laser4-研深圳大學-高等激光物理學期末復習課件

1、Unit 4 From amplifiers to oscillators,Light amplifiers Amplifier bandwidthGain saturation From amplifiers to oscillatorsThe laserResonatorsPlane-mirror resonatorsSpherical-mirror resonatorsCavity modes in cav

2、ities with curved mirrors #,From amplifiers to oscillators,the laser: an optical amplifier a source of light amplifier : bandwidth and gain saturation amplifiers with positive feedback optic

3、al oscillators. laser #,Light amplifiers,Comparing optical amplifiers with electronic amplifiersSimilarities: both rely on an external power source to supply

4、energy; both are characterised by a gain coefficient, which is frequency dependent; both are influenced by noise, gain saturation, and other non-linearities. #,Differences b

5、etween optical and electronic amplifiers,Phase The optical amplifier increases the magnitude of the optical field while maintaining its phase. Phase is not relevant in electronic amplifiers.Frequency response

6、 In optical amplifiers the basic frequency selection is determined by the energy levels in atoms Electronic amplifiers rely on electronic circuits made of capacitors, inductors, etc

7、 #,Differences between optical and electronic amplifiers,The source of external power Electronic amplifiers can only be powered by electrical energy Optical amplifiers can be ‘pumped’ by electrical, optic

8、al, chemical, mechanical and even nuclear power sources. #,Amplifier bandwidth,Bandwidth : amplifier’s frequency response In the optical amplifier the frequency response is determined by the frequenc

9、y dependence of the gain coefficientThe frequency response is proportional to the lineshape function of the given transition. #,Amplifier bandwidth,The frequency response is proportional to the lin

10、eshape function of the given transition. In the case of homogeneous broadening G(?) is a Lorentzian function I→0,Gain saturation,At low power, optical amplify function I(

11、z) = I(0)exp(Gz) the exponential growth of the intensity At high power levels ,this is not correct, it will produce gain saturation.#,Gain saturation,The intensity increases the rate of stimulated emission i

12、ncreases population from the upper level is reduces the degree of population inversion is reduced the gain is also reduced. #,Gain saturation,The intensity increases in the amplifier, it stimulates more and m

13、ore excited atoms to emit photons. This can only go on as long as the number of stimulating photons is less than the number of excited atoms. Once the number of photons overtakes the number of excited atom

14、s, the exponential growth comes to an end. #,Gain saturation,The population difference is a function of the energy density : (ν=ν0)The saturated gain decreases as the intensity increasesThe saturatio

15、n intensity #,the gain coefficient the saturated gainsmall-signal gain coefficient The saturation intensity#,Gain saturation,From a

16、mplifiers to oscillators,Lasers are sources of light.What is the link between an amplifier and a light source?The Optical feedback an optical amplifier with positive feedback the amplifier between mirrorsOpt

17、ical cavity or resonator the initial signal triggers the whole process. the spontaneously emitted photons Optical oscillator --Laser the intensity will quickly build up and reach a steady-state value.

18、#,To have stable output from a laser, two conditions have to be met : (i) the amplifier gain should be larger than the losses (ii) the total phase shift in a round trip of the radiation shou

19、ld be equal to an integer multiple of 2?. Both these conditions are related to the optical cavity or optical resonator. #,Laser,Resonator,an optical cavity or optical resonator Electro-magnetic theory

20、— Boundary condition form standing wavesthe special wavelength and frequencise resonant wavelengths resonant frequencies plane-mirror, spherical-mirror resonators. #,Plane-mirror resonat

21、ors,Fabry-Perot resonator (F-P) The resonant frequencies m, longitudinal mode frequency separation between the longitudinal modes,Finesse of the cavity,The intensity distribution of a cavity, Transmiss

22、ion spectrum :F -- the finesse of the cavity The finesse is an important parameter of a cavity #,Finesse of the cavity,The finesse is an important parameter of a cavity quantifies the width of a resonant line.

23、 The finesse : F = ??/ ?? ??: width of the resonance ??: the separation of the resonant frequencies for high finesse, highly reflective mirrors, the spectral response is shar

24、ply peaked for low finesse, the resonances are broad around the resonant frequencies. #,Plane-mirror resonators,Three parameters: characterise the spectral response of Fabry-Perot resonators:(i) the resonant freque

25、ncies: ?q = (c/2d)q(ii) the spacing between the resonant frequencies: ?? = c/2d(iii) the width of each resonance: ??= ?? / F F is the finesse of the cavity#,Kind of open resonator,Stab

26、le resonator. the beam is confined in the cavity even after many reflectionsUnstable resonator the beam leaves the cavity after only a few reflections#,Conditions of stabiliry :Not all unstable resonator

27、s are useless.,Some special cavity configurations,Cavity modes in cavities with curved mirrors,q,l,m-- a distinctive standing wave-- a mode. Each mode -- a specific frequency and intensity distribution in the cavity.

28、longitudinal or axial modes, q waves travelling along the optical axis of the cavity.transverse modes: l, m,Cavity modes in cavities with curved mirrors,l= m = 0 but q? 0 The intensity distribution across t

29、he beam profile Gaussian function -- the lowest beam divergence, highest energy density. -- for most applications l ? 0 or m ? 0 beam divergence angles, beam profile,Unit 4 From amplifiers t

30、o oscillators,Learning outcomes discuss bandwidth in optical amplifierscalculate the bandwidth in a homogeneously broadened optical amplifierdiscuss gain saturation in optical amplifiers calculate the saturated gain

31、and the small-signal gain coefficient in optical amplifiers discuss the laser in terms of an amplifier with feedback discuss the optical properties of optical cavity discuss the stability criterion of optical resonato