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