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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(gè)坐標(biāo)參數(shù)來(lái)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(shí)，?為正；反之，為負(fù)。光線在自由空間行進(jìn)距離L時(shí)所引起的坐標(biāo)變換為球面鏡對(duì)傍軸光線的變換矩陣為（R為球面鏡的曲率半徑）球面鏡對(duì)傍軸光線的反射變換與焦距為f=R/2的薄透鏡對(duì)同一光線的透射變換是等效的。用一個(gè)列矩陣描述任一光線的坐標(biāo)，用一個(gè)二階方陣描
2、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(duì)光線的變換矩陣。Rayoptics---bywhichwemeanthegeometricallawsforopticalraypropagation,withoutincludingdiffraction---isatopicthatisnotonlyimportantinitsownright,butalsoveryusefulinunderstandingthefulldiffractivepropagationoflightwavesinopticalresonatorsandbeams.Raymatricesorparaxial
3、rayopticsprovideageneralwayofexpressingtheelementarylenslawsofgeometricaloptics,orofspherical-waveoptics,leavingouthigher-orderaberrations,inaformthatmanypeoplefindclearerandmoreconvenient.Rayopticsandgeometricalopticsinfactcontainexactlythesamephysicalcontent,expressedindifferentfashion.Raymatric
4、esor“ABCDmatrices”arewidelyusedtodescribethepropagationofgeometricalopticalraysthroughparaxialopticalelements,suchlenses,curvedmirrors,and“ducts”.Theseraymatricesalsoturnouttobeveryusefulfordescribingalargenumberofotheropticalbeamandresonatorproblems,includingevenproblemsthatinvolvethediffractiven
5、atureoflight.Sincearayis,bydefinition,normaltotheopticalwavefront,anunderstandingoftheraybehaviormakesitpossibletotracetheevolutionofopticalwaveswhentheyarepassingthroughvariousopticalelements.Wefindthatthepassageofaray(oritsreflection)throughtheseelementscanbedescribedbysimple2x2matrices.Furtherm
6、ore,thesematriceswillbefoundtodescribethepropagationofsphericalwavesandofGaussianbeamssuchasthosewhicharecharacteristicsoftheoutputoflasers.Raypropagationthroughcascadedelements:Asingle4-elementraymatrixequaltotheordinarymatrixproductoftheindividualraymatricescanthusdescribethetotaloroverallraypro
7、pagationthroughacomplicatedsequenceofcascadedopticalelements.Note,however,thatthematricesmustbearrangedininverseorderfromtheorderinwhichtherayphysicallyencountersthecorrespondingelements.二腔內(nèi)光線往返傳播的矩陣表示由曲率半徑為R1和R2
