Introduction to Optical Electronics

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. Wave Equations for Particles with Mass • Schrödinger's Equation – behavior of a single nonrelativistic particle of mass m, potential energy V(r,t) • Born Postulate – probability of finding a particle within an incremental volume dV in time interval dt is • Time Independent - separation of variables Used to find allowed energy levels

3. O O O O C C C O O C Atoms, Molecules & Solids • Vibrations • Diatomic • CO2 • Asymmetric Stretch; Symmetric Stretch; Bending • Rotations of a Diatomic Molecule • Electron Energy Levels • Isolated Atoms

4. Eg 3p 3s 2p Energy 2s 1s Isolated Atom Metal Semi- conductor Insulator Electron Energy Levels

5. Em Energy Levels E3 E2 E1 P(Em) Occupation Occupation of Electron Energy Levels in Thermal Equilibrium • Boltzmann Distribution – collection of identical molecules in a dilute medium • Probability that an arbitrary atomis in energy level Em: • Population ratio (on average) • Accounting for degeneracies • Fermi-Dirac Distribution – electrons in a semiconductor (Pauli exclusion principle) • Fermi-Dirac Distribution • Probability Density f(E)

6. Thermal Light • Blackbody Radiation Spectrum • Average Energy of a radiation mode (since in thermal equilibrium) • Spectral Energy Density (energy per unit bandwidth per unit cavity volume)

7. 2 2 2 1 1 1 h h h h h Atom – Photon Interactions Spontaneous Emission Absorption Stimulated Emission

8. 2 2 h 1 1 h h h h Atom Many Optical Modes Spontaneous Emission • Single-Mode Light with an Atom (spontaneous emission into a specific mode of frequency ) • Probability of emission between time t and t+t • The fraction of atoms that undergo spontaneous emission in interval t • Transition Cross-section: () = S g() • Spontaneous emitting a photon into any mode at the same frequency  • Probability density • Density of Modes M()?

9. Transition cross section: • Define transition strength S: • Define lineshape function g(): • Full-Width Half-Max (FWHM):

10. 2 2 1 1 h h h h c t  A Absorption and Stimulated Emission AbsorptionStimulated Emission • Transitions given n photons in modeProbability of a transition given mode of frequency  and volume V • Transitions by Monochromatic LightProbability of a transition given anatom in a stream of single-modephotons (Photons per Unit Area per Unit Time)

11. Absorption and Stimulated Emission • Transitions in Broadband Light • Atom in cavity of volume V with multimode polychromatic light • Light is broadband compared with atomic linewidth • Spectral energy density: • Probability of absorption or stimulated emission is:

12.  E2  21 h E1 E0 g() Line Shape 1. Lifetime Broadening

13. Line Broadening • Collision Broadening • Inhomogeneous Broadening

14. Loss From Stimulated Emission Gain fromN1 Absorption - + - Thermal Light • Thermal Equilibrium Between Photons and Atoms • Rate Equation • Steady state • Thermal Equilibrium (Boltzmann Distribution) Loss From Spontaneous Emission

15. Spectral Energy DensityBlackbody Radiation

16. Summary • Atomic Transition • Spontaneous Emission • Probability density (per second) of emitting spontaneously into one prescribed mode of frequency  • Probability density of spontaneous emission into any of the available modes is • Probability density of emitting into modes lying only in the frequency band  and  +d

17. Summary Stimulated Emission if atom is in the upper energy state and Absorption if in the lower energy state: • If the mode contains n photons, the probability density of emitting a photon or absorbing a photon • Atom is illuminated by a monochromatic beam of light • Atom is illuminated by a polychromatic but narrowband in comparison with atomic linewidth • Atom is illuminated with a broadband polychromatic light

18. Em Energy Levels E3 E2 E1 P(Em) Occupation Fermi-Dirac Distribution Boltzmann Distribution Electron Occupation of Energy LevelsThermal Equilibrium

19. Spontaneous Emission 2 2 2 • Probability Density of Spontaneous Emission into a Single Prescribed Mode • Probability Density of Spontaneous Emission into any Prescribed Mode h 1 1 1 h • Probability Density of Absorption of one photon from a single mode containing n photons • Probability Density of Absorption of one photon from a stream of “single-mode” light by one atom • Probability Density of Absorption of one photon in a cavity of volume V containing multi-mode light Absorption h h h • Probability Density of Stimulated Emission of one photon into a single mode containing n photons • Probability Density of Stimulated Emission of one photon into a stream of “single-mode” light by one atom • Probability Density of Stimulated Emission of one photon into a cavity of volume V containing multi-mode light Stimulated Emission Atom – Photon Interactions

20. Interactions of Photons with Atoms Where the transition cross section is with lineshape g() given by: • Homogeneous broadening (Lorentzian): • Inhomogeneous broadening (Collision): • Inhomogeneous broadening (Doppler):

21. Rate EquationThermal Equilibrium