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1、§2.2共轴球面腔的稳定性条件光线传输矩阵(opticalraymatricesorABCDmatrices)腔内光线往返传播的矩阵表示共轴球面腔的稳定性条件常见的几种稳定腔、非稳腔、临界腔稳区图一光线传输矩阵腔内任一傍轴光线在某一给定的横截面内都可以由两个坐标参数来表征：光线离轴线的距离r、光线与轴线的夹角。规定：光线出射方向在腔轴线的上方时，为正；反之，为负。光线在自由空间行进距离L时所引起的坐标变换为球面镜对傍轴光线的变换矩阵为（R为球面镜的曲率半径）球面镜对傍轴光线的反射变换与焦距为f=R/2的薄透镜对同一光线的透射变换是等效的。用一个
2、列矩阵描述任一光线的坐标，用一个二阶方阵描述入射光线和出射光线的坐标变换。该矩阵称为光学系统对光线的变换矩阵。Rayoptics---bywhichwemeanthegeometricallawsforopticalraypropagation,withoutincludingdiffraction---isatopicthatisnotonlyimportantinitsownright,butalsoveryusefulinunderstandingthefulldiffractivepropagationoflightwavesinoptic
3、alresonatorsandbeams.Raymatricesorparaxialrayopticsprovideageneralwayofexpressingtheelementarylenslawsofgeometricaloptics,orofspherical-waveoptics,leavingouthigher-orderaberrations,inaformthatmanypeoplefindclearerandmoreconvenient.Rayopticsandgeometricalopticsinfactcontainexac
4、tlythesamephysicalcontent,expressedindifferentfashion.Raymatricesor“ABCDmatrices”arewidelyusedtodescribethepropagationofgeometricalopticalraysthroughparaxialopticalelements,suchlenses,curvedmirrors,and“ducts”.Theseraymatricesalsoturnouttobeveryusefulfordescribingalargenumberof
5、otheropticalbeamandresonatorproblems,includingevenproblemsthatinvolvethediffractivenatureoflight.Sincearayis,bydefinition,normaltotheopticalwavefront,anunderstandingoftheraybehaviormakesitpossibletotracetheevolutionofopticalwaveswhentheyarepassingthroughvariousopticalelements.
6、Wefindthatthepassageofaray(oritsreflection)throughtheseelementscanbedescribedbysimple2x2matrices.Furthermore,thesematriceswillbefoundtodescribethepropagationofsphericalwavesandofGaussianbeamssuchasthosewhicharecharacteristicsoftheoutputoflasers.Raypropagationthroughcascadedele
7、ments:Asingle4-elementraymatrixequaltotheordinarymatrixproductoftheindividualraymatricescanthusdescribethetotaloroverallraypropagationthroughacomplicatedsequenceofcascadedopticalelements.Note,however,thatthematricesmustbearrangedininverseorderfromtheorderinwhichtherayphysicall
8、yencountersthecorrespondingelements.二腔内光线往返传播的矩阵表示由曲率半径为R1和R2
