1、Unit 4 From amplifiers to oscillators n Light amplifiers n Amplifier bandwidth n Gain saturation n From amplifiers to oscillators n The laser n Resonators n Plane-mirror resonators n Spherical-mirror resonators n Cavity modes in cavities with curved mirrors #From amplifiers to oscillators n the lase
2、r: an optical amplifiera source of light n amplifier : bandwidth and gain saturation n amplifiers with positive feedback n optical oscillators. n laser #Light amplifiers Comparing optical amplifiers with electronic amplifiers n Similarities: both rely on an external power source to supply energy; bo
3、th are characterised by a gain coefficient, which is frequency dependent; both are influenced by noise, gain saturation, and other non-linearities. #Differences between optical and electronic amplifiers Phase The optical amplifier increases the magnitude of the optical field while maintaining its ph
4、ase. Phase is not relevant in electronic amplifiers. Frequency responseIn optical amplifiers the basic frequency selection is determined by the energy levels in atomsElectronic amplifiers rely on electronic circuits made of capacitors, inductors, etc #Differences between optical and electronic ampli
5、fiers The source of external power Electronic amplifiers can only be powered by electrical energy Optical amplifiers can be pumped by electrical, optical, chemical, mechanical and even nuclear power sources. #Amplifier bandwidth n Bandwidth : amplifiers frequency response n In the optical amplifiert
6、he frequency response is determined by thefrequency dependence of the gain coefficient n The frequency response is proportional to thelineshape function of the given transition. n #Amplifier bandwidth n The frequency response is proportional to the lineshape function of the given transition. n In th
7、e case of homogeneous broadeningG( ) is a Lorentzian function n I0Gain saturation n At low power, optical amplify function I(z) = I(0)exp(Gz)the exponential growth of the intensity n At high power levels ,this is not correct,it will produce gain saturation. #Gain saturation n The intensity increases
8、 n the rate of stimulated emission increases n population from the upper level is reduces n the degree of population inversion is reduced n the gain is also reduced. n #Gain saturation n The intensity increases in the amplifier, it stimulates more and more excited atoms to emit photons. n This can o
9、nly go on as long as the number of stimulatingphotons is less than the number of excited atoms. n Once the number of photons overtakes the number of excited atoms, the exponential growth comes to an end. n #Gain saturation n The population difference is a function of the energy density : (= 0 ) n Th
10、e saturated gain decreases as the intensity increases n The saturation intensity #n the gain coefficient n the saturated gain n small-signal gain coefficient n The saturation intensity # Gain saturationFrom amplifiers to oscillators n Lasers are sources of light. n What is the link between an amplif
11、ier and a light source? n The Optical feedbackan optical amplifier with positive feedbackthe amplifier between mirrors n Optical cavity or resonator n the initial signal triggers the whole process.the spontaneously emitted photons n Optical oscillator -Laserthe intensity will quickly build up and re
12、ach a steady-state value. # n 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 should be equal to an integer multiple of 2 . n Both these conditions are related to the
13、 optical cavity or optical resonator. # LaserResonator n an optical cavity or optical resonator n Electro-magnetic theory Boundary condition n form standing waves n the special wavelength and frequenciseresonant wavelengthsresonant frequencies n plane-mirror, spherical-mirror resonators. #Plane-mirr
14、or resonators n Fabry-Perot resonator (F-P) n The resonant frequencies n m, longitudinal mode n frequency separation between the longitudinal modes Finesse of the cavity n The intensity distribution of a cavity,Transmission spectrum : n F - the finesse of the cavity n The finesse is an important par
15、ameter of a cavity # Finesse of the cavity n The finesse is an important parameter of a cavity n quantifies the width of a resonant line. n The finesse : F = / : width of the resonance : the separation of the resonant frequencies n for high finesse, highly reflective mirrors,the spectral response is
16、 sharply peaked n for low finesse, the resonances are broad around the resonant frequencies. #Plane-mirror resonators n Three parameters: characterise the spectral response of Fabry-Perot resonators: n (i) the resonant frequencies: q= (c/2d) q n (ii) the spacing between the resonant frequencies: = c
17、/2d n (iii) the width of each resonance:= / FF is the finesse of the cavity #Kind of open resonator n Stable resonator. the beam is confined in the cavity even after many reflections n Unstable resonatorthe beam leaves the cavity after only a fewreflections #n Conditions of stabiliry : n Not all uns
18、table resonators are useless. Some special cavity configurationsCavity modes in cavities with curved mirrors n q,l,m- a distinctive standing wave- a mode. n Each mode - a specific frequency and intensity distribution in the cavity. n longitudinal or axial modes, qwaves travelling along the optical a
19、xis of the cavity. n transverse modes: l, m Cavity modes in cavities with curved mirrors n l= m = 0 but q 0The intensity distribution across the beam profile Gaussian function - the lowest beam divergence, highest energy density.- for most applications n l 0 or m 0beam divergence angles, beam profil
20、eUnit 4 From amplifiers to oscillators Learning outcomes n discuss bandwidth in optical amplifiers n calculate the bandwidth in a homogeneously broadened optical amplifier n discuss gain saturation in optical amplifiers n calculate the saturated gain and the small-signal gain coefficient in optical amplifiers n discuss the laser in terms of an amplifier with feedback n discuss the optical properties of optical cavity n discuss the stability criterion of optical resonators #
