1. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 1 Chapter 3 Laser Amplifiers

2. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 2 Concept of the laser amplifier Pump Input photons Laser amplifier Ouput photons atoms

3. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 3 Optical Regeneration Ideal analog amplification Faithfully reproduces input signal with minimal distortion Can be used as a linear repeater by periodically boosting optical power Can be used in nonlinear region as a level clamping amplifier Single amplifier can be used as a multichannel amplifier ideally with minimal crosstalk and distortion

4. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 4

5. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 5 Real Amplifier Gain Bandwidth Phase shift Power source Nonlinearity and gain saturation Noise

6. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 6 Optical Amplifier Figure 5.1-1 The laser amplifier. An external power source (called a pump) excites the active medium (represented by a collection of atoms), producing a population inversion. Photons interact with the atoms; when stimulated emission is more prevalent than absorption, the medium acts as a coherent amplifier. Pump Input photons Laser amplifier Ouput photons atoms

7. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 7 Optical Amplifier Physics An atomic system with two energy levels can ◆ absorb light ◆ amplify light ◆ spontaneously emit light Stimulated and spontaneous emission are achieved by pumping the amplifier electrically or optically. Absorption Stimulated emission Spontaneous emission

8. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 8 ……(13.1-3) Figure 13.1-1 The photon-flux density  (photons/cm2-s) entering an incremental cylinder containing excited atoms grows to  + d  after length dz. Input light Output light Amplifier 0 d z+dz z +d+d 

9. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 9

10. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 10 Homogeneous and inhomogeneous broadening To describe the distribution of the emitted intensity versus the frequency v, we define a lineshape function g(v): →g(v)dv can be considered as a priori probability that a given spontaneous emission 2→1 will result in a photon whose frequency is between v and v+dv →Both the emission and the absorption are described by the same lineshape function g(v) →g(v) can be measured by measuring the profile of the absorption spectrum for the transition 1→2

11. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 11 Lorentzian lineshape The gain coefficient is then also Lorentzain with the same width, i.e.,

12. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 12 Homogeneous Broadening Radiated field Field decay rate Fourier Transform At the vicinity of the resonant frequency w 0 Coresponded curves are called Lorentzian

13. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 13 Linewidth Lineshape function

14. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 14 0 1 Figure 13.1-2 Gain coefficient of a Loretzian-lineshape laser amplifier.

15. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 15 Amplifier phase shift Figure Gain coefficient and phase-shift coefficient for a laser amplifier with a Lorentzian line-shape function

16. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 16 Features of homogeneous broadening: 1. Each atom in the system has a common emitting spectrum widthΔv.g(v) describes the response of any of the atoms, which are indistinguishable 2. Due most often to the finite interaction lifetime of the absorbing and emitting atoms Mechanisms of homogeneous broadening: 1. The spontaneous lifetime of the exited state 2. Collision of an atom embedded in a crystal with a phonon 3. Pressure broadening of atoms in a gas

17. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 17 Features of Inhomogeneous Broadening 1. Individual atoms are distinguishable, each having a slightly different frequency. 2. The observed spectrum of spontaneous emission reflects the spread in the individual transition frequencies (not the broadening due to the finite lifetime of the excited state). Typical Examples: The energy levels of ions presents as impurities in a host crystal. Random strain Crystal imperfection

18. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 18 Rate Equation Gain constant Amplification Attenuation

19. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 19 (a) Amplification of a traveling electromagnetic wave in an inverted population (N2>N1), and (b) attenuation in a absorbing medium (N2<N1). Ampilifying medium (N2>N1) Output wave Atoms in upper state 2 Atoms in lower state 1 Absorbing medium (N2<N1) Output wave (a) (b)

20. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 20 Population Inversion Negative temperature At thermal equilibrium As usual, T>0 Negative temperature Population Inversion Wave intensity grows exponentially!!

21. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 21 Atomic rate equations 1. Radiation-atom interaction: Stimulated emission Absorption 2. Population inversion and laser pumping: 3. Lifetime of atoms in upper energy level :  : lifetime of atoms in the upper energy level.

22. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 22 Either the radiation-atom interaction, laser pumping and energy decay change the population density distribution. To describe in details the rates of these changes Atomic rate equations

23. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 23 Two level system (13.2-1) 2 1 t sp  nr  20 11 22  21 Figure 13.2-1 Energy levels 1 and 2 and their decay times.

24. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 24 Figure 13.2-2 Energy levels I and 2, together with surrounding higher and lower energy levels. R2 2 1R1

25. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 25 Rate equations in the absence of amplifier radiation ……(13.2-2) ……(13.2-3) Steady-state population difference (in absence of amplifier radiation)

26. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 26 For large N o Large R 1 and R 2 Long   (but t sp which contributes to   through  21 must be sufficiently long so as to make the radiative transition large) Short   if R 1      R 2 ……13.2-4(a)

27. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 27 Rate equations in the presence of amplifier radiation ……(13.2-5) ……(13.2-6)

28. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 28 ……(13.2-7) Steady-state population difference (in absence of amplifier radiation) ……(13.2-8) Saturation time constant

29. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 29 Saturation time constant

30. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 30 Derivation of atomic rate equations 1. Four-level pumping schemes Figure 5.1-11 Energy levels and decay rates for a four-level system. 点击查看 flash 动画

31. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 31 Typically as ……(5.1-23) ……( 5.1-24 ) ……( 5.1-25 ) ……( 5.1-26 )

32. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 32 If considering and Then At that time, the pump rate R is a linearly decreasing function of population difference, not independent of it. (5.1-26) becomes

33. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 33 ……(5.1-30) ……(5.1-31)

34. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 34 Derivation of atomic rate equations Three-level pumping scheme Figure 5.1-12 Energy levels and decay rates for a three-level system. Short-lived level Long-lived level Ground state     Rapid decay 1 2 3 Laser RPump 点击查看 flash 动画

35. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 35 In the steady state, from (5.1-19) and (5.1-20), we have Note FromWe have Then ……(5.1-32)

36. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 36 We have but now ……( 5.1-38 ) ……( 5.1-39 )

37. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 37 Gas S Rod Flashlamp Laser diode Lens Nd3+:YAG rod Lens Laser diode Er3+ : silica fiber Figure 5.1-13 Examples of electrical and optical pumping. a b c d Examples of Laser Amplifiers

38. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 38 Ruby Figure 5.1-14 Energy levels pertinent to the 694.3nm red ruby transition. The three interacting levels are indicated in circles. 4 3 2 1 0 ev R1R1 Ruby Energy 694.3nm laser   4F1 4F2 1 2 3 Pump

39. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 39 Ruby rod Flashlamp Input photons Ouput photons Capacitor Power supply Flashlamp Ruby rod Elliptical mirror Figure 5.1-15 The ruby laser amplifier. (a) Geometry used in the first laser oscillator built by Maiman in 1960. (b) Cross sction of a high-efficiency geometry using a rod-shaped flashlamp and a reflecting elliptical cylinder. (a) (b)

40. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 40 Nd3+:YAG and Nd3+:Glass Figure 5.1-16 Energy levels pertinent to the 1.064um Nd3+:YAG laser transition. The energy levels for Nd3+:glass are similar but the absorption bands are broader. 2 1 0 ev Nd3+:YAG Energy 1.064um laser   4F 3/2 1 2 3 Pump 0 4I 11/2 4I 9/2

41. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 41 Er3+:Silica Fiber

42. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 42

43. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 43 Amplifier nonlinearity and gain saturation Then (5.1-41) (5.1-42) Saturated Gain Coefficient (5.1-43) Small-signal Gain Coefficient

44. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 44 Figure 5.1-17 Dependence of the normalized saturated gain coefficient on the normalized photon-flux densit.

45. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 45 Gain where ……(5.1-44) ……(5.1-45) ……(5.1-46)

46. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 46 (a) A nonlinear (saturated) amplifier. (b) Relation between the normalized output photon-flux density Y and the normalized input photon-flux density X. For X >1, the gain Y=X+ r 0 d. (c) Gain as a function of the input normalized photon-flux density X in an amplifier of length d when r 0 d=2.

47. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 47 Saturable Absorbers

48. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 48 1 Inhomogeneous Homogeneous Fig.5.1-20 Comparison of gain saturation in homogeneous and inhomogeneous broadened media Difference of gain saturation between inhomogeneous and homogeneous media

49. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 49 1 Gain coefficient Figure 5.1-21 The gain coefficient of an inhomogeneously broadened medium is locally saturated by a large flux density of monochromatic photons at frequency  Hole burning

50. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 50 Gain saturation in homogeneously and inhomogeneously broadened systems: (Homogeneous)(Inhomogeneous) Spectral hole-burning 点击查看 flash 动画点击查看 flash 动画

51. CHAPTER 3---- Laser Amplifiers 2015-7-2Fundamentals of Photonics 51 In the homogeneously broadened lasers, when gain saturation occurs, the entire gain curve saturates proportionally. The stronger the saturation effect, the lower the gain curve (or the smaller the gain coefficients). In the inhomogeneously broadened lasers, saturation at one particular frequency causes a reduction in the gain profile only near that frequency. Effectively, a hole is burned in the gain profile at the frequency---- phenomenally it is called spectral hole burning. No effect it will have on the gain at other frequencies!

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