非线性光学英文版课件：Lecture 11- Difference-Frequency Generation and Parametric Amplification

2011-8-29DepartmentofPhysicsSoutheastUniversityLectureeleven:

Difference-FrequencyGenerationandParametricAmplification

A.Difference-FrequencyGenerationAnalogously,thecoupled-amplitudeequationsdescribingthisinteractioncanbereadilyobtainedandhavetheform(1)(2)where(3)

(4)

(5)Thegeneralsolutiontothisequationis(6)

Wenowassumetheboundaryconditions(7)(8)ThesolutiontoEqs.(1)and(2)thatmeetstheseboundaryconditionsisreadilyfoundtobe(9)Fromthissolutionwenotethat

(3)Thisbehaviorofmonotonicgrowthofbothwavesisqualitativelydissimilarfromthatofsum-frequencygeneration,whereoscillatorybehavioroccurs.Thereasonforthedifferentbehaviorcanbeunderstoodintuitivelyintermsoftheenergyleveldiagramshownbelow.

Suchadeviceisknownasanopticalparametricoscillatorandisdescribedingreaterdetaillater.HyperbolicFunctions

B.OpticalParametricOscillators(1965)Wenotedintheprevioussectionthattheprocessofdifference-frequencygenerationnecessarilyleadstotheamplificationofthelower-frequencyinputfield.Thisamplificationprocessisknownasopticalparametricamplification,andthegainresultingfromthisprocesscanbeusedtoconstructadeviceknownasanopticalparametricoscillator(OPO).Difference-frequencygenerationOpticalparametricoscillator

Letusrecallhowtocalculatethegainoftheprocessofopticalparametricamplification.Thecoupled-amplitudeequationsread

(10)(11)Asinthesum-frequencygeneration,Eqs.(10)and(11)canbesolvedexactlyusingatrialsolutionmethod.Theseequationspossessthesolution(12)(13)wherewehaveintroducedthequantities(14)

Wethenconsiderthethresholdconditionfortheestablishmentofparametricoscillation.

Wecanexpressthethresholdconditionasastatementthatthefractionalenergygainperpassmustequalthefractionalenergylossperpass,Ormoregenerally,wecanexpressthethresholdconditionasastatementthatthefieldswithintheresonatormustreplicatethemselveseachroundtrip.

(15)(16)

(17)

(18)

逆水行舟用力撑,一篙松劲退千寻;古云此日足可惜,吾辈更应惜秒阴。 董比武

Exercise(作