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Chapter 4 Laser

Chapter 4 Laser. LASERS. In 1958 Arthur Schawlow, together with Charles Townes, showed how to extend the principle of the maser to the optical region. He shared the 1981 Nobel Prize with Nicolaas Bloembergen. Maiman demonstrated the first successful operation of the ruby laser in 1960.

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Chapter 4 Laser

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  1. Chapter 4Laser Fundamentals of Photonics

  2. LASERS In 1958 Arthur Schawlow, together with Charles Townes, showed how to extend the principle of the maser to the optical region. He shared the 1981 Nobel Prize with Nicolaas Bloembergen. Maiman demonstrated the first successful operation of the ruby laser in 1960. Fundamentals of Photonics

  3. Two conditions for an oscillation:1. Gain greater than loss: net gain2. Phase shift in a round trip is a multiple of 2π LASERS an oscillator is an amplifier with positive feedback Fundamentals of Photonics

  4. Gain Loss 0 Power Steady-state power If the initical amplifier gain is greater than the loss, oscillation may initiate. The amplifier then satuates whereupon its gain decreases. A steady-state condition is reached when the gain just equals the loss. Stable condition: gain = loss An oscillator comprises: ◆ An amplifier with a gain-saturation mechanism ◆ A feedback system ◆ A frequency-selection mechanism ◆ An output coupling scheme Fundamentals of Photonics

  5. Light amplifier with positive feedback Gain medium (e.g. 3-level system w population inversion) When the gain exceeds the roundtrip losses, the system goes into oscillation + g + Fundamentals of Photonics

  6. Gain medium (e.g. 3-level system w population inversion) LASERS 点击查看flash动画 Amplified once Initial photon Reflected Output Amplified twice Reflected Amplified Again Partially reflecting Mirror Light Amplification through Stimualted Emission Radiation Fundamentals of Photonics

  7. Mirror Active medium Partially transmitting mirror Laser output d A laser consists of an optical amplifier (employing an active medium) placed within an optical resonator. The output is extracted through a partially transmitting mirror. Fundamentals of Photonics

  8. ★ Gain medium The laser amplifier is a distributed-gain device characterized by its gain coefficient Optical amplification and feedback 5.1-43 Small signal Gain Coefficient 5.1-42 Saturated Gain Coefficient Fundamentals of Photonics

  9. Phase-shift Coefficient (Lorentzian Lineshape) Figure 5.1-5 Spectral dependence of the gain and phase-shift coefficients for an optical amplifier with Lorentzian lineshape function Fundamentals of Photonics

  10. Optical Feedback-Optical Resonator Feedback and Loss: The optical resonator A Fabry-Perot resonator, comprising two mirrors separated by a distance d, contains the medium (refractive index n). Travel through the medium introduces a phase shift per unit length equal to the wavenumber In traveling a round trip through a resonator of length d, the photon-flux density is reduced by the factor R1R2exp(-2asd). The overall loss in one round trip can therefore be described by a total effective distributed loss coefficient ar, where Fundamentals of Photonics

  11. Loss coefficient Photon lifetime ar represents the total loss of energy (or number of photons) per unit length, arc represents the loss of photons per second Fundamentals of Photonics

  12. Resonator response Resonator modes are separated by the frequency and have linewidths . Fundamentals of Photonics

  13. Conditions for laser oscillation Gain condition: Laser threshold Threshold Gain Condition where or Threshold Population Difference Fundamentals of Photonics

  14. For a Lorentzian lineshape function, as If the transition is limited by lifetime broadening with a decay time tsp As a numerical example, if l0=1 mm, tp=1 ns, and the refractive index n=1, we obtain Nt=2.1×107 cm-3 Fundamentals of Photonics

  15. Conditions for laser oscillation(2) Phase condition: Laser Frequencies Frequency Pulling or Fundamentals of Photonics

  16. Laser Frequencies Fundamentals of Photonics

  17. The laser oscillation frequencies fall near the cold-resonator modes; they are pulled slightly toward the atomic resonance central frequency n0. Fundamentals of Photonics

  18. Characteristics of the laser output Internal Photon-Flux Density Gain Clamping Fundamentals of Photonics

  19. Laser turn-on Steady state Time ar Loss coefficient g(u) Gain coefficient 0 Photon-flux density Determination of the steady-state laser photon-flux density f. The smaller the loss, the greater the value of f. Fundamentals of Photonics

  20. Steady Photon Density Since and Steady-State Laser Internal Photon-Flux Density Fundamentals of Photonics

  21. Steady-state values of the population difference N, and the laser internal photon-flux density f, as functions of N0 (the population difference in the absence of radiation; N0, increases with the pumping rate R). Output photon-flux density Optical Intensity of Laser Output Fundamentals of Photonics

  22. Optimization of the output photon-flux density From We obtain When, use the approximation Then Fundamentals of Photonics

  23. Fundamentals of Photonics

  24. Spectral Distribution Determined both by the atomic lineshape and by the resonant modes Number of Possible Laser Modes Linewidth ? Schawlow-Townes limit Fundamentals of Photonics

  25. Gain ar Loss B n0 n nF Resonator modes n n1n2……nM Allowed modes Figure 5.3-3 (a) Laser oscillation can occur only at frequencies for which the gain coefficient is greater than the loss coefficient (stippled region). (b) Oscillation can occur only within dn of the resonator modal frequencies (which are represented as lines for simplicity of illustration ). Fundamentals of Photonics

  26. Homogeneously Broadened Medium 点击查看flash动画 Fundamentals of Photonics

  27. n Frequency Inhomogeneously Broadened Medium 点击查看flash动画 ar (a) (b) Figure 5.3-6(a) Laser oscillation occurs in an inhomogeneously broadened medium by each mode independently burning a hole in the overrall spectral gain profile. (b) Spectrum of a typical inhomogeneously broadened multimode gas laser. Fundamentals of Photonics

  28. Hole burning in a Doppler-broadened medium 点击查看flash动画 Fundamentals of Photonics

  29. Hole burning in a Doppler-broadened medium 点击查看flash动画 Fundamentals of Photonics

  30. x,y Laser intensity Spherical mirror Spherical mirror Spatial distribution and polarization Spatial distribution The laser output for the (0,0) tansverse mode of a spherical-mirror resonator takes the form of a Gaussian beam. Fundamentals of Photonics

  31. TEM0,0 a11 a00 B11 B00 n (1,1) modes (0,0) modes Laser output TEM1,1 n Figure 5.3-8The gains and losses for two transverse modes, say (0,0) and (1,1), usually differ because of their different spatial distributions. Fundamentals of Photonics

  32. Two Issues: Polarization, Unstable Resonators Fundamentals of Photonics

  33. Mode Selection Selection of 1. Laser Line 2. Transverse Mode 3. Polarization 4. Longitudinal Mode Fundamentals of Photonics

  34. High reflectance mirror Output mirror Laser output Active medium Prism Aperture Unwanted line Figure 5.3-9 A paticular atomic line may be selected by the use of a prism placed inside the resonator. A transverse mode may be selected by means of a spatial aperture of carefully chosen shaped and size. Fundamentals of Photonics

  35. Brewster window Active midum Brewster window Polarized laser output qB High reflectance mirror Output mirror Figure 5.3-10 The use of Brewster windows in a gas laser provides a linearly polarized laser beam. Light polarized in the plane of incidence (the TM wave) is transmitted without reflection loss through a window placed at the Brewster angle. The orthogonally polarized (TE) mode suffers reflection loss and therefore does not oscillate. Fundamentals of Photonics

  36. Etalon Selection of Longitudinal Mode Active midum High reflectance mirror Output mirror d1 d Resonator loss c/2d Resonator mdoes Etalon mdoes c/2d1 Laser output Figure 5.3-11 Longitudianl mode selection by the use of an intracavity etalon. Oscillation occurs at frequencies where a mode of the resonator coincides with an etalon mode; both must, of course, lie within the spectral window where the gain of the medium exceeds the loss. Fundamentals of Photonics

  37. Multiple Mirror Resonators (a) (b) (c) Figure 5.3-12 Longitudinal mode selection by use of (a) two coupled resonators (one passive and one active); (b) two coupled active resonators; (c) a coupled resonator-interferometer. Fundamentals of Photonics

  38. Characteristics of Common Lasers Solid State Lasers: Ruby, Nd3+:YAG, Nd3+:Silica, Er3+:Fiber, Yb3+:Fiber Gas Lasers: He-Ne, Ar+; CO2, CO, KF; Liquid Lasers: Dye Plasma X-Ray Lasers Free Electron Lasers Fundamentals of Photonics

  39. Fundamentals of Photonics

  40. Modulator Modulator Average power CW power t t (a) (b) Figure 5.4-1 Comparison of pulsed laser outputs achievable with (a) an external modulator, and (b) an internal modulator Pulsed Lasers Method of pulsing lasers External Modulator or Internal Modulator? • Gain switching 2. Q-Switching • 3. Cavity Dumping 4.Mode Locking Fundamentals of Photonics

  41. Gain Switching Fundamentals of Photonics

  42. Modulator Loss Gain t t Laser output t Q- Switching Figure 5.4-3 Q-switching. Fundamentals of Photonics

  43. Cavity Dumping Figure 5.4-4 Cavity dumping. Fundamentals of Photonics

  44. Laser modes coupling together Lock their phases to each other Mode locking

  45. Rate equation for the photon-number density photon lifetime Probability density for induced absorption/emission From We have Photon-Number Rate Equation Fundamentals of Photonics

  46. Rate equation for the Population Difference For a three level system Note Then Where the small signal population difference Substituting Population-difference rate equation (Three-level system) We have Fundamentals of Photonics

  47. Situation for the gain switching Fundamentals of Photonics

  48. Situation for the Q-switching 点击查看flash动画 Fundamentals of Photonics

  49. Dynamics of a Q-Switching process Dynamics of the Q-switching process Note the time relationship between the photon density and the population inversion variations! 49 Fundamentals of Photonics 2014/11/3

  50. Determination of the peak power, energy, width and shape of the optical pulse Dividing Fundamentals of Photonics

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