Absorption

1
Absorption
2
Absorption

• Light passing through a material medium will
• a) travel at a slower v c/n where n(f)
  dispersion
• b) have some absorption depending on the
  electric dipole moment and orientation of the
  incident light E
• c) the absorbed energy become the heat or light.

3
Absorption

• Gross description
• where cconcentration, ? extinction coeff.
• Integrates to (Beer-Lambert Law)

4

• Lambert law
• Beer law

    
5
Optical Density

• In terms of A ecl absorbance, we have
• ln(Io/I) A or log10(Io/I) A/2.303 O.D.
• OD 1 means 1/10 is transmitted
• OD 2 means 1/100 is transmitted
• OD 1, followed by OD 2 results in OD 3
• Transmittance T I/Io e-A
• Transmittance (I/Io) x 100

6
Absorption

• In simpler molecules there will be a number of
  discrete absorption lines
• In macromolecules there are so many lines that a
  broad absorption band forms
• The type of incident light used (uv, IR, etc.)
  determines the type of absorption that is probed
  uv probes electronic ir probes vibrational,
  etc.
• How are the measurements made?

7
Spectrophotometer

• Used to measure OD vs l
• Simplest l varies with dial setting (rotation
  of prism or grating photocell detector
  single beam compare sample to blank of buffer
• If e known you can determine concentration
• Fancier double-beam instruments with
  monochromator and recorder coupled to grating
  read OD vs l directly with a constant comparison
  to blank

8
Details I

• Animation
• Light source incandescent tungsten for near IR
  to vis Hg arc lamp for 250 350 nm Xe lamp for
  lt250 nm

9
DNA hypochromism

• More order means less absorption perfect
  crystals are clear (diamonds)
• So, ss DNA absorbs more than ds DNA at same
  concentration more base stacking means less
  absorption- so can monitor DNA melting by
  absorption

10
Applications II

1. Monitor denaturation/renaturation e.g.
   helix-coil in ds transition of DNA

11
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17
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19
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21
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22
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23
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24
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25
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26
Scattering
27
Scattering of Light
Scattering of light is what we call the
phenomenon in which light waves interact with
particles (molecules) and are removed from an
incident light beam. For an example, put a
few drops of milk into a container of water.
Shine a flashlight through the water. The
transmitted light looks orange or red (looking
back into the flashlight), while the light
scattered out the sides is blue or gray.
28
Scattering of Light
Question if the amount of scattering depends on
the number of scatterers, why do we not see much
scattering when a laser passes through glass?
Answer We return to the idea of
interference. For a relatively dense medium,
there is a good chance that for each molecule
scattering light, another one is one-half
wavelength away.
29
Scattering of Light
For light scattered sideways from a beam, this
results in destructive interference.
In the forward direction, the interference is
constructive, so the result is that the beam
continues to propagate.
30
Scattering
Why is the sky black when seen from outer
space? There are no particles to speak of, so
there is no scattered light we thus see a
black sky.
31
Scattering

• First quantitative experiments in 1869 by Tyndall
  (scattering of small particles in the air
  Tyndall effect)
• 1871 Lord Rayleigh started a quantitative study
  and theory
• Basic idea incident monochromatic linearly
  polarized light beam incident on a sample.
  Assume
• No absorption
• Randomly oriented and positioned scatterers
• Isotropic scatterers
• Independently scattering particles (dilute)
• Particles small compared to wavelength of light

32
Classical Wave description

• The incident electric field is
• E Eocos(2px/l 2pt/T)
• Interaction with molecules drives their electrons
  at the same f to induce an oscillating dipole
• pinduced a Eocos(2px/l 2pt/T)
• This dipole will radiate producing a scattered
  E field from the single molecule

dipole
Obs. Pt.
r
f
33
Rayleigh scattering

1. E1/r. So I1/r2.- necessary since I
   energy/time/area and A r2
2. E1/l2. So I1/l4 blue skies and red sunsets
   (rises)
3. Elastic scattering same f
4. sinf dependence when f 0 or p at poles of
   dipole no scattering max in horizontal plane

34
Polarizability and index of refraction

• a related to n , but how?
• Note that if n 1
• where c is the weight concentration
• Then
• where N number concentration

35
Polarizability and index of refraction

• So,
• For a particle in a solvent with nsolv, we have
  n2 n2solv 4pNa. We get

36
Scattered Intensity

• Detect intensity, not E, where
• Substituting for ?, we have

37
Scattered Intensity

• If there are N scatterers/unit volume and all are
  independent with N NAc/M, then
• We define the Rayleigh ratio Rq

38
Basic Measurement

• If the intensity ratio Iq/Io, nsolv, dn/dc, l, c,
  f, and r are all known, you can find M.
• Usually write Kc/Rq 1/M
• Measurements are usually made as a function of
  concentration c and scattering angle q
• The concentration dependence is given by
• Where B is called the thermodynamic virial

39
Polydispersity

• If the solution is polydisperse has a mixture
  of different scatterers with different Ms - then
  we measure an average M but which average?
• So the weight-averaged M is measured!

40
Angle Dependence

• If the scatterers are small (d lt l/20), they are
  called Rayleigh scatterers and the above is
  correct the scattering intensity is independent
  of scattering angle
• If not, then there is interference from the light
  scattered from different parts of the single
  scatterer
• Derivation of Particle Scattering Factor P(q)

41
Particle Scattering Factor

• Different shapes give different P(q)

42
Rayleigh Scattering
Scattering of white light from very small objects
depends strongly on the wavelength of the light -
short wavelengths are scattered most easily
smaller than the wavelength
43
Rayleigh Scattering
Scattering of white light from very small
objects depends strongly on the wavelength of the
light - short wavelengths are scattered most
easily
Light passing through more of the atmosphere is
scattered more.
The sun at noon appears pale yellow, and at
sunset it is red.
44
Rayleigh Scattering
The sky appears blue, for the same reason as
we look up in the sky, we see light that has been
scattered by molecules. More blue light is
scattered than green or red, although some of
these colors are present as well. The result
we see unsaturated blue.
Red light keeps going over our heads and out
the other side of the atmosphere.
45
Mie Scattering - Large Particles
Now consider the cigarette smoke that is exhaled.
Does it look blue?
Exhaled smoke tends to look pretty much white (or
gray).
Water condenses on the particles making them much
larger - scattering is independent of the
wavelength.
46
Mie Scattering
Why are clouds white (cumulus clouds)?
Lots of large water droplets scatter light of
all wavelengths equally. Light is scattered
multiple time in traversing the cloud.
47
Mie Scattering

• When the particles are larger than about
  one-tenth of a wavelength.
• The light scattered from one point of the
  particle may well be out of phase with light
  scattered from another point. The two beams then
  interfere and the scattered-light intensity is no
  longer symmetrical as in Rayleigh case.

48
Mie Scattering

• Mies theory takes into account the size of
  the particles, their refractive index, the
  refractive index of the surrounding of the
  particles, as well as the shape, dielectric
  constant, and absorptivity of the particles,
  leading to a series (in theory an infinite
  number) of partial waves. In Rayleigh scattering,
  only the first few terms need to be consider. Mie
  scattering includes Rayleigh scattering as a
  special case.

49
Mie Scattering

• The ratio i/I0 in Mie scattering is
  determined by Mie extinction coefficient, µ,
  which gives

K, extinction factor, is the ratio of cross
section of the light affected by a particle to
the cross section of the particle. It is
generally larger than unity because of the
refractive index difference between particles and
the medium between them.
50
Polarization
x
An x-polarized field
z
y
(Side view of wave)
51
Polarization
y
y
y
x
x
x
Head-on view of polarization
52
Polarization by Scattering
Rayleigh scattering in addition to
being wavelength dependent is also polarization
dependent (leads to polarized light).
53
Polarization by Scattering
y
x
Scattering molecule
z
Electric field causes charge to oscillate
54
Polarization by Scattering
55
Raman Scattering

• High energy photon (with E hf, much greater
  than DE hf vibrational energy transition)
  scatters from a sample and gives rise to 2
  shifted frequency components in the scattered
  light one at ff and one at f-f.
• Its as if part of the photon were absorbed
  Efinal h(f-f)or the transition energy added
  to the photon that leaves Efinal h(ff)

56
Non-linear Stuff

• Suppose the incident E field is E Eocos(2pft)
  and it interacts with the polarizability of the
  molecule to produce an induced dipole
• p(t) a(t) Eocos(2pft)
• But a(t) ao(t) a(t)cos(2pft) since the
  vibrations of the molecule lead to a time varying
  polarizability at natural frequency f
• Therefore p(t) Eoao(t) a(t)cos(2pft)cos(2p
  ft) Eoa(t)cos(2pft) Eoa(t)cos(2pft)cos(2pft
  )
• The first term oscillates in phase with the
  incident light elastic (Rayleigh) scattering
  well see later and represents the bulk of the
  light the second term is the Raman scattering
  term

57
Raman term

• Using cosA cosB ½ cos(AB)cos(A-B)
• The Raman term can be re-written as
• ½ Eoa(t)cos2p(ff)t cos2p(f-f)t

Anti-Stokes
Stokes
58
Raman Experiment
Very low scattered intensity need high
concentration, good collection optics, long cell,
cooled photomultiplier tube, long
experiments Calculate Df from laser line (laser
f not important) same info as IR absorption,
even using visible light and water as solvent
59
Example Data
acetaminophen
Plotted Intensity vs 1/l wavenumber (cm-1)
60
Raman Scattering

• Cascaded Raman Scattering, Stimulated Raman
  Scattering.
• Application
• Raman Scattering, nonlinear interaction between
  incident light and lattice of solid state media
  (Optical Branch), 10cm-1 to 103cm-1

61
Brillouin Scattering

• Similar as Raman Scattering, nonlinear
  interaction between incident light and lattice of
  solid state media (Phonon Branch), lt10cm-1.

62
Holography
63
History of Holography

• Invented in 1948 by Dennis Gabor for use in
  electron microscopy, before the invention of the
  laser
• Leith and Upatnieks (1962) applied laser light to
  holography and introduced an important off-axis
  technique

British physicist Dennis Gabor won the Nobel
Prize in physics in 1971.
64
Conventional photography

• Conventional
• 2-d version of a 3-d scene
• Photograph lacks depth perception or parallax
• Film sensitive only to radiant energy
• Phase relation (i.e. interference) are lost

65
Holographic photography

• Hologram
• Interfere wavefront of light from a scene with a
  reference wave
• Converts phase information into amplitude
  information
• Freezes and reconstruct the intricate wavefront
  of light that carries all the original
  information of the scene
• holos Greek for whole message
• graphein Greek for write

66
In-line (Gabor) Hologram
Recording
x
z
z0
Coherent source
Photographic plate
object
lens

• Object a small scattering objects on a
  transparent background
• transmitted wave - relatively strong uniform
  plane wave

- complex amplitude R (a real constant)
(reference wave)

• scattered wave - a weak wave due to
  transmittance variations
• in the object

(object wave)
- complex amplitude O(x,y)-
67
Recording

• Reference wave
• Object wave
• Intensity distribution on plate

68
Linear development

• When developed the photographic plate will have a
  transmittance which depends on the intensity
  distribution in the recorded plate
• tb background transmittance due to R2
  term
• B parameter which is a function of the
  recording an developing process

69
Hologram reconstruction

• When illuminated by a coherent wave, A(x,y),
  known as the reconstruction wave, the optical
  field emerging from the transparency is,
• i.e. a superposition of 4 waves
• If A(x,y)R(x,y), i.e. reconstruction and
  reference waves are identical,

70
Hologram reconstruction

• Three terms in the reconstructed wave

Direct wave identical to reference wave except
for an overall change in amplitude
Object wave identical to object wave except for
a change in intensity
Conjugate wave complex conjugate of object wave
displaced by a phase angle 2 ?
71
Hologram reconstruction

• Three terms in the reconstructed wave of the
  point hologram

Direct wave identical to reference wave
(propagates along z) except for an overall change
in amplitude

• Conjugate wave spherical wave collapsing to a
  point at a distance z to the right of the
  hologram
• a real image
• displaced by a phase angle 2kz

Object wave Spherical wave except for a change
in intensity Br2 i.e. reconstructed wavefront
72
Direct, object and conjugate waves
Object wave
Reference wave
Real image
Virtual image
Direct wave
Conjugate wave
-z
z
z0
73
Direct, object and conjugate waves

• Direct wave corresponds to zeroth order grating
  diffraction pattern
• Object wave gives virtual image of the object
  (reconstructs object wavefront) first order
  diffraction
• Conjugate wave conjugate point, real image (not
  useful since image is inside-out due to negative
  phase angle) first order diffraction
• In general, we wish to view only the object wave
  the other waves just confuse the issue

74
Off-axis (Leith-Upatnieks) Hologram
Leith Upatnieks (1962-64)
Recordings
x
z
q
Photographic plate
object

• Object beam

• Reference beam

75
Off-axis (Leith-Upatnieks) Hologram
Interference pattern on the photographic plate
With linear development, the photo plate has
transmittance
76
Reconstruction of off-axis hologram
Directly transmitted wave
Halo
Original object wave(virtual image)
Conjugate real image
z
halo
Object wave is separable from the other waves.
Itovercome the major drawback of Gabors in-line
hologram
x
Hologram
Transmitted wave
Virtual image
Real image
77
Fourier Hologram (Vander Lugt, 1964)
x
x
Recordings
Object O(x,y)
Photographic plate
reference
f
f
d(xb,y)
Complex amplitude of object wave at photographic
plate
O(x,y) complex amplitude of object leaving the
object plane F Fourier transform
78
Record and Reconstruction
Reference wave at photographic plate
Intensity interference pattern at photographic
plate
Reconstructions
x
z
Fourier hologram
f
f
x
79
Reconstruction
Complex amplitude in the back focal plane of the
lens
focus on the axis
halo around a focus
original object wave shifted downwards by a
distance b
conjugate of original object wave inverted and
shifted upwards by a distance b
where the symbol ? denotes the correlation
operation.
b
b
O(-xb,-y) conjugate inverted
O(x-b,y) original object
Direct halo
80
Image Hologram
A hologram made by placing a photographic plate
near the location of the real image formed by a
lens.
d2
f
Image
object
photographic plate
d1
Gauss imaging condition (lens law)
The position of the reconstructed image is on the
hologram itself. Therefore, the distance from the
hologram to the image is very short consequently
image hologram is insensitive to the coherency of
the reconstructed beam. Application
White-light hologram
81
Fraunhofer Hologram
x
x
z
object
photographic plate
z0
Object is small enough for its far-field
diffraction pattern (Fraunhofer diffraction)to be
formed at the photographic plate.
82
Making a hologram
83
Hologram Reflection vs. Transmission

• Transmission hologram reference and object waves
  traverse the film from the same side
• Reflection hologram reference and object waves
  traverse the emulsion from opposite sides

View in Transmission
View in reflection
84
Phase hologram
Amplitude(absorption) hologram
Phase modulations due to variation of refractive
index or thickness.
Amplitude modulations due to absorption changes
of photographic materials, Da(x) regime
Thin(or plane) hologram Raman-Nath diffraction
Thick (or volume) hologram Bragg diffraction
The thickness of the recording material is small
compared with the interference fringe spacing.
(L grating period)
L
L
d
cf. Q-parameter
Qlt1 thin hologram Qgt1 volume hologram
85
1-3. Thin Hologram
Thin phase hologram Thin amplitude hologram

• Complex amplitude transmittance

(a) Thin amplitude hologram
saptially varying
Recording
x
O(x,z)
L
q
z
q
R (x,z)
d
86
where
grating wavevector (or grating period)
interference fringe spacing
where t0 average amplitude transmittance of
the grating t1 amplitude of spatial
variation
87
Reconstructions
transmitted beam
incident
diffracted beam
(reference beam)
Diffraction efficiency h
Maximum diffracted amplitude is obtained when
t0t11/2 , i.e.
88
Diffracted amplitudes
0th diffraction beam (directly transmitted)
-1st-order diffraction beam
1st-order diffraction beam
-1st-order diffraction beam
0th diffraction beam (directly transmitted)
1st-order diffraction beam
hmax for amplitude grating
89
(b) Thin phase hologram
For phase grating (no loss),

• complex amplitude transmittance

• Phase shift

• Complex amplitude transmittance of the grating

where Jn Bessel function of the first kind of
order n
A thin phase grating diffracts a wave incident on
hologram into a large number of orders.
q
Raman-Nath diffraction
q
Recording
Reconstruction
90

• nth-order diffraction efficienty

• Only first-order diffracted wave contributes to
  the desired image.

91
1-4. Volume Hologram
Typically,
Volume hologram
3-D system of layers
Reflection hologram
recording medium (bulk) ex) crystal
thick film
q10o
The diffracted amplitude is a maximum only when
the Bragg condition is satisfied.
Reflection hologram
reconstruction
recording
O
R
92
(A) Coupled Wave Theory (A. Kogelnik, 1969)
Ref.gt Bell System Technical Journal, 48,
2909-2947 (1969) Coupled wave theory
for thick hologram gratings
Recordings
x
x
S(l0)
q0
z
q0
z
q0
q0
R(l0)
R(l0)
S(l0)
(a) Transmission volume grating
(b) Reflection volume grating
93
Reconstructions
b
z
z
q
q
R(l)
S(l)
Vector diagram for Bragg incidence
(a) Volume transmission grating
x
S(l)
b
q
z
z
q
R(l)
(b) Volume reflection grating
94
Assumed equations for gratings

• refractive index changes (phase hologram)

• absorption index changes (amplitude hologram)

where n0 and a0 average values of refractive
and absorption constant, respectively.
grating vector

• scalar wave equation

where E total electric field k
spatially varying propagation constant in grating

• Assuming that

95
The propagation constant can be written a
where
coupling constant
Interaction between reference wave R and signal
wave S.
For k0, no modulation of phase or absorption
gratings and hence, no diffraction.

• Total electric-field E in the grating

where
propagation vectors for two waves with
Derivation of coupled wave equations
Substituting total E-field into wave equation and
comparing the terms involving and
96
We get
terms
terms
where (prime) denote differentiation w, r, f, z
Note that term is
introduced for non-Bragg condition.

• Define dephasing measure as

for transmission grating
for reflection grating
where
and
recording(writing) wavelength
reading wavelength
It is useful parameter for evaluating the effects
of deviations from the Bragg condition.
97

• Slowly-varying Amplitude Approximation(SVAA)

and
(i.e. energy interchange between R and S is
small.)
Coupled wave equations
where obliquity factors
for transmission hologram
for reflection hologram
Coupled wave equations can be solved for the
appropriate boundary conditions.

• Transmission hologram R(0)1, S(0)0
• Reflection hologram R(0)1, S(d)0

Trial solution
98
(B) (volume) Transmission Holograms
(i) Pure Phase Holograms
For pure phase hologram, a0a10

• Diffracted amplitude

where
For incidence at Bragg condition, x0

• Diffraction efficiency at Bragg condition

99

• When the angle of incidence or the wavelength of
  the incident beam deviates from the values of
  Bragg condition, the diffraction efficiency is
  given by

where or
100
(ii) Pure phase hologram with loss
For a lossy phase grating ( ),
101
(iii) Amplitude Hologram
For a pure amplitude hologram,
where
Diffraction efficiency
0.04
a0a1
For incidence at Bragg angle, x0, the
diffraction efficiency is
1.0 2.0 3.0
where a0a1
102
(iv) Mixed Holograms
103
(C) (volume) Reflection Holograms
(i) Pure Phase Hologram
For non-Bragg incidence, diffraction amplitude
where
1
For Bragg incidence,
1.0 2.0 3.0
104
(ii) Amplitude Holograms
where
For Bragg incidence
For the special case of a0a1,
105
Theoretical Maximum Diffraction Efficiency
Hologram Type
Thin Transmission
Volume Transmission
Volume Reflection
Modulation
Amplitude
Phase
Amplitude
Phase
Amplitude
Phase
h()
6.25
33.9
3.7
100
7.2
100
106
Volume Holography

• In volume holography, we apply an object beam and
  a reference beam simultaneously on a
  photosensitive material that records the
  interference pattern.
• Applying one of these beams to the resultant
  recording recreates the other.

107
Bragg Selectivity

• The hologram is sensitive to the exact recreation
  of the reference beam. A change in angle,
  position, or wavelength of the beam will lead to
  a failure to reconstruct the image.
• The sensitivity increases with thickness of the
  holographic material.

108
Multiplexing

• This can be used to our advantage. We record one
  object image with our hologram.
• We then change the beam angle, wavelength, or
  position, until the image disappears, and record
  another image in the holographic material.
• By this method, multiple object images may be
  stored in a single piece of holographic material.

109
Storing Data

• We can convert binary data to an array of
  black-and-white pixels with a spatial light
  modulator (SLM).
• We can store multiple pages of data in our
  holographic crystal.
• We can then read back out our pages via the
  reference beam.

110
Multiplexing Methods

• Angle one changes the angle of the reference
  beam.
• Wavelength one changes the wavelength of the
  reference beam.
• Shift one changes the position of the
  holographic material relative to the beams.
• Coherence one changes the position of the
  material and the coherence function of the
  reference beam.

111
? ? ? ?
112
1. Optical source and laser
2. Physical Process in lasing medium
3. Population Inversion
4. Components of laser
113
Sources of Radiation

• In order to be suitable for spectroscopic
  studies, a source must generate a beam of
  radiation with sufficient power for easy
  detection and measurement and its output power
  should be stable for reasonable periods. Sources
  are of two types.
• 1. Continuum sources
• 2. Line Sources

114
(No Transcript)
115

• Continuum Sources
• Continuum sources emit radiation that changes in
  intensity slowly with wavelength. It is widely
  used in absorption and fluorescence spectroscopy.
  For the ultraviolet region, the most common
  source is the deuterium lamp. High pressure gas
  filled arc lamps that contain argon, xenon, or
  mercury serve when a particular intense source is
  required. For the visible region of the spectrum,
  the tungsten filament lamp is used universally.
  The common infrared sources are inert solids
  heated to 1500 to 2000 K.

116

• Line Sources
• Sources that emit a few discrete lines find wide
  use in atomic absorption spectroscopy, atomic and
  molecular fluorescence spectroscopy, and Raman
  spectroscopy. Mercury and sodium vapor lamps
  provide a relatively few sharp lines in the
  ultraviolet and visible regions and are used in
  several spectroscopic instruments. Hollow cathode
  lamps and electrodeless discharge lamps are the
  most important line sources for atomic absorption
  and fluorescence methods.

117
Laser Sources

• The term LASER is an acronym for Light
  Amplification by Stimulated Emission of
  Radiation. Laser are highly useful because of
  their very high intensities, narrow bandwidths,
  single wavelength, and coherent radiation. Laser
  are widely used in high-resolution spectroscopy.

118
Characteristics of Laser
(a) ????
?????????????????604.7nm, ??????0.00047nm,
He-Ne??
(b) ???????
??P100????? W 100??, t1?.
? t10-11?, ?P1015??. ? t10-15sec, then
119
(c) ?????,????
????,???360?, ??????1/10?.
(d) ???
??????????????,??????????????????????10??.
(e) ????
??????????, ???????????.???????????????????.
120

• Laser Examples
• Solid state
• NdYAG1064 nm IR 523 nm green, cw/pulsed
• Gas
• He-Ne 632.8 nm red, cw
• Ar 488 nm (blue) or 514.5 nm (green) also UV
  lines, cw (4-level system
• Dye
• Organic dye solutions ? tunable outputs (various
  distinct ?s), pulsed (4-level system)

121

• Laser Examples
• Semiconductor laser
• Free electrons laser

Application of Laser
????,????,???,????, ????????.????.????, ????,
????.
????, ????,????.
???????,?????.
?????.????.???.
122

• Four processes in Lasing Mechanism
• 1. Pumping
• 2. Spontaneous emission (fluorescence)
• 3. Stimulated emission
• 4. Absorption

123

• Pumping
• Molecules of the active medium are excited to
  higher energy levels
• Energy for excitation ? electrical, light, or
  chemical reaction

124
(No Transcript)
125

• 2. Spontaneous Emission
• A molecule in an excited state can lose excess
  energy by emitting a photon (this is
  fluorescence)
• E h? hc/? E Ey Ex
• E (fluorescence) lt E (absorption) ?
• ? (fluorescence) gt ? (absorption) fluorescent
  light is at longer wavelength than excitation
  light

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• 3. Stimulated Emission
• Must have stimulated emission to have lasing
• Excited molecules interact with photons produced
  by emission
• Collision causes excited molecules to relax and
  emit a photon (i. e., emission)
• Photon energy of this emission photon energy of
  collision photon ? now there are 2 photons with
  same energy (in same phase and same direction)

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• 4. Absorption
• Competes with stimulated emission
• A molecule in the ground state absorbs photons
  and is promoted to the excited state
• Same energy level as pumping, but now the photons
  that were produced for lasing are gone

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• Population Inversion
• Must have population inversion to sustain lasing.
  
• Population of molecules is inverted (relative to
  how the population normally exists).
• Normally there are more molecules in the ground
  state than in the excited state (need gt 50 ).
• Population inversion More molecules in the
  excited state than in the ground state.

132

• Why is it important?
• More molecules in the ground state ? more
  molecules that can absorb photons
• Remember absorption competes with stimulated
  emission
• Light is attenuated rather than amplified
• More molecules in the excited state ? net gain in
  photons produced

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134
??????????
??????????T,???En??????Nn, ?
K???????,?????????????????, g n??????n ??? (???E
n)???.
(????????????????.)
N1?????E1????,
N2?????E2????,
E2gtE1,?1???,2???????
135
?
????,?????????????????? ????.?
???????????
136
?????
E2????????dt????????E1????????-dN2 ,?
A21??????E2???E1???????.??
?????,?
137
?
??
????????, ????????E2??????????,??????????????,
????(?????),??????????????
???????????????,??????????10-8,???10-31??????,
????.
??????????????,?????????????(10-8)??????.
138
??????
?dN21?dt????E2?????E1???????,?
??????????????,?????????????????????????????.??
??????.
139
???????, ?????,????????????????????????????.??
?
??
????????
140
??????
????????,?
?????????h?/kT?????,????????.
141
?
???????????????,?????????????,????????????.
B12 ????????E1?????E2??????,
B21 ????????E2?????E1??????.
142
?????????
???????,????????,??????????,????????????.
??????????,????. ?????????????????????????????
,?????????,??,?????.
dt ?????????
dt ???????????
143
????
?
????.
?????,???????,??
???????????.
??????????,????????,??????????????,?????????.
144

• How to achieve population inversion?
• Laser systems 3-level or 4-Level
• 4-level is better ? easier to sustain population
  inversion
• 3-level system lasing transition is between Ey
  (excited state) and the ground state
• 4-level system lasing transition is between two
  energy levels (neither of which is ground state)
• All you need is to have more molecules in Ey than
  Ex for population inversion (4-level system) ?
  easier to achieve than more molecules in Ey than
  ground state (3-level system)

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146
????????????
(a) ?????
?????? ?694.3nm
?????
147
????????, ??????????????????E3,?????????E3????
????10-1110-8,???????????E2????
E2????, ????10-31??E2??????????,
???????????????????
???????.
E1?E2??????????????.
???????????.??????.
148
(b)????? He-Ne??????
149
He?????????,3s?1s?????????????????,???3s?1s???
????.
Ne???2s?3s???He???3s?1s????,??,?????????He??????
????Ne?????,?????????????.?????,??3s?3p,
2s?2p????????,??3p?2p????????,??,??3s?2s??????,???
???.
150
Components of Lasers
(1) ????(?????).
(2) ????.
(3) ?????.
151

• Component of Lasers
• The important components of laser source are
  lasing medium, pumping source, and mirrors. The
  heart of the device is the lasing medium. It may
  be a solid crystal such as ruby, a semiconductor
  such as gallium arsenide, a solution of an
  organic dye or a gas such as argon or krypton.

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153
??????
(1)???????
????????????????
???????????,
154
(2) ????????
??
????????.
????,??????????.
????????
??????
????
????
155
(3) ??????????????
?????
156
?????????
????G??????????????????.
X
??????????
N2gtN1?,G?? N2ltN1?,G??
157
????
????????,????????
? ?????????,?????
? ??????, ?????,??????.
??,?????,???????????????????,????????????????.
158
gt1,???
lt1,???
1,??????
GM??????????.?GgtGM?,??????????,??????,??????.
?????,????????????????????,???????????,G??,?G?GM?,
??????.