1. 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

3. -σ12FN1 -σ21FN2 Stimulated Emission Rate: Absorption Rate:
Number of atoms or
molecules in lower
energy level (Unit: per cm3)
Number of atoms or
molecules in lower
energy level (Unit: per cm3)
-σ12FN1
-σ21FN2
Absorption
Cross-Section
Units → cm2
Photon Flux
Units → #/cm2sec
Stimulated emission
Cross-Section
Units → cm2
(typical value ~ 10-19
to cm2)
Photon Flux
Units → #/cm2sec

5. Einstein showed: σ12 = σ21 -σ12FN1 -σ21FN2 Stimulated Emission Rate:
Absorption Rate:
Number of atoms or
molecules in lower
energy level (Unit: per cm3)
Number of atoms or
molecules in lower
energy level (Unit: per cm3)
-σ12FN1
-σ21FN2
Absorption
Cross-Section
Units → cm2
Photon Flux
Units → #/cm2sec
Stimulated emission
Cross-Section
Units → cm2
(typical value ~ 10-19
to cm2)
Photon Flux
Units → #/cm2sec
Einstein showed:
σ12 = σ21

6. Population Inversion: is the condition for light amplification through stimulated emission.
Population inversion is not achievable through direct excitation in a two-level system.

7. Lasing begins as fluorescence
Lasing begins as fluorescence

8. 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)

9. = 0

10. 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

11. Gain Log(Iout/Iin) Absorption Pump Gain region No absorption
Below energy
gap
Loss region
Log(Iout/Iin)
Photon Energy
Absorption

12. So What Is LASER? Population inversion in lasing medium
cavity
Pump
output
Population inversion in lasing medium
Laser cavity to create the resonance amplification
Gain from the medium > loss in the optics of the cavity

13. 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

14. Each line allowed by the cavity is a longitude mode.
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: nm nm
Each line allowed by the cavity is a longitude mode.

15. Propagate ?
Cross-section

16. 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

17. Gaussian Beam Propagation
Near
Field
Far
Field
Beam
waist
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.

18. 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 = 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.

19. 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.

20. Embedded Gaussian A mixed-mode beam:
Has a waist M (not M2) times larger than the embedded Gaussian.
Will propagate with a divergence M times greater than the embedded Gaussian
Has the same curvature and Raleigh range.

21. 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.

22. Some Common Lasers To build a laser, you need Two Mirrors Gain Medium
Pump

23. Nd:YAG Four level laser
Host solid is single crystal YAG: yttrium aluminum garnet Y3Al5O12
Optically active atoms Nd. Only <1% of the Medium.
Useful for cw operation, becauseYAG has high thermal conductivity and can handle a lot of heat.
Also useful for pulsed operation

26. Ar Ion Laser One electron gets pulled off of one atom.
In the large field, the electron gets accelerated and impacts other atoms, knocking off other electrons.
A current of electrons is now flowing; the positive ions also cause a current.
Multiple electron collisions pump the Ar+, which emit light nm
Very inefficient. 0.03%

29. Semiconductor Laser
Mobile electrons
Mobile holes

30. A better band picture Many-state system Optical transition reserves k
Population inversion easily achievable k

31. P-N Junction N type P type Emission Hole Injection Electron Injection+ -
N type
P type

33. 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.

34. DPSS Laser

36. Common Continuous Wave (CW) Lasers for Microscopy
Argon UV (cw) 364 nm
Argon Vis 488, 514 nm (458, 477 nm)
Argon-Krypton 488, 568, 647 nm
He-Ne nm (laser pointer)
DPSS laser 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

37. Wide Field vs Confocal Fluorescence Imaging
Greatly reduces
Out of focus blur
Wide-field
Brighter but
No sectioning

38. More examples
widefield
confocal
pollen
medulla
muscle

39. 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

40. Out of Plane Rejection of Light
Pinhole aperture blocks
out-of focus light
Fewer photons collected than
Widefield fluorescence
only from plane in focus
Also losses from optical path
Worse S/N
But Better Resolution than
~30% lateral
Widefield does not have
Axial resolution

41. Confocal detection with 3 dimensional scanning
Image one plane,
Move focus

43. Confocal Aperture Limits:
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

44. Signal, S/N (out of focus) opposite trends
Signal, S/N (out of focus) opposite trends
Closed: better axial sectioning, but no photons for contrast
Open: no sectioning, lots of photons

47. 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

48. Intermediate Optical Path of Confocal Microscope
Requirements:
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:
Pupil transfer lens mm fl to fill lens
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

49. Scanning Galvanometers Much faster than stage scanning (1000x)
Point Scanning
Mirrors on magnets x y
Laser out To
Microscope
Laser in

50. Olympus Fluoview

51. Scan Time Issues t = 0 X = 512 t = 0 X = 128 Y = 512 Y = 128
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
t = 0
t = 0.25 sec
Y = 512
t = 1 sec

52. Scan Time Issues Two scan types: 1. 2. 2)Unidirectional:flyback
1) Bidirectional:
Resonant galvos, Very fast
Require post imaging
Processing, cannot change
Speed for zoom 2.
2)Unidirectional:flyback
Normal for galvo scanners:
Have hysteresis, settling time:
30% duty cycle

53. Digital Zoom: Reducing scan angle, higher pixel density per area
Not equivalent to changing objective lens magnification
1 x
1024 points
2 x
1024 points
4 x
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

54. Confocal Parameters and Intensity, Resolution

55. Point Scan Detection: Photomultiplier (PMT)
Photocathode creates Secondary electrons
-1000V
Usually dynodes in practice
Gain ~105-7 detected at anode

56. PMT APD Both can work under Single-photon Counting mode
Both can work under
Single-photon Counting
mode

57. 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

58. Silicon Response for (Avalanche) Photodiodes
Avalanche Photodiodes: used sometimes in imaging
75% efficiency at nm
Better than PMTs in visible, near IR
Very small areas ~200 microns: difficult to align in confocal
Low max count rates (small dynamic range)

59. Efficiency & Signal/Noise?
Collection efficiency of microscopy: ~25%
Detector quantum yield: ~70-90%
Thermal noise
Shot noise (quantum noise):
Read noise (A/D conversion)
V^2 = 4kTR

60. Typical Dark Counts CCD APD Temperature -70 C -20 C Sensitive Area
0.001 e/sec/pixel
e/sec/pixel

61. Gain of PMTs with Applied Voltage
2 Modes:
Analog Detection
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

62. Photodiode
PMT: photomultiplier
CCD
APD: Avalanche Photodiode