1
Q
FWHM of homogenous lineshape
A
1/t_1 + 1/t_2
2
Q
Most important broadening in a gas laser
A
Doppler broadening
3
Q
Important environmental aspects of doped solid state laser (3)
A
- Strain of the crystal latice - affects local electric field so alters Stark effect
- Presence of impurity ions
- Variations in the orientation of the crystal lattice
4
Q
2 differneces between homogenous and inhomogenous broadening
A
- For a specific frequncy, all atoms in a homogenously broadened laser will interact with the same strenght; for an inhomogenous laser the strength will be different for different ions.
- The central frequency of the spectrum is independent of frequncy in an homogenous laser but dependent on frequency in an inhomogenous laser
5
Q
Population inversion density =
A
N* = N2-g2/g1 N1
6
Q
Gain saturation =
A
where the optical gain depends on the intesnsity of the radiation interacting with the gain medium
7
Q
Rate equations for upper and lower levels
A
8
Q
How is a spectral hole formed?
A
In an inhomogenously broadened laser the degree of saturation will be different for different class of atoms ie will be different for atoms with differnt central frequencies. For those classes where saturation occurs the population inversion will be burnt down.
9
Q
What is the frequency differnce between two adjacent longitudianl modes?
A
w(p) - w(p-1) = pi c / L
10
Q
How is a spatial hole formed?
A
At the anti-nodes of a longitudinal mode the population inversion will be burnt down whilst at the nodes the intensity is low so N* will be unsaturated. In regions where the population inversion is unsaturated other modes can feed off the inversion causing multimode oscilation.
11
Q
Why do inhomogenous lasers exhibit multimode oscialltion?
A
Different classes of atoms interact with different modes.
12
Q
Sketch how pumping power affects output power and gain for homogenous and inhomogenous lasers
A
13
Q
Advantages of solid state lasers (3)
A
- Robust
- Chemically inert
- Don’t degrade or become contaminated with use
14
Q
Explain the Stark effect
A
The crystal field adds an extra term to the Hamiltonian
H_c = -e V_crystal
This splits the energy levels
15
Q
Causes of broadening in crystals (3)
A
- Temperature dependent lifetime broadening - lines are broadened due to non-radiative phonon transitions
- Two phonon Raman scattering
- Vibronic transitions - photon emission can be accomponied by phonon emission or absorbtion
16
Q
Uses of Nd:YAG laser (4)
A
- Pump laser
- Removing secondary cateracts
- Laser drilling
- Laser welding
17
Q
What kind of a laser is an Nd:YAG
A
4 level
18
Q
How is gain calculated when multiple transitions contribute to gain eg in an Nd:YAG laser?
A
Calculate a weighted effective gain cross section
19
Q
Benfits of an Nd:Glass lasder
A
Line broadening is homogeneous
Gain cross section is small so a large population inversion can be achived. This means laser pulses can be amplified to large energies
20
Q
Uses of an Erbium glass laser (4)
A
- Optical communication
- Medicine
- Telemetry
- Laser ranging
21
Q
Why is broadening complex in an erbium laser?
A
There are 56 possible transitions
22
Q
How many levels does and erbium laser have?
A
At long wavelengths - 4 level behaviour as positive gain is achieved for low levels of pumping
At short wavelengths - 3 level as positive gain only achieved for high pump intensity
23
Q
What is the configuration coordinate Q
A
The average separation of active and neighbouring ions
24
Q
How and why does Stoke’s shift depend on Q
A
Stokes shift is larger when there is a larger difference in Q for the upper and lower levels
25
Describe the Stoke's shift of a Ti:saphire laser
Large stokes shift due to large difference in Q for upper and lower levels
26
Why is laser pumping required in a Ti:Saphire laser?
Becuase the upper level has a short fluroescence lifetime
27
Desirable properties of solid state host materials
1. Hard so can be polished
2. High themal conductivity so heat removed fast
3. Easy to grow sufficiently large high quality crystal
4. Low thermal lensing
5. Low thermally induced biregringence
28
Advantages (3) and disadvantages (2) of crystal hosts
advantages
* high thermal conductivity
* homogenous broadening
* narrow line width for non-vibronic transitions
distadvantages
* often birefingent so polarisation sensitive
* can be difficult to grow
29
Advantages (4) and disadvantages (2) of glass hosts
Advantages
1. Can be cast in many forms
2. cheap
3. low birefringence
4. easy to adjust composition
Disadvantages
1. low thermal conductivity
2. inhomogenous broadening so low gain x section
30
What is laser spiking?
Sharp peaks when a laser is first swtiched on. Spikes are irregularly spaced.
31
What are relaxation oscillations?
Regularly spaced oscillations with exponentially decaying amplitude. Caused by perturbation to laser system.
32
How do laser spikes occur?
1. After the laser is switched on the pupulation of the upper level will grow in a time ~t\_2. Photon density in the cavity is low becasue only spontaneous emission occurs.
2. At some point N\* reaches the threshold value. However, lasing won't occur because photon density is low.
3. Eventually the photon density becomes sufficiently high that a spike occurs. N\* will be burnt down.
4. N\* is burnt below the threshold value which means lasing will stop.
5. repeat
33
Why does laser spiking stop?
Each time N\* is burnt below the threshold value its minimum point approaches the threshold value.
34
Why is spiking associated with jumps in mode?
Whichever mode oscilalles during the spike will only burn down population at its antinodes. The population left at the nodes can be fed off of by other modes which may then reach threshold first.
35
When does spiking occur
When the cavity lifetime (time on which photon density changes) is much shorter than the lifetime of the upper level (time on which laser responds to pumping).
36
Rate equation for photon density
37
Give an expression for the threshold population inversiton
38
Derive the cavity lifetime
39
What value of m means relaxation oscillations occur?
complex m
40
What is r
r = R t\_2/ N\*\_th
Overpumping ratio - the ratio of N\* in the absence of radiation to the threshold value
41
What is the point of Q switching?
Generating high peak power pulses
42
How does Q switching work?
1. The cavity is deliberately spoiled (ie by covering one mirror). Since the losses are high N\* becomes high without lasing occuring.
2. Once N\* is sufficiently high the cavity is unspoiled. This switches Q to a higher value.
3. Stimulated emission is high so N\* is rapidly burnt below its threshold value.
43
How can larger population inversion in Q switching be achieved?
By using pulsed pumping
44
How does a rotating mirror achieve q-switching?
Mirror is rotated by motor. A roof prism means the mirror will work at any angle where it is facing the radiation
45
Advantages (2) and disadvantages (2) of q-switching using a rotating mirror
A:
1. Easy to implement
2. Works with vibration
D:
1. Switching is slow
2. Timing is uncertain
46
How does electro-optic switching achieve q switching?
Q is low when a voltage is applied to the pockels cell. A polariser is placed before the pockels cell
If vertical light is incident on the pockel's cell, it will gain circular polarisation. After being reflected by a mirror the handedness of the polarisation will have changed. Upon passing through the pockels cell the light will have horizontal polarisation, and will thus be rejected by the polariser.
47
Advantages (2) and disadvantages (2) of electro-optic switching
A:
* Fast
* High hold-off ratio - means populatyion inversion can be many times the treshold value
D:
* Several instruments must be inserted into cavity - expensive
* Devices are expensive
48
How does acousto optic switching achieve Q-switching?
To reduce Q, RF radiation is applied to the crystal. This makes an accoustic wave propagate in the crystal, which varies its refractive index periodically. Some of the energy will be Brag reflected away from the optical axis, and thus be lost.
49
Advantages (2) and disadvantages (2) of acousto-optic switching
A:
* Cheap
* Insertion losses can be reduced by orienting the crystal at Brewster's angle
D:
* Slow
* Low hold-off ratio
50
How do satruable abosrbers achieve Q switching?
1. During the pump pulse the absorber prevents lasing by introducing a large loss
2. Once N\* reaches a high value there will be a high photon flux and the absorber will saturate.
3. At full saturation there will be zero loss and a large pulse will develop.
51
Advantages (2) and disadvantages (2) of using a saturable absorber for q-switching
A:
* Cheap
* Simple - no external driving
D:
* High uncertainity in energy and timing of pulse
* Absorber degrades over time
52
Assumptions involved in deriving q switching behaviour
Ignore pumping during pulse development
Ignore spontaneous emission
We have a four level laser
53
Modelocking =
where all longitudinal modes of a laser cavity have the same phase. These modes interfere constructively, generating a train of short pulses.
54
carrier envelope offset =
the phase of the carrier wave at the peak of the envelope wave
55
Difference between active and passive modelocking =
active - there's an external signal which introduces modulation
passive - involves placing some element into the cavity which introduces self modulation
56
How does AM modelocking work?
Adds frequncy sidebands at p +/-1. A steady state is reached when this balances with the finite bandwidth over which gain can be achieved.
The frequency of the shutter must be the same as the mode spacing
57
How does FM modelocking work?
Modulate the refractive index of the cavity at frequency delta omega. This introduces sidebands given by a Bessel function.
58
How can FM modelocking be implemented?
Using a pockels cell with its axis parallel to the angle of polarisation.
59
How can modulating the gain be used to implement mode locking?
Modulate at delta omega to introduce sidebands like in AM modelocking.
In a dye laser modulate the pumping, in a semiconductor laser modulate the driving current.
60
How can modelocking be achieved using a saturable absorber?
When intensity is below saturation intensity absorbtion is high; when intensity is above saturation intensity absorbtion is low.
61
How can modelocking be acheived using a Ker lens?
A Kerr lens has a refractive index linear with intensity. When a Gaussian beam is incident on a Kerr lens the refractive index is greatest closer to the centre of the beam so the beam will be focused. Lower intensity beams will be focussed less. Therefore, introducing an aperture will prevent low intensity beams propagating in the cavity.
62
group velocity
dw/dk
63
phase velocity
w/k
64
What is group delay?
dphi/dw evaluated at w\_o. Gives the time for the group to propagate between two planes.
65
What is group delay dispersion?
d^2phi/dw^2 - describes the distortion of the pulse. If positive, high frequency componets travel more slowly.
66
Effect of positive dispersion
A positive frequency chirp - frequency increases as it passes observer.
Longer pulse.
67
Time bandwidth product of Gaussian pulse
4 ln2 sqrt(1+(b/a)^2)
68
What is a B integral
The non linear phase picked up by propagating in a non linear material
69
Why does frequency vary within a pulse propagating in a non linear material?
Intensity is not constant with time. Therefore, the B intergral varies non linearly with time. This means the instantaneous frequency dphi/dt is not constant. This is called self phase modulation
70
How can dispersion be controlled?
By introducing controlled, geometric dispersion. Generall need to add negative dispersion.
71
When is dispersion control most important?
For wide bandwidth ie short pulse
72
How can negative dispersion be introduced geometrically?
Using refraction
73
How is a grating pair used to introduce negative dispersion?
74
How can a prism pair be used to introduce negative dispersion?
75
How can chriped mirrors be used to introduce dispersion?
A chirped mirror is comprised of a stack of materials with alternating high and low refractive index and varying thickness. Different wavelengths will be reflected more strongly at different depths. Positive and negative dispersion can be introduced.
76
Why are very high power TW and PW lasers hard to acheive?
THey tend to self focus and destroy optical conponents. This means large diameter optical components are required which is expensive.
77
How is chirped pulse amplification achieved?
1. The pilses are stretched in time by introducing a large positive GDD.
2. The stretched pulses are then amplified.
3. The pulses are then compressed and negative GDD is introduced.
78
What is a regenerative amplifier?
An ampliefier where a pulse completes multiple round tripes through the gain medium due to the presence of a pockels cell and polariser. The exact number of round trips is determined by the voltage applied to the pockels cell.
79
As (1) and Ds (2) of regenerative amplifier
A:
1. Cavity imposes good transverse mode structure so the beam is high quality.
D:
1. Leakage through polarsiers can cause a train of low energy pre pulses
2. Long path lenght through material
80
What is a multipass amplifier?
An amplifier where the pulse is sent of multiple round trips by reflection from mirrors
81
As (2) and ds (1) of multipass amplifier
A:
* High single passs gain
* Less material in path
D:
* Poor overlap between pump and pulse means low efficiency.
82
Applications of ultrafast lasers (6)
1. Driving table top x-ray lasers
2. Plasma accelerators
3. Laser driven fusiton
4. Generating ultra intense B fields
5. Genration of intense, short pulse proton or ion beams
6. 'Laboratory astrophysics'
83
Derive the joint density of states
84
Derrive the density of possible transitions in terms of the proabilities of each level being occupied
85
Derive the small signal gain coefficient for a semiconductor laser
86
What are quasi fermi levels?
As n-type doping is increased, the fermi energy moves towards the conduction band from the centre of the energy gap (and vice versa for p-type doping). Analagous to N\*
87
Derive the condition for gain in a semiconductor laser
88
What is injection density?
The electrons per volume moved from the valence to conduction band
89
When is the threshold for gain met in a semiconductor laser?
When the sum of the conduction and valence Fermi energies is positive
90
Sketch and explain the populations in a homojunction diode laser
a) When the sections are brought into contact electrons will flow n to p. This generates an electric field, as well as a region where there are no charge carriers (depletion zone)
b) This field increases the potential energy of electrons in the p type material and lowers it in the n type material.
c) A forwared biased voltage is applied. This means there are electrons in the conduction band and holes in the valence.
91
What is the main problem with homojunction diode lasers?
The forward bias means electrons diffuse into the p-type material, increasing the thickness of the active region. This means a large current and thus cryogenic temperature is required.
92
Sketch populations in double heterostructure laser
93
3 reasons why threshold current is reduced for double heterostructure laser
1. Photon confinement - active layer is surrounded by area with low refractive index so acts like a waveguide
2. Carrier confinement - active layer is surrounded by area with large band gaps
3. Reduced absorbtion - large band gap in surrounding medium means laser light unlikely to be absorbed.
94
Properties of cladding layers in double heterostructure lasers (3)
1. Larger band gap than intrinsic layer
2. Easy to grow on active region - must have similar lattice constant
3. Lower RI than intrisic
95
Example materials in double heterostructure laser
GaAd - intrinsic
AlGaAs - cladding
96
What is slope efficiency?
dPout/dPin
97
Why is output power low in a diode laser?
Overheating
98
How can larger power diode lasers be created
Stacking - into bars or arrays
99
Describe the frequency spectrum of a diode laser
Depends on driving current
At threshold very large bandwidth but as current is increased a dominant mode becomes established
100
How can one mode be selected in a diode laser?
Using a fibre Bragg grating. A fibe core with a periodically varying RI means only waves satisfying the Bragg condition are effectively coupled back into the gain region.
101
What is a fibre laser?
A semiconductor laser wher teh active ion is doped into the core fo an optical fibre. Pumped by radiation propagating through fibre.
102
Advantages of fibre lasers over rod or disk geometries (6)
1. Low pump power threshold - inversion density requires an intensity but since area is small the power required is low.
2. Radiation from pump beam is naturally guided by fibre
3. High efficiciency - good overlap between pump and laser radiation.
4. Good thermal management - high SA to V ratio
5. Compact gain medium - can be coiled
6. Robust
103
Disadvantages of fibre lasers (2)
1. Small gain volume - can't reach high energies
2. Long length associated with scattering
104
Describe cladding pumping and its main advantage
Allows greater pump powers - when pump is enclosed in core in mus tbe close to diffraction limited.
105
What is the requirement for single mode oscillation by limiting cavity lenght?
range of oscillation frequencies \< mode spacing = c/2L
106
Conditions for single mode oscillation using intra-cavity etalon
1. Width sufficiently narrow to discrimate adjacent modes
2. FSR sufficiently large that adjacent peaks lie out the range of frequencies for which oscialltion is possinle
107
Limiting factor of linewidth =
spontaneous emission. Photons emitted by spontaneous emission have a random phase which spoils the perfectly coherent phase of the laser light.
108
Derive the Shalow Townes linewidth
Since energy is proportional to E\_o^2 and to n we know E\_0 is proportional to n
(see 32)
109
Why is ST linewidth infeasible in practice?
Temperature or vibration can change cavity length and thus frequency
110
What is the process of frequency locking?
1. Compare output frequency to some reference
2. Convert to an error signal proportional to the difference in frequncy
3. Adjust the frequency by adjusting the cavity length.
111
How can frequencies be locked to an atomic or molecular frequency?
Use a gaseous sample (with doppler free techniques)
Use a weak probe and a strong saturateing beam, Measure the output from the probe. Transmission is greatest when two beams have similar frequency (gain is saturated) or very different (threshold not met)
112
Sketch the error signal of frequency locking to an external cavity
113
Sketch optical diagram of frequency locking to an atomic or molecular transition
114
Sketch optical diagram of frequency locking to refernce cavity
115
Derive the energy of a Q switched pulse
116
What's the trick for deriving n(t) for a q switched laser?
Divide the rate equaltions
dn/dN = dn/dt / dN/dt
117
Relation between fwhm and fsr of Fabry Perot
fwhm = fsr/ finesse
118
fsr of fabry perot
c/nd
C2
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