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: -σ 12 FN 1 Absorption Cross-Section Units → cm2 Photon Flux Units → #/cm 2 sec Number of atoms or molecules in lower energy level (Unit: per cm 3 ) Stimulated Emission Rate: -σ 21 FN 2 Stimulated emission Cross-Section Units → cm2 (typical value ~ to cm 2 ) Photon Flux Units → #/cm 2 sec Number of atoms or molecules in lower energy level (Unit: per cm 3 )

Einstein showed: σ 12 = σ 21 Absorption Rate: -σ 12 FN 1 Absorption Cross-Section Units → cm2 Photon Flux Units → #/cm 2 sec Number of atoms or molecules in lower energy level (Unit: per cm 3 ) Stimulated Emission Rate: -σ 21 FN 2 Stimulated emission Cross-Section Units → cm2 (typical value ~ to cm 2 ) Photon Flux Units → #/cm 2 sec Number of atoms or molecules in lower energy level (Unit: per cm 3 )

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

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/  /  20 2→(anything) Need at least a three-level system

= 0

Four Level System is Most Common for Lasing E 3 -E 2 radiationless decay E 2 -E 1 spontaneous lifetime of E 2 -E 1 stimulated emission of E 1 -E 0 radiationless decay

0 Log(I out /I in ) Gain Absorption Photon Energy No absorption Below 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=  / = / 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 Each line allowed by the cavity is a longitude mode. Lines adjacent to the 500nm line are very close: nm 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 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. R -> z if z >> 0 At which point Gaussian beam looks like a point source. w = w0 if z <<  w 0 2 /  z R If = 500nm w0 = 2mm z R = m z R 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: M 2 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 M 2 ~1.05. Most lasers does not have such ideal beam.

Embedded Gaussian A mixed-mode beam: 1.Has a waist M (not M 2 ) 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 nm 5.Very inefficient. 0.03%

Semiconductor Laser Mobile electronsMobile 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 typeP type Electron Injection Hole Injection 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 nm Argon Vis488, 514 nm (458, 477 nm) Argon-Krypton488, 568, 647 nm He-Ne633 nm (laser pointer) DPSS laser532 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 reduces Out of focus blur Brighter but No sectioning

More examples medullamuscle pollen widefield confocal

Epi-illumination widefield is form of Kohler Illumination: Objective is also condenser Lamp or laser detector Detect at 90 degrees Split with dichroic mirror lens

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 sub- resolution 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 well- corrected 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 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) x y Laser in Laser out Point Scanning To Microscope Mirrors on magnets

Olympus Fluoview

Scan Time Issues Typical scan rate 1s /scan 512X 512 Faster 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: ) 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 1 x 1024 points 2 x 1024 points 4 x 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) Usually dynodes in practice Gain ~ detected at anode Photocathode creates Secondary electrons -1000V

PMT APD Both can work under Single-photon Counting mode

1,2,3: Alkali Photocathodes 4: GaAS Photocathode Spectral Response and QE of PMTs 10-15% QE: probably optimistic weakest link on Confocal Scope PMTs best in UV Alkali lousy in visible

Silicon Response for (Avalanche) Photodiodes Avalanche Photodiodes: used sometimes in imaging 1)75% efficiency at 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 APD e/sec/pixel e/sec/pixel Dark Counts Temperature -70  C -20  C Sensitive Area  m  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 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/n 1/2 More complex, more expensive Not used commercially

Photodiode PMT: photomultiplier APD: Avalanche Photodiode CCD