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Introduction to Optical Electronics

Semiconductor Photon Detectors (Ch 18). Semiconductor Photon Sources (Ch 17). Lasers (Ch 15). Photons in Semiconductors (Ch 16). Laser Amplifiers (Ch 14). Photons & Atoms (Ch 13). Quantum (Photon) Optics (Ch 12). Resonators (Ch 10). Electromagnetic Optics (Ch 5). Wave Optics (Ch 2 & 3).

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Introduction to Optical Electronics

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  1. Semiconductor Photon Detectors (Ch 18) Semiconductor Photon Sources (Ch 17) Lasers (Ch 15) Photons in Semiconductors (Ch 16) Laser Amplifiers (Ch 14) Photons & Atoms (Ch 13) Quantum (Photon) Optics (Ch 12) Resonators (Ch 10) Electromagnetic Optics (Ch 5) Wave Optics (Ch 2 & 3) Ray Optics (Ch 1) Optics Physics Optoelectronics Introduction to Optical Electronics

  2. Output light Amplifier Input light Laser Amplilfiers

  3. Gain & Phase CoefficientsLorentzian Lineshape

  4. Exercise 13.1-1Attenuation and Gain in a Ruby Laser Amplifier • Consider a ruby crystal with two energy levels separated by an energy difference corresponding to a free-space wavelength 0 = 694.3 nm, with a Lorentzian lineshape of width  = 60 GHz. The spontaneous lifetime is tsp = 3 ms and the refractive index of ruby is n = 1.76. If N1 + N2 = Na = 1022 cm-3, determine the population difference N = N2 – N1 and the attenuation coefficient at the line center (0) under conditions of thermal equilibrium (so that the Boltzmann distribution is obeyed) at T = 300 K. • What value should the population difference N assume to achieve a gain coefficient (0) = 0.5 cm-1 at the central frequency? • How long should the crystal be to provide an overall gain of 4 at the central frequency when (0) = 0.5 cm-1 ?

  5. 2 1 Rate Equations Understanding Lifetimes • 1 and 2 are overall lifetimes for atomic energy levels 1 and 2. • Lifetime of level 2 has two contributions (where rates are inversely proportional to decay times) and • Population densitiesN1 and N2 will vanish unless another mechanism is employed to increase occupation

  6. 2 2 1 1 Rate Equations Absence of Amplifier Radiation • Pumping Rates – R1 & R2 defined • Rate Equations: • Steady-State Conditions

  7. Exercise 13.2-1Optical Pumping Assume that R1 = 0 and that R2 is realized by exciting atoms from the ground state E = 0 to level 2 using photons of frequency E2 / h absorbed with a transition probability W. Assume that 2≈tsp, and 1 << tsp so that in steady state N1≈ 0 and N0 ≈ R2tsp. If Na is the total population of levels 0, 1, and 2, show that R2 ≈ (Na – 2N0)W, so that the population difference is N0 ≈ NatspW / (1 + 2 tsp W)

  8. Rate Equations Presence of Amplifier Radiation • Pumping Rates • Four Case Studies (Homogeneous Broadened Transitions) • I = 0, R2(t) = R20u(t), R1(t) = 0 • 1 = 0, R2(t) = R20u(t) • 1 = 0, R2(t) = R20, I = Pulse • Steady State - 2 1

  9. Case 1I = 0, R1(t) = 0, R2(t) = R20u(t)

  10. Solving Differential Equations • Obtain Forms • General Form • Particular Form • Homogeneous (Natural) and Particular (Forced) Response • Particular Solution • Note: initial conditions not set • Homogeneous • Use initial conditions (removes the effect of the particular solution’s i.c.)

  11. Case 1I = 0, R1(t) = 0, R2(t) = R20u(t)

  12. Case 21 = 0, R2(t) = R20u(t)

  13. Case 21 = 0, R2(t) = R20u(t)

  14. Case 31 = 0, R2(t) = R20, I = Pulse

  15. Case 31 = 0, R2(t) = R20, I = Pulse

  16. Approach to Case 4Steady-State Rate Equations Rate Equations describe the rates of change of the population densities N1andN2as a result of pumping, radiative, and nonradiative transitions. • Determine rate equations in the absence of Amplifier Radiation (i.e., no stimulated emission or absorption) • Find steady-state population difference N0 = N2 – N1 • Determine rate equations in the presence of Amplifier Radiation (non-linear interactions) • Find steady-state population difference N = f(N0) • Determine the saturation time constant s

  17. 2 1 Case 4: Steady State • Pumping Rates • Steady State • Steady-state Population Differences • N = N2-N1 • N0 = N2-N1 w/o amp. rad. • s – Saturation Time Constant

  18. 3 Short-lived level Rapid decay Long-lived level 2 Laser Short-lived level Pump 1 Rapid decay 0 Ground state 3 Short-lived level Rapid decay Long-lived level 2 Pump Laser 1 Ground state Rate Equations in the Absence of Amplifier Radiation • Four-Level Pumping Schemes • Three-Level Pumping Schemes

  19. 3 Short-lived level Rapid decay Long-lived level 2 Laser Short-lived level Pump 1 Rapid decay 0 Ground state 3 Short-lived level Rapid decay Long-lived level 2 Pump Laser 1 Ground state Rate Equations in the Absence of Amplifier Radiation • Four-Level Pumping Schemes • Three-Level Pumping Schemes

  20. Population Inversion *What is the small-signal approximation?

  21. Exercise 13.2-3Pumping Powers in Three- and Four-Level Systems • Determine the pumping transition probability W required to achieve a zero population difference in a three- and a four-level laser amplifier • If the pumping transition probability W = 2 / tsp in the three-level system and W = 1 / 2 tsp in the four-level system, show that N0 = Na / 3. Compare the pumping powers required to achieve this population difference.

  22. Amplifier Nonlinearity Gain Coefficient Note: 0() is called the small-signal gain coefficient. Why?

  23. Amplifier Nonlinearity Gain

  24. Saturable Absorbers

  25. Gain CoefficientInhomogeneously Broadened Medium Gain Coefficient  

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