Stimulated Emission
LASER: Light Amplification by Stimulated Emission Radiation
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
Absorption Rate:
-σ12FN1
AbsorptionCross-SectionUnits → cm2
Photon FluxUnits → #/cm2sec
Number of atoms ormolecules in lowerenergy level (Unit: per cm3)
Stimulated Emission Rate:
-σ21FN2
Stimulated emissionCross-SectionUnits → cm2(typical value ~ 10-19
to 10-18 cm2)
Photon FluxUnits → #/cm2sec
Number of atoms ormolecules in lowerenergy level (Unit: per cm3)
Einstein showed:σ12 = σ21
Absorption Rate:
-σ12FN1
AbsorptionCross-SectionUnits → cm2
Photon FluxUnits → #/cm2sec
Number of atoms ormolecules in lowerenergy level (Unit: per cm3)
Stimulated Emission Rate:
-σ21FN2
Stimulated emissionCross-SectionUnits → cm2(typical value ~ 10-19
to 10-18 cm2)
Photon FluxUnits → #/cm2sec
Number of atoms ormolecules in lowerenergy level (Unit: per cm3)
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
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)
22 R
dt
dN 22 )/1( N )( 12 NNF
Need at least a three-level system
22 R
dt
dN 22 )/1( N )( 12 NNF
111222121 )/1()()/1( NNNFNR
dt
dN
= 0
= 0
F
RRNN
)(1
)1(
212121
112112212
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
0
Log(
I out/I i
n)
Gain
Absorption
Photon Energy
No absorptionBelow energy gap
Gain region
Loss region
Pump
So What Is LASER?
Pump
cavity
output
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=/ = / 2nLor
= c / 2nL
: frequencyc: speed of lightn: refractive indexL: 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
Each line allowed by the cavity is a longitude mode.
Lines adjacent to the 500nm line are very close:
500.0013 nm499.9987 nm
Cross-section
Propagate
?
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 Field
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.
Beam waist
R: wavefront curvaturez: propagation distancew: Beam width defined as the width at 1/e (13.5%) of the peak intensity.w0: Beam width at beam waist.
R -> z if z >> 0At which point Gaussian beam looks like a point source.
w = w0 if z << w02/ zR
If = 500nm w0 = 2mmzR = 25.12 m
zR also called Raleigh range
For a theoretical single transverse mode Gaussian beam, the value of the waist radius–divergence product is:
Beam Quality
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 Gaussian3. 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 geometryof the laser itself.
Some Common Lasers
To build a laser, you need
1. Two Mirrors2. Gain Medium3. Pump
Nd:YAG1.Four level laser2.Host solid is single crystal YAG: yttrium aluminum
garnet Y3Al5O123.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 nm5. Very inefficient. 0.03%
Semiconductor Laser
Mobile electrons Mobile holes
k
• Many-state system
• Optical transition reserves k
• Population inversion easily achievable
A better band picture
N type P type
P-N Junction
----
++++
N type P type
ElectronInjection
HoleInjection
Emission
• 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) 364 nmArgon Vis 488, 514 nm (458, 477 nm)Argon-Krypton 488, 568, 647 nmHe-Ne 633 nm (laser pointer)DPSS laser 532 nm, 565 nm
Not tunable
None appropriate for 2-p absorption, wrong colors, low power
Dye lasers are tunable and covers broad spectrum, but very difficult to operate.
Wide Field vs Confocal Fluorescence Imaging
Confocal
Wide-field
Greatly reducesOut of focus blur
Brighter butNo sectioning
More examples
medulla muscle pollen
widefield
confocal
Epi-illumination widefield is form of Kohler Illumination:Objective is also condenser
Lamp orlaser
detector
Detect at 90 degreesSplit with dichroic mirror
lens
Confocal detection with3 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 sub-resolution point.
Limits: Open pinhole: nearly widefield resolution (still some confocality)Closed: no image
Signal, S/N (out of focus) opposite trendsClosed: better axial sectioning, but no photons for contrastOpen: 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 well-corrected lenses
Intermediate Optical Path of Confocal Microscope
Requirements:1) Laser path has same conjugate planesas 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 illuminationBrightfield and epi-fluorescence
Scanning GalvanometersMuch faster than stage scanning (1000x)
xy
Laser in
Laser out
Point Scanning
ToMicroscope
Mirrors on magnets
Olympus Fluoview
Scan Time Issues
Typical scan rate 1s /scan 512X 512Faster is not stable with galvos, but can reduce #pixels
t = 1 sec
X = 512
Y =
512
t = 0
X = 128
Y =
128
t = 0
t = 0.25 sec
Scan Time Issues
Two scan types:
1.
2.
1) Bidirectional:Resonant galvos, Very fastRequire post imagingProcessing, cannot changeSpeed 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 areaNot equivalent to changing objective lens magnification
1 x1024
points
2 x1024 points
4 x1024 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)
Usually 12-13 dynodes in practiceGain ~105-7 detected at anode
Photocathode creates Secondary electrons
-1000V
PMT
APD
Both can work under Single-photon Countingmode
1,2,3: Alkali Photocathodes
4: GaAS Photocathode
Spectral Response and QE of PMTs
10-15% QE: probably optimisticweakest link on Confocal Scope
PMTs best in UVAlkali lousy in visible
Silicon Response for (Avalanche) Photodiodes
Avalanche Photodiodes: used sometimes in imaging1) 75% efficiency at 700-800 nm2) Better than PMTs in visible, near IR3) Very small areas ~200 microns: difficult to align in confocal4) 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 APD
0.001 e/sec/pixel 10-100 e/sec/pixelDark Counts
Temperature -70 C -20 C
Sensitive Area 10-20 m 100-500 m
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 sampleFor best S/N. used in commercial instruments
2) Counting (>1200V): detector in saturation:Every photon produced same voltage pulseIncreased sensitivity, but smaller rangePoisson statistics~ 1/n1/2
More complex, more expensiveNot used commercially
Photodiode
PMT: photomultiplier
APD: Avalanche Photodiode
CCD