Quantum Optics

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Quantum Optics
Page 127

• Behavior of light at the atomic level
• Best explains the interaction of light with
  matter
• Wave theory starts to break down at the atomic
  level the classical example of this breakdown is
  the photoelectric effect

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The Photoelectric Effect
Collector Plate (Anode)
VACUUM TUBE
Light shone at the metal cathode in a vacuum tube
causes electrons to be released toward the anode
? current flows in the circuit
Current flows
Ammeter
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Photoelectric Effect

• When light energy is shone on a metal plate,
  electrons are released by the metal
• Wave theory predicts that
• the cumulative energy of absorbed light will
  eventually cause an electron to escape
  (sunbathing effect)
• Any wavelength of light will produce stimulated
  emission of electrons provided sufficient total
  energy is incident
• The more intense the incident light energy, the
  higher the energy contained in released electrons

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Photoelectric Effect
Quantum theory proves wave theory wrong, showing
that
(a) the cumulative energy of absorbed light will
eventually cause an electron to escape
electron release is instantaneous provided
incident photon energy exceeds electron-binding
energy
(b) any wavelength of light will produce
stimulated emission of electrons provided
sufficient total energy is incident
Only wavelengths of light that deliver energygt
binding energy will stimulate electron release

• (c) The more intense the incident light energy,
  the higher the energy contained in released
  electrons

Kinetic energy of released electrons is
independent of incident light intensity
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Atomic Energy Levels(not accounted for by Wave
Theory)

• At the atomic level, light exists as packets of
  energy (photons)
• Photons have discrete energy levels
• Electrons orbiting an atomic nucleus also have
  discrete energy levels

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Quantum Optics Photon Energy
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Frequency (wavelength) vs. Photon Energy

• Compare the energy carried by a green photon
  (587.6 nm) to that of a 400 nm blue photon

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Defining the electron Volt (eV)

• Avoid dealing with large negative exponents
  (10-19 range) for photon energy (joules) ? define
  a more convenient energy unit

• 1 electron volt energy obtained by a photon
  when it is accelerated through a potential
  difference of 1 volt (J/C)

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Photon Energy in eV
Blue light (400 nm) E 3.10 eV Green light
(587.6 nm) E 2.11 eV Red light (700 nm)
E 1.77 eV
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Atomic Energy Levels explain the Photoelectric
Effect
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Energy Levels Photon Absorption
Absorbing a photon of sufficient energy, an
electron jumps to a higher energy level
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Energy Levels Photon Emission
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Energy Levels Photon Emission
When an electron drops to a lower energy level, a
photon is emitted
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Atomic Energy Levels
Page 128

• Ground state (E0) lowest, most stable energy
  level in an atom
• strongest electrostatic attraction between
  nucleus and electron
• lowest electron kinetic energy
• Excited states (E1 E2 etc.) with elevation to
  higher energy levels, electrons become less
  stable
• weaker electrostatic attraction
• higher electron kinetic energy
• farther (on average) from nucleus

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Atomic Energy LevelsHydrogen Atom
Page 129
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Energy Levels Hydrogen Atom

• Negative sign ? indicates electrostatic
  attraction to nucleus (Binding Energy)
• Consider negative electron energy as the
  electrostatic hill that the electron must climb
  to be freed from the atom
• Zero energy ? free electron

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Atomic Energy Diagram

• Shows all the valid energy levels for the atom.
• Energy required for an electron to jump to a
  higher level
• Photon energy released as an electron drops to a
  lower level

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Hydrogen Energy Diagram
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Ionization State
13.6 eV
0
E5
E4
E3
12.74 eV
-1
12.09 eV
E2
Fig 78, p 128
-2
486 nm
656 nm
-3
E1
10.2 eV
-4
-5
-6
-7
-8
Transition Level above Ground State (eV)
121 nm
Electron Energy (eV)
-9
-10
HYDROGEN ENERGY LEVEL DIAGRAM
-11
-12
-13
E0
0 eV
-14
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Hydrogen Balmer series encompasses transitions up
or down to/from the first excited state
(E1). Note the hydrogen F line (E3 ? E1) and C
line (E2 ? E1)
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Energy Levels Hydrogen Atom

• After absorbing energy, the electron remains in
  an excited state for an extremely short period (
  10 nsec)
• Spontaneous emission as the unstable, excited
  electron drops to a lower energy level, it emits
  a photon.
• Photon energy is equal to the difference in
  atomic energy levels

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Energy Levels Hydrogen Atom
Photon energy for the transition from E2 to E1
Hydrogen C-line
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Energy Levels Hydrogen Atom

• A single energy jump from a higher excited state
  causes a smaller energy transition (e.g. from E3
  to E2)

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Energy Levels Hydrogen Atom

• Multi-level energy transitions can also occur
  (e.g. from E3 to E1)

Hydrogen F-line

• The greater the energy transition as an electron
  jumps to a lower energy level, the shorter the
  wavelength of the emitted photon

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Atomic Spectra Hydrogen

• All energy transitions (single-level and
  multi-level) are possible for the hydrogen atom.
• Photons corresponding to all possible transitions
  are emitted
• gives rise to characteristic discrete spectral
  lines of low pressure H2 gas

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Atomic Spectra Hydrogen

• Discrete hydrogen spectral lines ? fingerprint
  for hydrogen.
• Discrete hydrogen spectra used extensively in
  astronomy
• Characteristic atomic spectra in a gas best seen
  at low pressure - at higher pressures, spectra
  begin to change

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Atomic Spectra
Spectroscope

• Bunsen burned salts containing various elements
  in a flame
• placed a series of slits in front of the flame
• directed the light through a prism to disperse
  ?s
• This allowed him to view the line spectra of
  elements

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Absorption vs. Emission Spectra
                                                
        
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Absorption Spectra
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700 nm
600 nm
500 nm
400 nm
www.chem.uidaho.edu
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Solar Spectrum
www.chem.uidaho.edu
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Emission Spectra
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(No Transcript)
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Atomic Spectra
The colors of fireworks are created by atomic
line spectra
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Atomic Spectra Hydrogen

• Increasing gas temperature excites a greater
  proportion of H atoms ? more atoms spontaneously
  emitting photons
• Explains why gas discharge lamps glow brighter as
  they warm up

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Atomic Spectra

• Increasing gas pressure changes atomic spectra ?
  collisions between molecules also cause energy
  exchanges.
• As pressure increases, collision frequency
  increases ? discrete spectra gradually give way
  to a continuous spectrum

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Continuous Spectrum
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QQ1. Which transition in the hydrogen atom would
result in emission of the shortest wavelength
photon?

1. E0 ? E1
2. E3 ? E1
3. E4 ? E1
4. E5 ? E2

wrong direction
3.4 0.85 2.55 eV
3.4 0.54 2.86 eV
?
1.51 0.38 1.13 eV
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QQ2. What type of atomic spectrum would most
likely be seen for a hydrogen gas cloud in space?

1. Absorption spectrum
2. Emission spectrum
3. Continuous spectrum
4. All of the above

? Low pressure, cold gas
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Fraunhofer Lines (Solar Absorption Spectrum
Page 129
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Major Fraunhofer Lines (Solar Spectrum)
Page 129
Designation Element Wavelength (nm) Designation Element Wavelength (nm)
y O2 898.765 c Fe 495.761
Z O2 822.696 F H ß 486.134
A O2 759.370 d Fe 466.814
B O2 686.719 e Fe 438.355
C H a 656.281 G' H ? 434.047
a O2 627.661 G Fe 430.790
D1 Na 589.594 G Ca 430.774
D2 Na 588.997 h H d 410.175
D3 He 587.565 H Ca 396.847
E2 Fe 527.039 K Ca 393.368
b1 Mg 518.362 L Fe 382.044
b2 Mg 517.270 N Fe 358.121
b3 Fe 516.891 P Ti 336.112
b4 Fe 516.751 T Fe 302.108
b4 Mg 516.733 t Ni 299.444
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Solar Spectrum

• Series of absorption lines produced when sunlight
  emitted from the hotter solar chromosphere is
  absorbed by the cooler outer solar photosphere
• Hydrogen makes up 92.1 of the suns atoms,
  helium 9.2, and sodium, calcium, and iron 0.1
• Overall, several thousand solar Fraunhofer lines
  representing 67 elements

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Table 1 Major Solar Fraunhofer Lines Table 1 Major Solar Fraunhofer Lines Table 1 Major Solar Fraunhofer Lines
Designation Wavelength (nm) Origin
A 759.4 terrestrial oxygen
B 686.7 terrestrial oxygen
C 656.3 hydrogen (Ha)
D1 589.6 neutral sodium (Na I)
D2 589.0 neutral sodium (Na I)
E 527.0 neutral iron (Fe I)
F 486.1 hydrogen (Hß)
H 396.8 ionized calcium (Ca II)
K 393.4 ionized calcium (Ca II)
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Fluorescence
Page 129
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Fluorescence
Page 129

• Fluorescence is an example of energy absorption
  followed by spontaneous photon emission.
• Many substances that can be raised by a
  stimulating source from ground state to an
  excited state, then spontaneously emit photons,
  will theoretically fluoresce.

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Fluorescence

• Typically a high frequency source (UV) is needed
  to raise atoms from the ground state.
• A fluorescent substance could undergo a single
  energy level transition E0 ? E1 for excitation,
  followed byE1 ? E0 for spontaneous emission.
  This is rare.
• Most fluorescent substances, after excitation,
  will undergo a non-radiative transition (e.g.
  E2 ? E1) followed by photon release (e.g. E1 ? E0)

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Fluorescence (typical case)
Fig 79, p 130
energy loss to surroundings
non-radiative transition
fluorescence emission
high frequency radiation (UV)
lower frequency radiation
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Fluorescence

• Most substances are not 100 efficient, emitting
  less energy than they absorbed.
• Thermal agitation (vibrational loss) is the most
  common cause of the energy loss between
  absorption and emission (non-radiative
  transition)
• The emitted photon will therefore have lower
  energy than the exciting photon

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Fluorescence Stokes Reaction
Fluorescence emission (photon)
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Fluorescence

• Thermal losses explain why fluorescent emission
  usually has longer wavelength (different color)
  than the excitation source.
• e.g. blue light may be absorbed by a fluorescent
  substance. Thermal agitation causes energy loss
  from the excited atoms, leaving less energy for
  emission. The emitted photon will have longer ?
  (e.g. green)
• The difference in energy between the excited and
  emitted photon is called Stokes shift

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Explaining Stokes Shift

• Molecules contain discrete electronic energy
  levels (E0, E1, E2 , etc. ..).
• Each energy level also consists of a series of
  vibrational sub-levels (due to motion of the
  non-rigid nucleus within the molecular
  framework)
• Interaction with surrounding molecules causes
  rapid loss of vibrational energy to the
  environment (this is the thermal agitation
  loss non-radiative transition)
• The various types of atomic energy (electronic,
  vibrational, spin angular momentum etc.) are
  depicted in Jablonski diagrams

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Jablonski Diagram for Fluorescence

• Incident radiation excites the ground state
  molecule (A)
• The molecule is also excited to vibrational
  levels of the excited state
• Vibrational levels rapidly deactivate due to
  collisions with the surrounding environment until
  the molecule reaches its lowest excited state
  (vibrational relaxation)
• If the interaction between the excited molecule
  and its surroundings is not enough to cause the
  large energy transfer to return it to ground
  state, the molecule fluoresces (F, radiative
  decay)

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Ophthalmic Applications of Fluorescence
Page 131
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Ophthalmic Applications of Fluorescence

• Sodium fluorescein has several applications in
  ophthalmic practice
• tear film instillation to
• visualize ocular surface anomalies
• evaluate tear film stability
• Fluorescein angiography

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Fluorescein

• A cobalt blue filter provides excitation energy
  (365 - 470 nm)
• Thermal agitation decreases the energy available
  for emission
• 522 nm green photons are emitted

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Fluorescein Ocular Surface Evaluation

• Includes detection of corneal surface abrasions,
  superficial punctate keratitis, foreign body
  tracks in contact lens wearers etc.
• Fluorescein is placed into the tear film and the
  green emission pattern is viewed through a
  (stimulating) cobalt blue filter (usually with a
  biomicroscope)

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Superficial punctate keratitis
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CorneaDouble Abrasion
Fluorescein
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Fluorescein Angiography
Page 132

• Fluorescein dye is injected into the blood (or
  may be taken orally)
• A retinal camera equipped with UV filter is used
  to monitor the passage of fluorescein through the
  pre-retinal vasculature
• Any fresh hemorrhages, vascular leak etc. shows
  up as fluorescent green patches outside the blood
  vessels (which also fluoresce)

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Fluorescein Angiography Eye
Arterial Phase NORMAL
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Fluorescein Angiography Eye
Early venous phase - Normal
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Fluorescein Angiography Eye
Complete Filling Arteries Veins NORMAL
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Fluorescein Angiography Eye
Late Phase - Fading of Dye NORMAL
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Fluorescein Angiography Eye
Early Phase - Dye leakage DIABETIC RETINOPATHY
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Fluorescein Angiography

• Fluorescein angiography is especially useful in
  diabetes where microaneursyms, and dot and
  blot hemorrhages show up.

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Fluorescein Angiography Eye
Arterio-venous Phase - Neovascularization
DIABETIC RETINOPATHY
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Fluorescein Angiography Eye
Late Phase - Hemorrhage from new vessels
DIABETIC RETINOPATHY
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Fluorescein Angiography Dot Hemorrhages
Microaneurysms
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Fluorescein Angiography Dot Hemorrhages
Microaneurysms
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Fluorescence Microscopy

• Fluorescence overlay antigen mapping (C) of a
  skin section using two Mabs.
• A RITC-conjugate
• B FITC-conjugate
• C overlay image of A and B shows yellow
  fluorescence on sites where both antigens are
  present (between arrows). (Bar, 50 microns)
• From Jonkman J Clin Invest, Volume 95(3).March
  , 1995.1345-1352

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Phosphorescence
Page 132
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Phosphorescence
Page 132

• Same principle as fluorescence, but atoms of a
  phosphorescent substance will remain in the
  excited state for a much longer period of time.
• This requires the existence of a metastable state
  - i.e. a relatively stable excited state that the
  atom may remain in from second to hours.
• To understand the basis of a metastable state
  (also applies to lasers) must look at sources of
  atomic energy beyond electronic energy

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Practice Problem I
Most fluorescent substances emit a photon of
different wavelength than the absorbed photon.
The reason for this is

1. spontaneous emission occurs in a random direction
   with a random wavelength
2. vibrational losses in the excited substance
   reduce the energy available for emission
3. thermal transfer increases the energy of the atom
   resulting in an emitted photon of shorter
   wavelength
4. metastable substances build up stored energy
   resulting in emission of a higher energy photon

?
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Practice Problem II
Fluorescence could be described as a process of

1. stimulated emission, where high energy photons
   cause an atom to drop immediately to the ground
   state, emitting photons of longer wavelength due
   to thermal loss
2. thermal agitation of an atom from a metastable
   state to a higher, unstable state, causing an
   immediate drop to ground state, accompanied by
   photon emission
3. spontaneous emission, where longer wavelength
   photons are absorbed and shorter wavelength
   photons are emitted due to thermal loss
4. spontaneous emission, where higher energy photons
   are absorbed, and lower energy photons are emitted

?
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Practice Problem III
In the process of fluorescence, Stokes shift
refers to

1. the almost immediate drop by an excited atom to a
   slightly lower energy level prior to spontaneous
   emission of a fluorescent photon of shorter
   wavelength than the exciting photon
2. the increase in atomic energy level that occurs
   when the atom absorbs a photon of sufficient
   energy to raise it to the required state to allow
   subsequent fluorescent emission
3. the difference in energy level between excitation
   and emission energy that is responsible for the
   characteristic wavelength of the emitted photon
4. the tendency of atoms to vibrate and make
   translational movements as they are raised to
   higher energy levels by exciting photons

?
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Practice Problem IV
Compared with fluorescence, phosphorescence
differs

1. in that phosphorescent atoms must be raised to
   substantially higher energy levels due to the
   much more significant thermal losses that occur
   for the prolonged life of the excited state
2. in that phosphorescence involves a combination of
   spontaneous and stimulated emission, while
   fluorescence involves only spontaneous emission
3. only in the presence of a metastable state to
   maintain excited phosphorescent atoms above
   ground state for prolonged time periods
4. only in the fact that phosphorescent atoms do not
   suffer any vibrational (thermal) loss after
   initial excitation, so the stimulating energy is
   equal to the transitional energy giving rise to
   the emitted photon

?