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1、§2.2共軸球面腔的穩(wěn)定性條件光線傳輸矩陣(opticalraymatricesorABCDmatrices)腔內(nèi)光線往返傳播的矩陣表示共軸球面腔的穩(wěn)定性條件常見的幾種穩(wěn)定腔、非穩(wěn)腔、臨界腔穩(wěn)區(qū)圖一光線傳輸矩陣腔內(nèi)任一傍軸光線在某一給定的橫截面內(nèi)都可以由兩個坐標(biāo)參數(shù)來表征：光線離軸線的距離r、光線與軸線的夾角?。規(guī)定：光線出射方向在腔軸線的上方時，?為正；反之，為負(fù)。光線在自由空間行進(jìn)距離L時所引起的坐標(biāo)變換為球面鏡對傍軸光線的變換矩陣為（R為球面鏡的曲率半徑）球面鏡對傍軸光線的反射變換與焦距為f=R/2的薄透鏡對同一光線的透射變換是等效
2、的。用一個列矩陣描述任一光線的坐標(biāo)，用一個二階方陣描述入射光線和出射光線的坐標(biāo)變換。該矩陣稱為光學(xué)系統(tǒng)對光線的變換矩陣。Rayoptics---bywhichwemeanthegeometricallawsforopticalraypropagation,withoutincludingdiffraction---isatopicthatisnotonlyimportantinitsownright,butalsoveryusefulinunderstandingthefulldiffractivepropagationoflightwa
3、vesinopticalresonatorsandbeams.Raymatricesorparaxialrayopticsprovideageneralwayofexpressingtheelementarylenslawsofgeometricaloptics,orofspherical-waveoptics,leavingouthigher-orderaberrations,inaformthatmanypeoplefindclearerandmoreconvenient.Rayopticsandgeometricalopticsin
4、factcontainexactlythesamephysicalcontent,expressedindifferentfashion.Raymatricesor“ABCDmatrices”arewidelyusedtodescribethepropagationofgeometricalopticalraysthroughparaxialopticalelements,suchlenses,curvedmirrors,and“ducts”.Theseraymatricesalsoturnouttobeveryusefulfordesc
5、ribingalargenumberofotheropticalbeamandresonatorproblems,includingevenproblemsthatinvolvethediffractivenatureoflight.Sincearayis,bydefinition,normaltotheopticalwavefront,anunderstandingoftheraybehaviormakesitpossibletotracetheevolutionofopticalwaveswhentheyarepassingthrou
6、ghvariousopticalelements.Wefindthatthepassageofaray(oritsreflection)throughtheseelementscanbedescribedbysimple2x2matrices.Furthermore,thesematriceswillbefoundtodescribethepropagationofsphericalwavesandofGaussianbeamssuchasthosewhicharecharacteristicsoftheoutputoflasers.Ra
7、ypropagationthroughcascadedelements:Asingle4-elementraymatrixequaltotheordinarymatrixproductoftheindividualraymatricescanthusdescribethetotaloroverallraypropagationthroughacomplicatedsequenceofcascadedopticalelements.Note,however,thatthematricesmustbearrangedininverseorde
8、rfromtheorderinwhichtherayphysicallyencountersthecorrespondingelements.二腔內(nèi)光線往返傳播的矩陣表示由曲率半徑為R1和R2
