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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

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
wave equations for particles with mass
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

atoms molecules solids

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
electron energy levels

Eg

3p

3s

2p

Energy

2s

1s

Isolated

Atom

Metal

Semi-

conductor

Insulator

Electron Energy Levels
occupation of electron energy levels in thermal equilibrium

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)

thermal light
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)
atom photon interactions

2

2

2

1

1

1

h

h

h

h

h

Atom – Photon Interactions

Spontaneous Emission

Absorption

Stimulated Emission

spontaneous emission

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()?
transition cross section
Transition cross section:
  • Define transition strength S:
  • Define lineshape function g():
    • Full-Width Half-Max (FWHM):
absorption and stimulated emission

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)

absorption and stimulated emission1
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:
line shape

E2



21

h

E1

E0

g()

Line Shape

1. Lifetime Broadening

line broadening
Line Broadening
  • Collision Broadening
  • Inhomogeneous Broadening
thermal light1

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

summary
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
summary1
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
electron occupation of energy levels thermal equilibrium

Em

Energy Levels

E3

E2

E1

P(Em)

Occupation

Fermi-Dirac Distribution

Boltzmann Distribution

Electron Occupation of Energy LevelsThermal Equilibrium
atom photon interactions1

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
interactions of photons with atoms
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):