Introduction to optical electronics
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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

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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


Spectral energy density blackbody radiation

Spectral Energy DensityBlackbody Radiation


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):


Rate equation thermal equilibrium

Rate EquationThermal Equilibrium


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