏｎｓｏｌｉｄｓｔａｔｅｐｌａｓｍａ[Ｊ].ＴｈｅＥｕｒｏｐｅａｎＰｈｙｓｉｃａｌＪｏｕｒｎａｌＡｐｐｌｉｅｄＰｈｙｓｉｃｓꎬ２０１６ꎬ７４(３):３０８０１.ＤＯＩ:１０.１０５１/ｅｐｊａｐ/２０１６１５０４５２.[１３]ＭＥＩＪＳꎬＳＨＵＣꎬＹＡＮＧＰＺ.Ｔｕｎａｂｌｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｉｎｇｒａｐｈｅｎｅｍｅｔａｍａｔｅｒｉａｌｉｎｔｗｏｐｅｒｐｅｎｄｉｃｕｌａｒｐｏｌａｒｉｚａｔｉｏｎｄｉｒｅｃｔｉｏｎｓ[Ｊ].ＡｐｐｌｉｅｄＰｈｙｓｉｃｓＢꎬ２０１９ꎬ１２５(７):１￣８.ＤＯＩ:１０.１００７/ｓ００３４０￣０１９￣７２４２￣８.[１４]ＦＥＤＯＴＯＶＶＡꎬＲＯＳＥＭꎬＰＲＯＳＶＩＲＮＩＮＳＬꎬｅｔａｌ.Ｓｈａｒｐｔｒａｐｐｅｄ￣ｍｏｄｅｒｅｓｏｎａｎｃｅｓｉｎｐｌａｎａｒｍｅｔａｍａｔｅｒｉａｌｓｗｉｔｈａｂｒｏｋｅｎｓｔｒｕｃｔｕｒａｌｓｙｍｍｅｔｒｙ[Ｊ].ＰｈｙｓｉｃａｌＲｅｖｉｅｗＬｅｔｔｅｒｓꎬ２００７ꎬ９９(１４):１４７４０１.ＤＯＩ:１０.１１０３/ＰｈｙｓＲｅｖＬｅｔｔ.９９.１４７４０１.[１５]ＭＥＮＧＤＪꎬＷＡＮＧＳＹꎬＳＵＮＸＬꎬｅｔａｌ.Ａｃｔｉｖｅｌｙｂｉａｓ￣ｃｏｎｔｒｏｌｌｅｄｍｅｔａｍａｔｅｒｉａｌｔｏｍｉｍｉｃａｎｄｍｏｄｕｌａｔｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙ[Ｊ].ＡｐｐｌｉｅｄＰｈｙｓｉｃｓＬｅｔｔｅｒｓꎬ２０１４ꎬ１０４(２６):２６１９０２.ＤＯＩ:１０.１０６３/１.４８８６１４８.[１６]ＷＥＩＺＣꎬＬＩＸＰꎬＺＨＯＮＧＮＦꎬｅｔａｌ.Ａｎａｌｏｇｕｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｂａｓｅｄｏｎｌｏｗ￣ｌｏｓｓｍｅｔａｍａｔｅｒｉａｌａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｉｎｎａｎｏｓｅｎｓｏｒａｎｄｓｌｏｗ￣ｌｉｇｈｔｄｅｖｉｃｅ[Ｊ].Ｐｌａｓｍｏｎｉｃｓꎬ２０１７ꎬ１２(３):６４１￣６４７.ＤＯＩ:１０.１００７/ｓ１１４６８￣０１６￣０３０９￣ｚ. [１７]ＣＨＥＮＣＹꎬＵＮＩＷꎬＴＡＩＮＨꎬｅｔａｌ.Ａｓｙｍｍｅｔｒｉｃｃｏｕｐｌｉｎｇｂｅｔｗｅｅｎｓｕｂｒａｄｉａｎｔａｎｄｓｕｐｅｒｒａｄｉａｎｔｐｌａｓｍｏｎｉｃｒｅｓｏｎａｎｃｅｓａｎｄｉｔｓｅｎｈａｎｃｅｄｓｅｎｓｉｎｇｐｅｒｆｏｒｍａｎｃｅ[Ｊ].ＯｐｔｉｃｓＥｘｐｒｅｓｓꎬ２００９ꎬ１７(１７):１５３７２.ＤＯＩ:１０.１３６４/ｏｅ.１７.０１５３７２.(下转第７１页)１７第１期盛冬冬ꎬ等:基于面板混合Ｌｏｇｉｔ模型的中长途高速客运方式分担率预测ｄｒｉｖｉｎｇｅｎｖｉｒｏｎｍｅｎｔａｌｂｉｇｄａｔａ[Ｊ].ＪｏｕｒｎａｌｏｆＳａｆｅｔｙＲｅｓｅａｒｃｈꎬ２０１８ꎬ６５:１５３￣１５９.ＤＯＩ:１０.１０１６/ｊ.ｊｓｒ.２０１８.０２.０１０. [１２]ＭＣＦＡＤＤＥＮＤꎬＴＲＡＩＮＫ.ＭｉｘｅｄＭＮＬｍｏｄｅｌｓｆｏｒｄｉｓｃｒｅｔｅｒｅｓｐｏｎｓｅ[Ｊ].ＪｏｕｒｎａｌｏｆＡｐｐｌｉｅｄＥｃｏｎｏｍｅｔｒｉｃｓꎬ２０００ꎬ１５(５):４４７￣４７０.ＤＯＩ:１０.１００２/１０９９￣１２５５(２００００９/１０)１５:５<４４７::ＡＩＤ￣ＪＡＥ５７０>３.０.ＣＯꎻ２￣１.[１３]ＨＥＮＳＨＥＲＤＡꎬＲＯＳＥＪＭꎬＧＲＥＥＮＥＷＨ.Ａｐｐｌｉｅｄｃｈｏｉｃｅａｎａｌｙｓｉｓ[Ｍ].Ｌｏｎｄｏｎ:ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓꎬ２０１５. [１４]方琪根.高速铁路运营成本作业成本法测算研究[Ｊ].交通科技ꎬ２００７(４):１３４￣１３６.ＤＯＩ:１０.３９６３/ｊ.ｉｓｓｎ.１６７１￣７５７０.２００７.０４.０４８.ＦＡＮＧＱＧ.Ｒｅｓｅａｒｃｈｏｎｏｐｅｒａｔｉｏｎｃｏｓｔｏｆｈｉｇｈ￣ｓｐｅｅｄｒａｉｌｗａｙ[Ｊ].ＴｒａｎｓｐｏｒｔａｔｉｏｎＳｃｉｅｎｃｅ＆Ｔｅｃｈｎｏｌｏｇｙꎬ２００７(４):１３４￣１３６.ＤＯＩ:１０.３９６３/ｊ.ｉｓｓｎ.１６７１￣７５７０.２００７.０４.０４８.[１５]张旭.高速铁路与民航客运竞争及协同发展研究[Ｄ].大连:大连海事大学ꎬ２０１２.ＺＨＡＮＧＸ.ＲｅｓｅａｒｃｈｏｎｃｏｍｐｅｔｉｔｉｏｎａｎｄｃｏｌｌａｂｏｒａｔｉｖｅｄｅｖｅｌｏｐｍｅｎｔｂｅｔｗｅｅｎＨＳＲａｎｄｃｉｖｉｌａｖｉａｔｉｏｎ[Ｄ].Ｄａｌｉａｎ:ＤａｌｉａｎＭａｒｉｔｉｍｅＵｎｉｖｅｒｓｉｔｙꎬ２０１２.[１６]干宏程.交通信息与出行者路线选择[Ｍ].北京:科学出版社ꎬ２０１４.ＧＡＮＨＣ.Ｔｒａｆｆｉｃｉｎｆｏｒｍａｔｉｏｎａｎｄｔｒａｖｅｌｅｒᶄｓｒｏｕｔｅｃｈｏｉｃｅ[Ｍ].Ｂｅｉｊｉｎｇ:ＳｃｉｅｎｃｅＰｒｅｓｓꎬ２０１４.(上接第３４页)[１８]ＨＵＳꎬＬＩＵＤꎬＬＩＮＨꎬｅｔａｌ.Ａｎａｌｏｇｕｅｏｆｕｌｔｒａ￣ｂｒｏａｄｂａｎｄａｎｄｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｄｅｐｅｎｄｅｎｔｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｕｓｉｎｇｐｌａｎａｒｍｅｔａｍａｔｅｒｉａｌ[Ｊ].ＪｏｕｒｎａｌｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓꎬ２０１７ꎬ１２１(１２):１２３１０３.ＤＯＩ:１０.１０６３/１.４９７９０１３.[１９]ＺＨＵＬꎬＦＵＪＨꎬＭＥＮＧＦＹꎬｅｔａｌ.Ｄｅｔｕｎｅｄｍａｇｎｅｔｉｃｄｉｐｏｌｅｓｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｉｎｍｉｃｒｏｓｔｒｉｐｌｉｎｅｆｏｒｓｅｎｓｉｎｇ[Ｊ].ＩＥＥＥＴｒａｎｓａｃｔｉｏｎｓｏｎＭａｇｎｅｔｉｃｓꎬ２０１４ꎬ５０(１):１￣４.ＤＯＩ:１０.１１０９/ｔｍａｇ.２０１３.２２７９１３９.[２０]ＺＨＵＬꎬＤＯＮＧＬꎬＧＵＯＪꎬｅｔａｌ.Ｐｏｌａｒｉｚａｔｉｏｎ￣ｉｎｄｅｐｅｎｄｅｎｔｔｒａｎｓｐａｒｅｎｔｅｆｆｅｃｔｉｎｗｉｎｄｍｉｌｌ￣ｌｉｋｅｍｅｔａｓｕｒｆａｃｅ[Ｊ].ＪｏｕｒｎａｌｏｆＰｈｙｓｉｃｓＤ:ＡｐｐｌｉｅｄＰｈｙｓｉｃｓꎬ２０１８ꎬ５１(２６):２６５１０１.ＤＯＩ:１０.１０８８/１３６１￣６４６３/ａａｃ５６０.[２１]ＴＩＡＮＹꎬＨＵＳꎬＨＵＡＮＧＸＪꎬｅｔａｌ.Ｌｏｗ￣ｌｏｓｓｐｌａｎａｒｍｅｔａｍａｔｅｒｉａｌｓｅｌｅｃｔｒｏｍａｇｎｅｔｉｃａｌｌｙｉｎｄｕｃｅｄｔｒａｎｓｐａｒｅｎｃｙｆｏｒｓｅｎｓｉｔｉｖｅｒｅｆｒａｃｔｉｖｅｉｎｄｅｘｓｅｎｓｉｎｇ[Ｊ].ＪｏｕｒｎａｌｏｆＰｈｙｓｉｃｓＤ:ＡｐｐｌｉｅｄＰｈｙｓｉｃｓꎬ２０１７ꎬ５０(４０):４０５１０５.ＤＯＩ:１０.１０８８/１３６１￣６４６３/ａａ８６５ｂ. [２２]ＺＨＵＬꎬＤＯＮＧＬꎬＭＥＮＧＦＹꎬｅｔａｌ.Ｉｎｆｌｕｅｎｃｅｏｆｓｙｍｍｅｔｒｙｂｒｅａｋｉｎｇｉｎａｐｌａｎａｒｍｅｔａｍａｔｅｒｉａｌｏｎｔｒａｎｓｐａｒｅｎｃｙｅｆｆｅｃｔａｎｄｓｅｎｓｉｎｇａｐｐｌｉｃａｔｉｏｎ[Ｊ].ＡｐｐｌｉｅｄＯｐｔｉｃｓꎬ２０１２ꎬ５１(３２):７７９４￣７７９９.ＤＯＩ:１０.１３６４/ＡＯ.５１.００７７９４.。
毕业设计说明书英文文献及中文翻译学生姓名：学号：学院：专业：指导教师：Novel Optical Sensor for Precise Tilt AngleMeasurementFan Hua, Ivan Reading and Fang ZhongPingSingapore Institute of Manufacturing TechnologyNanyang Avenue 71, Singapore 638075, Email: hfan@.sgABSTRACTA novel optical sensor, which can measure inclination angle or tilt angle of two axes simultaneously and precisely, is introduced. This sensor is based on the principle of laser interference so it has very high accuracy. A prototype sensor is designed, built and evaluated to demonstrate the novel concept. It is an optoelectronic sensor. There are no moving parts in the sensor. A fluid horizontal that is absolutely perpendicular to the true vertical provides the reference plane. The angle between the sensor and the absolute horizon changes with the inclination of the object being measured. These changes are reflected in the way of fringe pattern’s cent re position shift. Different interference patterns centre locations are generated when tilt angle varied. The interference fringe pattern are recorded and processed to translate into the tilt angles of two axes, horizontal and vertical. The accuracy can reach as high as +/- 1 arc second with the measurement range of 700 arc seconds when 1024 by1024 pixels image sensor is utilized.Key words: tilt angle sensor, inclinometers, laser interferenceI. INTRODUCTIONThere are several kinds of commercial sensor for tilt angle measurement, which are available in the market. Some known as tilt angle sensor, some are known as inclinometers. They base on different working principles. Electrolytic liquid[1], capacitance [2]and pendulum [3]are the three main working principles that most tilt angle sensor or inclinometer usually base on. Here we propose a novel optical methodand build up an optoelectronic sensor with laser, optical components and image sensor. It can do precise tilt angle measurement simultaneously. There is no mechanical movement part. The working principle is based on optical interferometry. Coherent laser is used as the lighting source. It will go through a liquid oil box, which is built by a glass container filled with liquid oil. A fluid horizontal that is absolutely perpendicular to the true vertical provides the reference plane. When laser beam pass through the oil box two beams are reflected back by surface of the liquid and container glass. Interference fringes are formed with these two beams. The fringe patterns will shift in corresponding to the changes of the tilt angles. The fringe patterns is captured and processed to give the tilt angle information. Optical working principle makes it insensitive to magnetic field. The sensor can measure two axes inclination angle simultaneously. A fluid horizontal make sure the reference plane is an absolute horizontal plane. High sensitive optical interference measurement principle assures the high accuracy.A prototype of the method has been built up and evaluated. Experimental results show the tilt angle changes relative to sea level can be detected at the accuracy of +-1 arc second within the measurement range of 700 arc seconds.II. PRINCIPLEFigure 1 illustrates the schematic diagram of working principle. Point O is the focal point of beam expanding lens. Point O can be considered as a point light source. It emits spherical wave-front. Liquid oil surface will always maintain horizontally due to the gravity force of the earth. The oil surface is used as the reference plane. The container is made of glass. Its bottom surface will incline together with the target object when the sensor is placed on the target. The light from oil surface and glass surface will interference to form circular fringes pattern (see Fig. 4). The incline angle can be measured with the centre position changes of circular fringes. P is the mirror image of O against to glass-air surface and Q is the mirror image of O against to oil-air surface. The oil-air surface represents the horizontal plane. When the glass surface positioned parallel with oil surface the P and Q are in the same lineperpendicular with oil surface. This line is also the optical axis of the optical system. The fringes are circular fringes with common center. When the oil box is inclined the glass surface has a tilt angle a against to the oil surface.αθsin sin n = （1）where n is the refraction index of glass.When the tilt angle is tiny, the above equation can be simplified asαθn ≈ （2）We can obtain the following equation from OPS ∆and OQS ∆nhD r D r n 222+-=α （3） where r is the center position of circular fringes. D is the distance of the receiving screen to the glass surface of oil box. h is the thickness of glass and oil. n is the refraction index of glass and oil ( here we assume the glass and oil have same index since they are very close).Assume that h nD >>so that h is negligible relative to D.222222Dn rh h nD r nD r ≈+-=α (4) From equation (4) n, D and h are fixed once the setup is assembled. Let 222D n h =η, called system constant. This system parameter can be obtained through calibration process.Hence equation (4) can be written asnr =α （5）where r can be calculated with image processing technique and hence do the tilt angle α.Fig. 1 Schematic diagram of measurement principleIII. DESCRIPTION OF SENSORFigure 2 shows the detail layout of the optical head of the sensor. It includes laser 1, beam expander 2, beam splitter 3, mirror 4 and liquid oil box 5. A point light source emits spherical wave-front. This beam goes through the oil box. It is reflected by the glass surface and oil surface respectively. These two wave-fronts meet together again after they pass different optical paths. If the coherent length of the point light source is longer than the optical path difference, these two beams will interfere and form circular fringes. When one surface tilts the center of the circular fringes will shift accordingly. When the optical path changes, the fringes will be generated orλoptical path absorbed accordingly. One fringe change occurs in corresponding to 2difference, where λis the wavelength of the light source.Fig. 2 Layout of optical sensor headAs illustrated in Figure 2, the laser 1 emits a laser beam. This laser beam is expanded by a beam expander 2 to form a spherical wave-front beam. Subsequently this beam goes through the liquid oil box 5 perpendicularly. The reflections occur in the surfaces formed by medias layers with different refraction indexes. The reflection ratio is determined by the formula when incident direction is perpendicularly to the reflection plane 。
