1. Laser Pulse Generation and Ultrafast Pump-Probe Experiments
By Brian Alberding

2. Goals Basic Laser Principles Techniques for generating pulses
Pulse Lengthening
Pulse Shortening
Ultrafast Experiments
Transient Absorption Spectroscopy

3. L.A.S.E.R Light Amplification by Stimulated Emission of Radiation
CHECK QUANTUM BOOK FOR DEFINITION OF STIMULATED EMISSION
Stimulated emission is the process by which a photon, with frequency equal to a transition in an atom or molecules, interacts with that atom or molecule in its excited state, causing the emission of radiation that corresponds to the transition frequency. The result is two photons that share the same frequency, phase, and direction of propogation.
“Ordinary” – broad frequency range, direction of propogation.
Coherent Light: Light waves with the same frequency and phase, such that they constructively interfere.
Temporal coherence: Two waves in phase at one moment, still in phase at another moment in time. They will be if there frequencies match.
Spatial Coherence: Distance by which waves can be separated and still interfere with one another.

4. Basic Laser Light Sources Gain medium Mirrors I I0 I1 I3 I2 R = 100%
Laser medium I
Light Sources: Pump atom or molecule into excited state. Cause an initial stimulated emission event.
Gain Media: material responsible for storing energy from the source, and emittng that energy as a photon with a frequency corresponding to the laser transition
Mirrors:
Allow further amplification by trapping laser photons in the gain media and stimulating additional excited states to emit. The lower reflectivity mirror allows a constant fraction of the laser photons to escape, while keeping other laser photons in the medium to cause further stimulated emission.
Mirrors also provide a narrowly focused beam. Only photons traveling perpendicular to the mirror surface will be able to be reflected by both mirrors.
R. Trebino

5. Laser Cavity
Lower reflectivity mirror allows only some of the laser beam to escape, while the intensity of the laser beam in the cavity continues to build. Eventually an equilibrium state is reached within the cavity and the emerging laser beam has a constant intensity equivalent to that inside the cavity.
Refer to the beam building up in the cavity as the “laser beam”.

6. Gain Medium Einstein Coefficients AN2 = rate of Spontaneous emission
BN2I = rate of Stimulated emission
There are three processes by which the gain medium can interact with radiation.
Relative populations of the states in the gain medium depend on the rates at which energy is absorbed and emitted.
Stimulated emission must be greater than the total of stimulated absorption and scattering and reflection processes in order to get a gain in the initial intensity of the desired laser beam. E1
E = hν E2
BN1I = rate of Stimulated absorption E1

7. To achieve lasing:
Stimulated emission must occur at a maximum (Gain > Loss)
Loss:
Stimulated Absorption
Scattering, Reflections
Energy level structure must allow for Population Inversion
Population inversion is a property of the collection of molecules as a whole that make up the gain medium. If there are more molecules within the population that are in the excited state, the laser photon is more likely to find an excited molecule and stimulate emission than it is likely to find a ground state molecule and stimulate absorption. E2 E1

8. Obtaining Population Inversion
2-level system
3-level system
4-level system
Fast decay
Laser Transition
Pump Transition 1 2 3
Laser Transition
Pump Transition
Fast decay 1 2 3 2 1 N2 N1
Laser
Only when there is population inversion will the rate of stimulated emission exceed the rate of stimulated absorption. (If a resonant photon encounters an excited molecule either stimulated absorption of emission must occur).
If level 3 has fast decay compared to level 2, the population of level 3 will be nearly zero and the population of level 2 will be increasing until a laser transition occurs. Likewise, if level 1 has fast decay, the population will decrease before another laser transition can occur to repopulate it. In short, the upper level is constantly being filled and the lower level is constantly being depleted. Population inversion occurs because the lifetime of the laser transition is greater than the decay rates for level 1 and 3.
2 level system: delta N is always positive
3 level system: delta N is negative with a high enough intensity
4 level system: ΔN is always negative.
Equations obtained by considering the rate equations for the population of each of the levels involved in the given system. N is the total number of states involved in the system and is therefore a constant. Also, Since N1 and N3 exhibit fast decay, there population is essentially constant. Set rate equation equal to zero, solve for ΔN and substitute I(sat).
I(sat) is the intensity required to place the maximum amount of molecules in their excited states.
Population Inversion is obtained for ΔN < 0 (ΔN = N1 – N2)

9. Summary – Basic Laser Source light Reflective Mirrors (cavity)
Gain Media
Energy Level Structure
Population Inversion
Pumping Rate ≥ Upper laser State Lifetime
Upper laser State Lifetime > Cavity Buildup time
Laser Transition
Pump Transition
Fast decay 1 2 3
A source is required to pump the gain media into the excited state. The cavity traps the initial laser allowing it further interaction with the gain media to amplify the signal. The gain media must exhibit an energy level structure such that the upper laser level is populated quickly after absorption and the lower laser level is depopulated quickly after emission. Population Inversion is further enhanced by adjusting the pumping rate compared to the excited state lifetime and the cavity buildup time (the time required for the cavity to maximize excited state population). The pumping rate should be greater than the excited state lifetime so that additional excited states are created before the initial excited states decay. The upper laser state lifetime should be greater than the cavity buildup time so that the cavity will store energy while waiting to be pumped.
Silvfast, pg. 440.

10. Types of Lasers
Solid-state lasers have lasing material distributed in a solid matrix (such as ruby or neodymium:yttrium-aluminum garnet "YAG"). Flash lamps are the most common power source. The Nd:YAG laser emits infrared light at nm.
Semiconductor lasers, sometimes called diode lasers, are pn junctions. Current is the pump source. Applications: laser printers or CD players.
Dye lasers use complex organic dyes, such as rhodamine 6G, in liquid solution or suspension as lasing media. They are tunable over a broad range of wavelengths.
Gas lasers are pumped by current. Helium-Neon lases in the visible and IR. Argon lases in the visible and UV. CO2 lasers emit light in the far-infrared (10.6 mm), and are used for cutting hard materials.
Excimer lasers (from the terms excited and dimers) use reactive gases, such as chlorine and fluorine, mixed with inert gases such as argon, krypton, or xenon. When electrically stimulated, a pseudo molecule (dimer) is produced. Excimers lase in the UV.
R. Trebino

11. Quality of laser beams Uncertainty Principle: Δt Δν ≥ 1/4π
Irradiance vs. time
Spectrum
Long pulse
time
frequency
Ultrafast spectroscopy desires a short pulse. The pulse must be short enough so that it can interact with the system before the state of the system has changed.
Example: Transient absorption spectroscopy. If you want to measure the absorbance of a molecule in its excited state, you must expose that molecule to a laser pulse before the excited state dissipates its energy. (ns lifetime requires a pulse shorter than a nanosecond)
Short pulse
time
frequency

12. Generating Pulses Q-switching Mode-Locking Pulse Shortening
Passive
Active
Pulse Shortening
Group Velocity Dispersion
Pulse Lengthening - Chirp
Since ultrafast spectroscopy requires a pulse, I will explain some methods by which laser pulses are generated. Also, pulse lengthening and shortening can occur when dealing with laser pulses. Sometimes these properties are taking advantage of and produced on purpose where as other times they occur unwanted and must be corrected.

13. Q-Switching
Alternate presence of oscillating laser beam within the cavity
Methods
Rotating mirror
Saturable Absorber
Electro-optic shutter
Pockels Cell
Kerr Cell
Nanosecond timescales
100% 0%
Time
Cavity Loss
Cavity Gain
Output intensity
When “laser beam” is not present, the upper level population grows as the medium is pumped, switch on the laser beam by introducing a mirror on both sides of the cavity and allowing the beam to oscillate in the “cavity” and increase in intensity. Removing the cavity mirror then reduces the intensity of the laser beam, by not allowing the beam to cause further stimulated emission, creating the pulse.
Rotating mirror is mechanically difficult. Requires fast speeds and causes vibrations
Saturable absorber: High absorptivity at the laser frequency. Once the absorber is saturated, the laser beam will pass through the absorber and oscillate in the cavity.
Electo-optic shutter: Employs a crystal that will rotate polarization of a beam when a voltage is applied. A special window (Brewster’s angle window) surrounding the gain medium is used to block entrance of the polarized beam.
R. Trebino

14. Mode-Locking Technique Types Shutter between mirror and gain medium
Shutter open: All modes gain at same time
Types
Active
Passive
Silvfast, pg 451.
The idea of mode locking is to control when the laser beam has access to the cavity so that it can reach its maximum gain. This is achieved by placing a shutter in between one of the mirrors and the laser cavity. When the shutter is closed, the beam is blocked and the gain medium stores energy in the upper lasing level. When the shutter is open, the laser beam traverses the cavity and experiences gain. This is true for all of the modes present in the laser cavity. Therefore, at the instant the shutter is opened, all of the modes have there maximum amplitude at the same time. They are in phase at that moment in time. At other times, the modes are not in phase and destructively interphere. The Result is a short pulse.
R. Trebino

15. Intra-cavity pulse compression
Mode-Locking Methods
Active – Mechanical Shutters
Acousto-Optic Switches (low gain lasers)
Synchronous Pumping
Passive
Colliding Pulse
Additive Pulse
Kerr Lens
'65
'70
'75
'80
'85
'90
'95 10
100
1000
Shortest Pulse Duration (fs)
Year
Active mode locking
Passive mode locking
Colliding pulse mode locking
Intra-cavity pulse compression
Ti-Sapphire
Just tell them the different types of methods and talk about the figure.
Acousto-optic switch: RF signal produces an acoustic wave inside the crystal that produces loss within the crystal. It represents a closed shutter when the RF signal is applied.
Colliding Pulse: Two pulses moving in opposite direction collide within a saturable absorber

16. Pulse Lengthening and Shortening
Group Velocity Dispersion – The velocity of different frequencies of light is different within a medium.
Pulse Lengthening:
Ultrashort Pulse
Any Medium
Chirped Pulse
Pulse Shortening:
When a pulse travels through a medium it lengthens in time because of the dependence of the index of refraction on the frequency of radiation moving through the medium.
By using a prism, in the correct orientation, the leading edges of the chirped pulse can be slowed down by forcing them to move in a medium with a higher index of refraction for a longer period of time. Likewise, the trailing edges of the pulse are required to move through less glass and therefore, catch up to the leading edge. The result is a pulse that is shortened in time.
Prism: Angle of incidence and the relative refractive indices of the two media (say, air and glass), determine by how much the light is refracted.
The longer wavelengths traverse more glass.

17. Pump-Probe Experiment
Delay
Slow
detector
Excite pulse
Sample
Lens
Probe pulse
Change in probe pulse energy
The excite pulse changes the sample absorption seen by the probe pulse.
R. Trebino

18. White-Light Generation
n(ν) = n0(ν) + n2(ν)I(ν)
Generally, small-scale self-focusing occurs, causing the beam to breakup into filaments.
The total index of refraction of a material consists of multiple terms, where the second term is dependent on the intensity of the light pulse traveling through the material. The larger the intensity, the more important the second term becomes. For a laser pulse, the intensity is largest at the transition frequency and decreases on either side. The effect is that as the leading edge of the pulse arrives at the medium, the index of refraction increases, causing the frequency and the speed of the pulse to decrease. As the trailing edge of the pulse arrives, the intensity decreases and the index of refraction decreases, causing the frequency and the speed of the trailing edge to increase. The net result is a pulse with a wider range of frequencies but about the same timescale. The significance of using water is that it will not absorb the frequencies that are being produced.
See “self phase modulation (sect silvfast)”, “cross phase modulation”, and “optical kerr effect”
R. Trebino

19. Types of Experiments Transient Absorption Fluorescence Upconversion
Time Resolved IR
Transient Coherent Raman and Anti-Stokes Raman
Transient photo-electron spectroscopy
Fluorescence Upconversion – Watch fluorescence decay as a function of time. Upconversion refers to enhancing the signal to be measured.
Time-Resolved IR: Can get a picture of the geometry and structure in the excited state
Photo-electron: Look at processes involved in ionized states.

20. Transient Absorption – Model System
Vibrational Relaxation (VR), Intersystem Crossing (ISC), and Internal Conversion (IC)
Aspects of VR
Pump wavelength dependence
Density of states
Probe wavelength dependence
Franck-Condon Factors
Full-spectrum, Kinetic trace
Needed Information
Steady State absorption and emission
geometry
Electron configuration
Pump Photons create the excited state in a given vibrational state. Probe photons are absorbed by the excited state. The difference in intensity between the incident and transmitted probe photons gives the measured signal. The transmitted intensity changes as the excited state population in the S1 state decays. Possible decay processes.
Changing Pump Wavelength places the S1 state in a different vibrational level. Higher in the vibrational manifold, there is a higher density of states due to anharmonicity. Increases the Franck-Condon overlap and facilitates vibrational decay.
Probe Wavelength: Higher vibrational states have a wider range of absorptions available due to greater franck-condon overlap with a larger number of vibrational states in the upper level. There are many more nodes in the highly excited vibrational wavefunction and more amplitude over the nuclear coordinate.
Reference: Cr(acac) paper.

21. James McCusker (MSU): Transition Metal Complexes
Cr(acac)3: ~Oh, d3 complex
Ligand field and charge transfer states
Ligand Field Emission
MLCT
Ground State: 4A2
Molar Absorptivity (M-1cm-1 x 103)
Ligand Field Abs
Photoluminescence Intensity (au)
Excited States:
2E, 4T2
2LMCT, 4LMCT
Wavelength (nm)

22. Ligand Field Transient Absorption
Cr(acac)3
Ligand Field Transient Absorption
100 fs excitation at 625 nm
Kinetic Data
Full Spectrum Data
The figure on the left shows the single wavelength trace for the absorption of the excited state at 480 nm following excitation at 625 nm (within the 4T2 absorption band). The data is fit to a monoexponential, indicating that a single decay process occurs. The subsequent dynamics occur with a time constant of 1.09 ps.
In order to better identify they state(s) involved in the decay process, a full spectrum for the excited state absorption at a time of 5 ps was included, after the dynamics of the first figure had been completed (red data points). For comparison, transient absorption data at 90 K was also taken. At 90 K, there would be little thermal excitation, so the state absorbing after 5 ps is doing so from its lowest vibrational state. Since there is agreement between the two curves, the offset shown in the left figure must correspond to absorptions from the lowest vibrational state in the excited state.
480 nm probe
τ = 1.09 ± 0.06 ps
Red is single wavelength data at Δt = 5 ps
Blue is nanosecond data at 90 K
Long Lived = 2E state

23. Cr(acac)3 Ligand Field Transient Absorption
100 fs excitation at 625 nm
Characteristic of Vibrational Relaxation
Pump Wavelength Dependence
C1 = initial Abs amplitude
a0 = Long time offset

24. Cr(acac)3
Jablonski Diagram

25. FeII polypyridyl complexes
Time scale of ΔS ≠ 0 transitions
[Fe(tren(6-R-py)3)]2+
d6 complex, ~ Oh geometry
R = H: Low Spin, 1A1 ground state
R = CH3: High Spin, 5T2 ground state
Reference: Coordination chemistry reviews
tren(py) = tris(2-pyridylmethyliminoethyl)amine

26. [Fe(tren(6-R-py)3)]2+ Complexes – Steady State Absorption
R = H
R = CH3: similar to [Fe(tren(6-H-py)3)] ground state
Calculated Difference = Middle – Top ( )
Nanosecond Data (dotted line)
Provides template for 5T2 excited state in low spin complex

27. [Fe(tren(6-H-py)3)]2+ ~100 fs excitation at 400 nm LMCT excitation
fs timescale decay
Bleach at long times
R = CH3 (5T2): No Abs at 620 nm
R = H (1A1): Abs at 620 nm
620 nm Probe
τ1 = 80 ± 20 fs, τ2 = 8 ± 3 ps
ps timescale decay is Vibrational Relaxation

28. Calculated difference of R = CH3/R = H (red line)
[Fe(tren(6-H-py)3)]2+
~100 fs excitation at 400 nm
5T2 state is populated in 700 fs
Other excited states decay faster than time resolution
Vibrational Relaxation occurs on ps timescale
ΔT = 700 fs (black line)
ΔT = 6 ps (blue line)
Calculated difference of R = CH3/R = H (red line)

29. Dynamics in Transition Metal Complexes
Relative Rates of VR, ISC, and IC can vary depending on the system
kISC > kVR
Fast spin forbidden transitions
ΔS = 1, ΔS = 2; Spin Orbit Coupling

30. Other Work and Applications
Transition Metal Complexes
Ligand Field States contribute to photosubstitution and photoisomerization processes
Electron transfer processes and photovoltaics
Dr. Bern Kohler: DNA photodamage, skin cancer

31. References
Stimulated Emission:
Laser Cavity:
Silvfast, Laser Fundamentals, 2nd ed., Cambridge University Press, pg
J. Am. Chem. Soc., 2005, 127,
J. Am. Chem. Soc., 2000, 122,
Coordination Chemistry Reviews, 250 (2006),
Nature, 436, 25, 2006,
Rick Trebino, Georgia Tech University, Optics 1 “Lasers”, Ultrafast Optics “Introduction”, Ultrafast Optics “Pulse Generation”, Ultrafast Optics “Ultrafast Spectroscopy”

32. A dye’s energy levels
Dyes are big molecules, and they have complex energy level structure.
S2: 2nd excited
electronic state
Lowest vibrational and rotational level of this electronic “manifold”
Energy
S1: 1st excited
electronic state
Excited vibrational and rotational level
Pump Transition
Laser Transition
Dyes can lase into any (or all!) of the vibrational/ rotational levels of the S0 state, and so can lase very broadband.
S0: Ground
electronic state

33. Saturable Absorber Intensity Short time (fs) Round trips (k)
Weak pulses suppressed because they are absorbed. Strong pulsed pass through.
Notice that the weak pulses are suppressed, and the strong pulse shortens and is amplified.
After many round trips, even a slightly saturable absorber can yield a very short pulse.
R. Trebino

34. Absorption spectra following oxidation and reduction

35. Jablonski Diagram [Fe(tren(6-H-py)3)]2+