Stimulated Emission
Spontaneous Emission
 Excited States are metastable and must decay
 Excited States have lifetimes ranging from milliseconds (10-3 s) to
nanoseconds (10-9 s)
Stimulated Emission: through collisions emitted photon
causes other excited atoms to decay in phase
• Faster emission than spontaneous
• Emitted Photons are indistinguishable
LASER: Light Amplification by Stimulated Emission Radiation
Stimulated Emission Rate:
Absorption Rate:
-σ12FN1
Absorption
Cross-Section
Units → cm2
Number of atoms or
molecules in lower
energy level (Unit:
per cm3)
Photon Flux
Units → #/cm2sec
-σ21FN2
Stimulated emission
Cross-Section
Units → cm2
(typical value ~ 10-19
to 10-18 cm2)
Number of atoms or
molecules in lower
energy level (Unit:
per cm3)
Photon Flux
Units → #/cm2sec
Stimulated Emission Rate:
Absorption Rate:
-σ12FN1
Absorption
Cross-Section
Units → cm2
Number of atoms or
molecules in lower
energy level (Unit:
per cm3)
Photon Flux
Units → #/cm2sec
-σ21FN2
Stimulated emission
Cross-Section
Units → cm2
(typical value ~ 10-19
to 10-18 cm2)
Einstein showed:
σ12 = σ21
Number of atoms or
molecules in lower
energy level (Unit:
per cm3)
Photon Flux
Units → #/cm2sec
Population Inversion: is the condition for
light amplification through stimulated
emission.
Population inversion is not achievable through direct excitation in a two-level system.
http://www.olympusconfocal.com/java/stimulatedemission/index.html
Lasing begins as fluorescence
Need at least a three-level system
R1 and R2 are the external “pump” rates.
1/20 is spontaneous emission rate 2→0
1/21 is spontaneous emission rate 2→1
1/1 is spontaneous emission rate 1→0
1/2= 1/ 21 + 1/20 2→(anything)
dN
dt
2
 R 2  (1 /  2 ) N 2   F ( N 2  N 1 )
dN
dt
dN 1
dt
2
 R 2  (1 /  2 ) N 2   F ( N 2  N 1 )
=0
 R 2  (1 /  21 ) N 2   F ( N 2  N 1 )  (1 /  1 ) N 1
N 2  N1 
R 2 2 (1   1  21 )  R1 1
1  ( 1   2   1 2  21 ) F 
=0
Four Level System is Most Common for Lasing
E3-E2 radiationless decay 10-12
E2-E1 spontaneous lifetime of 10-6
E2-E1 stimulated emission of 10-9
E1-E0 radiationless decay 10-12
Log(Iout/Iin)
Gain
Pump
Gain region
No absorption
Below energy
gap
Loss region
0
Photon Energy
Absorption
So What Is LASER?
cavity
output
Pump
Population inversion in lasing medium
Laser cavity to create the resonance amplification
Gain from the medium > loss in the optics of the cavity
Laser Cavity
Laser Cavity is also a Fabry-Perot
optical resonator
Not too different from the soap bubble
FSR=/ =  / 2nL
or
 = c / 2nL
: frequency
c: speed of light
n: refractive index
L: cavity length
For an optical cavity of 20 cm emitting
visible laser light at 500nm (blue)
the number of integer wavelengths
between the two mirrors would be
Lines adjacent to the 500nm line are
very close:
500.0013 nm
499.9987 nm
Each line allowed by the cavity is a longitude mode.
Propagate
Cross-section
?
Transverse Modes
Low-order axisymmetric
resonator modes
Low-order Hermite-Gaussian resonator modes
A single mode (such as TEM00) maintain beam cross-section shape during propagation
Gaussian Beam Propagation
Near
Beam Field
waist
Far
Field
• Light is a wave and diffract. It is therefore impossible to have a perfectly
collimated beam.
• If a Gaussian TEM00 laser-beam wavefront were made perfectly flat at some
plane, it would quickly acquire curvature and begin spreading.
R -> z if z >> 0
At which point Gaussian beam
looks like a point source.
w = w0 if z << w02/  zR
If  = 500nm w0 = 2mm
zR = 25.12 m
zR also called Raleigh range
R: wavefront curvature
z: propagation distance
w: Beam width defined as the width at 1/e (13.5%) of the peak intensity.
w0: Beam width at beam waist.
Beam Quality
For a theoretical single transverse mode Gaussian beam, the value
of the waist radius–divergence product is:
For any real laser beam:
M2 is a dimensionless parameter to describe how “clean” is the mode
of the laser beam, i.e., how close is it to a true Gaussian beam.
Very good quality laser beam from low power He-Ne laser can have
a M2 ~1.05. Most lasers does not have such ideal beam.
Embedded Gaussian
A mixed-mode beam:
1. Has a waist M (not M2) times larger than the embedded Gaussian.
2. Will propagate with a divergence M times greater than the embedded Gaussian
3. Has the same curvature and Raleigh range.
Mode Control
• Larger (therefore higher order) modes are easier to get into lasing
condition, because it goes through more active medium.
• Aperture is commonly used to increase the loss for larger modes, so
that only TEM00 mode is allowed to survive.
• In many lasers, the limiting aperture is provided by the geometry
of the laser itself.
Some Common Lasers
To build a laser, you need
1. Two Mirrors
2. Gain Medium
3. Pump
Nd:YAG
1. Four level laser
2. Host solid is single crystal YAG: yttrium aluminum
garnet Y3Al5O12
3. Optically active atoms Nd. Only <1% of the
Medium.
4. Useful for cw operation, becauseYAG has high
thermal conductivity and can handle a lot of heat.
5. Also useful for pulsed operation
Ar Ion Laser
1. One electron gets pulled off of one atom.
2. In the large field, the electron gets accelerated and impacts other atoms,
knocking off other electrons.
3. A current of electrons is now flowing; the positive ions also cause a
current.
4. Multiple electron collisions pump the Ar+, which emit light 400-500 nm
5. Very inefficient. 0.03%
Semiconductor Laser
Mobile electrons
Mobile holes
A better band picture
• Many-state system
• Optical transition reserves k
• Population inversion easily achievable
k
P-N Junction
P type
N type
Emission
Electron
Injection
N type
+
+
+
+
-
Hole
Injection
P type
• Small size
• Very small cavity, large mode spacing.
• Very efficient: ~50% efficiency
• Most band gap is small, so emit IR light
(shortest wavelength at ~760nm)
• Can easily form arrays to increase total
power output.
• Mostly used as pump laser in
microscopy applications.
DPSS Laser
Common Continuous Wave (CW) Lasers for Microscopy
Argon UV (cw)
Argon Vis
Argon-Krypton
He-Ne
DPSS laser
364 nm
488, 514 nm (458, 477 nm)
488, 568, 647 nm
633 nm (laser pointer)
532 nm, 565 nm
Not tunable
Dye lasers are tunable and covers broad spectrum, but very difficult to operate.
None appropriate for 2-p absorption, wrong colors, low power
Wide Field vs Confocal Fluorescence Imaging
Confocal
Greatly reduces
Out of focus blur
Wide-field
Brighter but
No sectioning
More examples
widefield
confocal
medulla
muscle
pollen
Epi-illumination widefield is form of Kohler Illumination:
Objective is also condenser
Lamp or
laser
lens
detector
Detect at 90 degrees
Split with dichroic mirror
Confocal detection with
3 dimensional scanning
Image one plane,
Move focus
Confocal Aperture
•Decreasing the pinhole size rejects more out of focus light,
therefore improving contrast and effective z resolution.
•Decreasing the pinhole will increase x,y resolution (1.3x
widefield)
•Decreasing pinhole size decreases the amount of the Airy
disk that reaches the detector. This results in less light from
each point being collected
•Generally, collecting the diameter of 1 Airy disk is considered
optimal. This collects about 85% of light from a subresolution point.
Limits:
Open pinhole: nearly widefield resolution (still some confocality)
Closed: no image
Signal, S/N (out of focus) opposite trends
Closed: better axial sectioning, but no photons for contrast
Open: no sectioning, lots of photons
Confocal Aperture
ALIGNMENT OF APERTURES IS CRITICAL
•X, Y alignment : Different wavelengths focus at different lateral
position.
Lateral color aberrations can be important for multi-color
imaging
(multiple dyes with multiple lasers)
•Z alignment: Different wavelengths focus at different depths in
image plane. Chromatic aberrations can be important. Need wellcorrected lenses
Intermediate Optical Path of Confocal Microscope
Requirements:
1) Laser path has same conjugate planes
as intermediate, detector, eyepieces
2) Laser Scans undeviated around pivot point:
Stays on optical axis
3) Back aperture of objective is always filled
For highest resolution
Consequences:
1) Pupil transfer lens 50-100 mm fl to fill lens
2) Max scan angle ~7 degrees while
still filling lens
3) Position of pupil lens is critical
for parfocality with Kohler illumination
Brightfield and epi-fluorescence
Scanning Galvanometers
Much faster than stage scanning (1000x)
Point Scanning
Mirrors on magnets
x
y
Laser out
To
Microscope
Laser in
Olympus Fluoview
Scan Time Issues
Typical scan rate 1s /scan 512X 512
Faster is not stable with galvos, but can reduce #pixels
t=0
X = 512
X = 128
Y = 128
Y = 512
t=0
t = 0.25 sec
t = 1 sec
Scan Time Issues
Two scan types:
1.
2.
1) Bidirectional:
Resonant galvos, Very fast
Require post imaging
Processing, cannot change
Speed for zoom
2)Unidirectional:flyback
Normal for galvo scanners:
Have hysteresis, settling time:
30% duty cycle
Digital Zoom: Reducing scan angle,
higher pixel density per area
Not equivalent to changing objective lens magnification
1x
1024
points
2x
1024 points
4x
1024 points
Note that we have
reduced the field of view
of the sample linearly
Note: There will only be a single zoom value where
optimal resolution can be collected : Nyquist Criterion zoom 2-3
Confocal Parameters and Intensity, Resolution
Point Scan Detection: Photomultiplier (PMT)
Photocathode creates Secondary electrons
-1000V
Usually 12-13 dynodes in practice
Gain ~105-7 detected at anode
PMT
APD
Both can work under
Single-photon Counting
mode
Spectral Response and QE of PMTs
1,2,3: Alkali Photocathodes
4: GaAS Photocathode
PMTs best in UV
Alkali lousy in visible
10-15% QE: probably optimistic
weakest link on Confocal Scope
Silicon Response for (Avalanche) Photodiodes
Avalanche Photodiodes: used sometimes in imaging
1) 75% efficiency at 700-800 nm
2) Better than PMTs in visible, near IR
3) Very small areas ~200 microns: difficult to align in confocal
4) Low max count rates (small dynamic range)
Efficiency & Signal/Noise?
•
•
•
•
•
Collection efficiency of microscopy: ~25%
Detector quantum yield: ~70-90%
Thermal noise
Shot noise (quantum noise):
Read noise (A/D conversion)
Typical Dark Counts
CCD
Temperature
Sensitive Area
Dark Counts
-70 C
10-20 m
0.001 e/sec/pixel
APD
-20 C
100-500 m
10-100 e/sec/pixel
Gain of PMTs with Applied Voltage
2 Modes:
1) Analog Detection
2) Single Photon Counting
Analog (<1000 V) : linear regime,
integrated current~number photons,
higher voltage=bigger current
(until dark current takes over)
Match gain (voltage) with dynamic range
of integration electronics, for each sample
For best S/N. used in commercial instruments
2) Counting (>1200V): detector in saturation:
Every photon produced same voltage pulse
Increased sensitivity, but smaller range
Poisson statistics~ 1/n1/2
More complex, more expensive
Not used commercially
Photodiode
PMT: photomultiplier
CCD
APD: Avalanche Photodiode