1、Unit 4 From amplifiers to oscillators,Light amplifiers Amplifier bandwidth Gain saturation From amplifiers to oscillators The laser Resonators Plane-mirror resonators Spherical-mirror resonators Cavity modes in cavities with curved mirrors #,From amplifiers to oscillators,the laser: an optical ampli

2、fier a source of light amplifier : bandwidth and gain saturation amplifiers with positive feedback optical oscillators. laser #,Light amplifiers,Comparing optical amplifiers with electronic amplifiers Similarities: both rely on an external power source to supply energy; both are characterised by a g

3、ain 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 phase. Phase is not relevant

4、 in electronic amplifiers. Frequency response 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 #,Differences between optical and electronic amplifiers,The source of ext

5、ernal 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,Bandwidth : amplifiers frequency response In the optical amplifier the frequency response is

6、determined by the frequency dependence of the gain coefficient The frequency response is proportional to the lineshape function of the given transition. #,Amplifier bandwidth,The frequency response is proportional to the lineshape function of the given transition. In the case of homogeneous broadeni

7、ng G() is a Lorentzian function I0,Gain saturation,At low power, optical amplify function I(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

8、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 more excited atoms to emit photons. This can only go on as long as the number of stimulating

9、photons is less than the number of excited atoms. Once the number of photons overtakes the number of excited atoms, the exponential growth comes to an end. #,Gain saturation,The population difference is a function of the energy density : (=0) The saturated gain decreases as the intensity increases T

10、he saturation intensity #,the gain coefficient the saturated gain small-signal gain coefficient The saturation intensity #,Gain saturation,From amplifiers to oscillators,Lasers are sources of light. What is the link between an amplifier and a light source? The Optical feedback an optical amplifier w

11、ith positive feedback the amplifier between mirrors Optical 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. #,To have stable output from a laser, two con

12、ditions 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. Both these conditions are related to the optical cavity or optical resonator. #,Laser,Resonator,an optical cavity

13、or optical resonator Electro-magnetic theory Boundary condition form standing waves the special wavelength and frequencise resonant wavelengths resonant frequencies plane-mirror, spherical-mirror resonators. #,Plane-mirror resonators,Fabry-Perot resonator (F-P) The resonant frequencies m, longitudin

14、al mode frequency separation between the longitudinal modes,Finesse of the cavity,The intensity distribution of a cavity, Transmission 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

15、quantifies the width of a resonant line. The finesse : F = / : width of the resonance : the separation of the resonant frequencies for high finesse, highly reflective mirrors, the spectral response is sharply peaked for low finesse, the resonances are broad around the resonant frequencies. #,Plane-m

16、irror resonators,Three parameters: characterise the spectral response of Fabry-Perot resonators: (i) the resonant frequencies: 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,Stable

17、 resonator. the beam is confined in the cavity even after many reflections Unstable resonator the beam leaves the cavity after only a few reflections #,Conditions of stabiliry : Not all unstable resonators are useless.,Some special cavity configurations,Cavity modes in cavities with curved mirrors,q

18、,l,m- a distinctive standing wave- a mode. Each mode - a specific frequency and intensity distribution in the cavity. 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 the beam profile Gaus