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Chapter 3 Laser Amplifiers

Chapter 3 Laser Amplifiers. Concept of the laser amplifier. Pump. atoms. Ouput photons. Input photons. Laser amplifier. Ideal analog amplification Faithfully reproduces input signal with minimal distortion Can be used as a linear repeater by periodically boosting optical power

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Chapter 3 Laser Amplifiers

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  1. Chapter 3Laser Amplifiers Fundamentals of Photonics

  2. Concept of the laser amplifier Pump atoms Ouput photons Input photons Laser amplifier Fundamentals of Photonics

  3. 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 Optical Regeneration Fundamentals of Photonics

  4. Fundamentals of Photonics

  5. Gain Bandwidth Phase shift Power source Nonlinearity and gain saturation Noise Real Amplifier Fundamentals of Photonics

  6. Optical Amplifier Pump atoms Ouput photons Input photons Laser 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. Fundamentals of Photonics

  7. Stimulated emission Spontaneous emission Absorption 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. Fundamentals of Photonics

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

  9. Fundamentals of Photonics

  10. Homogeneous and inhomogeneousbroadening • 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 Fundamentals of Photonics

  11. Lorentzian lineshape The gain coefficient is then also Lorentzain with the same width, i.e., Fundamentals of Photonics

  12. Homogeneous Broadening Radiated field Field decay rate Fourier Transform At the vicinity of the resonant frequency w0 Coresponded curves are called Lorentzian Fundamentals of Photonics

  13. Linewidth Lineshape function Fundamentals of Photonics

  14. Figure 13.1-2 Gain coefficient of a Loretzian-lineshape laser amplifier. 1 0 Fundamentals of Photonics

  15. Amplifier phase shift Figure Gain coefficient and phase-shift coefficient for a laser amplifier with a Lorentzian line-shape function Fundamentals 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 Fundamentals 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 Fundamentals of Photonics

  18. Rate Equation Gain constant Amplification Attenuation Fundamentals of Photonics

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

  20. Population Inversion Negative temperature At thermal equilibrium As usual, T>0 Negative temperature Wave intensity grows exponentially!! Population Inversion Fundamentals 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. Fundamentals 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 Fundamentals of Photonics

  23. 2 t2 t21 tsp tnr 1 t1 t20 Two level system Figure 13.2-1 Energy levels 1 and 2 and their decay times. (13.2-1) Fundamentals of Photonics

  24. R2 2 1 R1 Figure 13.2-2 Energy levels I and 2, together with surrounding higher and lower energy levels. Fundamentals 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) Fundamentals of Photonics

  26. Large R1and R2 Long t2 (but tsp which contributes to t2 through t21 must be sufficiently long so as to make the radiative transition large) Short t1 if R1<(t2/t21)R2 For large No ……13.2-4(a) Fundamentals of Photonics

  27. Rate equations in the presence of amplifier radiation ……(13.2-5) ……(13.2-6) Fundamentals of Photonics

  28. ……(13.2-7) Steady-state population difference (in absence of amplifier radiation) ……(13.2-8) Saturation time constant Fundamentals of Photonics

  29. Saturation time constant Fundamentals of Photonics

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

  31. Typically as ……(5.1-23) ……(5.1-24) ……(5.1-25) ……(5.1-26) Fundamentals 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 Fundamentals of Photonics

  33. ……(5.1-30) ……(5.1-31) Fundamentals of Photonics

  34. Derivation of atomic rate equations Three-level pumping scheme 点击查看flash动画 3 Short-lived level t32 Rapid decay Long-lived level R Pump 2 t21 Laser 1 Ground state Figure 5.1-12 Energy levels and decay rates for a three-level system. Fundamentals of Photonics

  35. In the steady state, from (5.1-19) and (5.1-20), we have ……(5.1-32) Note From We have Then Fundamentals of Photonics

  36. We have but now ……(5.1-38) ……(5.1-39) Fundamentals of Photonics

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

  38. 2 3 1 Ruby ev Ruby 4 4F1 3 Energy t32 4F2 2 R1 Pump 1 694.3nm laser 0 Figure 5.1-14Energy levels pertinent to the 694.3nm red ruby transition. The three interacting levels are indicated in circles. Fundamentals of Photonics

  39. Ruby rod Flashlamp Flashlamp Input photons Ouput photons Capacitor Ruby rod Power supply Elliptical mirror (a) (b) Figure 5.1-15The 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. Fundamentals of Photonics

  40. 2 0 3 1 Nd3+:YAG and Nd3+:Glass ev Nd3+:YAG 2 t32 Energy 4F3/2 1 1.064um laser Pump 4I11/2 4I9/2 0 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. Fundamentals of Photonics

  41. Er3+:Silica Fiber Fundamentals of Photonics

  42. Fundamentals of Photonics

  43. Amplifier nonlinearity and gain saturation (5.1-41) Then (5.1-42) Saturated Gain Coefficient (5.1-43) Small-signal Gain Coefficient Fundamentals of Photonics

  44. Figure 5.1-17 Dependence of the normalized saturated gain coefficient on the normalized photon-flux densit. Fundamentals of Photonics

  45. Gain ……(5.1-44) ……(5.1-45) ……(5.1-46) where Fundamentals 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=exp(r0d). For X>>1, the gain Y=X+r0d. (c) Gain as a function of the input normalized photon-flux density X in an amplifier of length d when r0d=2. Fundamentals of Photonics

  47. Saturable Absorbers Fundamentals of Photonics

  48. Difference of gain saturation between inhomogeneous and homogeneous media 1 Inhomogeneous Homogeneous Fig.5.1-20 Comparison of gain saturation in homogeneous and inhomogeneous broadened media Fundamentals of Photonics

  49. Gain coefficient 1 Hole burning Figure 5.1-21The gain coefficient of an inhomogeneously broadened medium is locally saturated by a large flux density of monochromatic photons at frequency n1 Fundamentals of Photonics

  50. Gain saturation in homogeneously and inhomogeneously broadened systems: Spectral hole-burning (Homogeneous) (Inhomogeneous) 点击查看flash动画 点击查看flash动画 Fundamentals of Photonics

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