1
Q
What are key properties of a laser?
A
- Highly monochromatic
- Highly coherent
- Highly collimated
- Focussed to a very small spot
- Composed of very short pulses
- Very bright (intense)
2
Q
What does monochromatic mean?
A
Single wavelength & frequency due to stimulated emission process.
3
Q
Why do we get high intensity in a laser?
A
Due to the directionality of lasers. This allows them to be focussed to a tight spot.
4
Q
What does coherence mean?
A
Steady phase relation between the laser beam at different times. This is characteristed by the stimulated emission process.
5
Q
What are some applications of lasers?
A
- Light source in optical fibres
- Industrial cutting and welding
- Detection of chemicals
6
Q
What does laser stand for?
A
Light amplification by stimulated emission of radiation.
7
Q
What is stimulated emission?
A
When a photon of appropriate energy passes it can stimulate the emission of another photon from an atom in an excited state.
8
Q
How is light amplified in a laser?
A
Through stimulated emission in the gain medium.
9
Q
What are the three components of a laser?
A
- Gain medium
- Optical resonator
- Pump
10
Q
What is the gain medium?
A
Where the stimulated emission occurs
11
Q
What is the pump component of a laser?
A
The pump is the mechanism that provides energy to the system. This can occur through electrical discharge, optical pumping or chemical reaction.
12
Q
What is the optical resonator component of a laser?
A
Mirrors form optical resonators which reflect photons through the gain medium multiple times, increasing amplification.
13
Q
What is a HeNe laser?
A
A helium neon laser is a helium neon gas mixture pumped by electrical discharge.
14
Q
What are the three processes in which radiation and an atom interact?
A
- Absorption
- Spontaneous emission
- Stimulated emission
15
Q
Describe the process of absorption.
A
An electron initially in a lower level absorbs a photon causing the electron to move to an excited state.
16
Q
Describe the process of spontaneous emission
A
An excited electron initially in an upper level will spontaneously decay back to the lower level emitting a photon in a random direction.
17
Q
Describe the process of stimulated emission
A
Excited electrons can be stimulated to emit coherently when illuminated by light of the same energy.
18
Q
What is spectral energy density?
A
A measure of how much energy per unit frequency there is in a radiation field.
19
Q
What are Einsteins three postulates?
A
- Rate of spontaneous emission is N2 A21
- Rate of absorption is N1 B12 ρ(ω21)
- Rate of stimulated emission is N2 B21 ρ(ω21)
20
Q
What is the critical assumption used in deriving Einsteins relations?
A
Thermal equilibrium
21
Q
Einsteins equations apply when?
A
They always apply - not just in thermal equilibrium
22
Q
When does optical gain occur?
A
If the rate of stimulated emission exceeds the rate of absorption
23
Q
What is population inversion
A
The population per state in the upper level must exceed the population per state in the lower level.
24
Q
What does population inversion imply?
A
Lower level has to empty quicker than it fills due to spontaneous emission from the upper level
25
What are the conditions for steady state population inversion?
One of the following must be met
- R2 > R1
- 𝜏2 > 𝜏1
- g2 > g1
26
What happens when population inversion has been achieved?
Light passing through the gain medium will be amplified by stimulated emission. Stimulated emission can occur.
27
What does the gain coefficient depend on?
Intensity - high intensity, more stimulated emission, reducing population inversion.
28
What is gain saturation
When stimulated emission rate > pumping rate, N2.
29
What is small signal gain?
The gain for small intensity, with no gain saturation
30
What kind of energies do atomic energy levels have?
A spread in energies rather than defined energies.
31
What is gain narrowing?
The spectral width of the amplified beam decreases as it passes through the inverted gain medium
32
What is line broadening?
Energy levels are not infinitely sharp - many processes can broaden the line width of emitted radiation
33
What is homogeneous broadening?
Broadening that affect’s all atoms in a sample equally
34
What are some examples of homogeneous broadening?
1. Natural broadening
2. Pressure broadening
3. Phonon broadening
35
What is natural broadening?
Broadening due to the finite lifetimes of energy levels. In the quantum picture - Heisenbergs uncertainty.
36
What is pressure broadening?
Collision broadening due to interactions between atoms. The collisions disrupt oscillations.
37
What is phonon broadening?
Thermal vibrations of crystal matrix interacting with atom. Important in solid state lasers.
38
What is inhomogeneous broadening?
Mechanisms that cause the transition frequency of different atoms to be shifted by different amounts.
39
What are some examples of inhomogeneous broadening?
1. Doppler broadening
2. Spread of atomic velocities
40
What is the Doppler effect?
A spread of atomic velocities results in spread of emitted frequencies.
41
What is a Voigt profile?
The overall line shape - a combination of both types of broadening (homogeneous, inhomogeneous), with profile given by the convolution of Gaussian and Lorentzian distributions.
42
Describe a 3-level system
Energy levels
1. Ground state
2. Upper laser state - meta stable
3. High energy state
43
Describe a four-level system
Energy levels
1. Ground state
2. Lower laser state
3. Upper laser state
4. High energy state
44
What are the differences between three level and four level lasers?
3 level laser needs many electrons excited to state 2 to achieve population inversion while 4 level laser immediately has population inversion as soon as any electron is in state 2. Therefore a 4 level laser requires less pump power.
45
Describe a ruby laser?
A ruby laser is a solid state laser that uses a solid state gain media dopped with rare earth or transition metals and optical pumping.
46
How does a solid state laser operate?
A solid state laser operates through non-radiative decays from unstable upper level through the mechanism of phonon de-excitation.
47
How is a solid state laser pumped?
Through flash lamps or laser diodes.
48
What are some of the pros and cons of solid state lasers?
Pros
- compact and rugged
- output between visible and mid-infrared with scope to extend to UV
Cons
- less suitable for very long/short wavelengths
- less suitable for very high powers.
49
What is a semi conductor laser?
Semi conductor lasers use a solid gain medium but the types of lasing energy levels and pumping mechanisms are different
50
How does a semi conductor laser operate?
An active region is formed between the p-type and n-type semi conducting layers. The laser beam diverges on exiting - beam emitted in plane of the interface.
51
What kind of band gap is required for a semi conductor laser?
Need a direct band gap to emit photons.
52
What are the benefits of a solid semiconductor laser?
Semiconductor lasers allow for a tunable wavelength.
53
What are gas lasers?
Gas lasers use gases as their gain medium with pumping done with electric discharge - helium neon laser.
54
What is spectroscopy?
Tuning a laser's wavelength to a particular transition in a particular chemical.
55
What are dye lasers?
Dye lasers are tunable lasers that use transitions in organic compounds. They tend to have high gain.
56
When do we get laser amplification
When the gain coefficient is larger than the loss if we have population inversion.
57
What is a laser amplifier on its own?
Amplified spontaneous emission laser
58
What is a laser oscillator?
A laser amplifier plus an optical resonator.
59
How does the resonator operate in a laser oscillator?
1. Stimulated emission builds up leading to multiple reflections
2. Define boundary conditions
-Restricts oscillations to longitudinal modes
- Restricts oscillations to particular transverse modes forming a standing wave.
3. Ensure optimum reflectivity
60
Modes with the same value of p are said to be in
The same longitudinal mode.
61
How many wavelengths fit into the length of the cavity?
Integer number of half wavelengths.
62
Modes with the same value of l and m are said to be in
The same transverse mode.
63
What are allowed transverse modes described by?
Hermite polynomials.
64
What is a Fabry-Perot Interferometer?
The simplest optical cavity. Fabry-perot acts like a filter with two parallel highly reflective mirrors with boundary conditions that result in standing waves that are spaced in frequency by the free spectral range.
Only standing waves can pass.
65
What is an optical cavity?
An optical cavity provides feedback and sets boundary conditions for the light field at the mirror surfaces.
66
What do we use an etalon for?
An etalon is used as a mode filter in a laser cavity. It can be used to achieve a single mode.
67
What is a stable cavity?
A stable cavity supports modes where the light field is confined close to the cavity axis and has low diffraction losses.
68
What is an unstable cavity?
An unstable cavity has high diffraction losses and the modes are not confined to be close to the axis.
69
How can we keep diffraction losses low?
By using concave mirrors - this refocuses the radiation.
70
Why do the peaks get sharper in a cold cavity?
Peaks get sharper as reflectivity parameter R increases in a cold cavity.
71
How is gain related to the path length and what is its profile related to?
The gain is related to path length through gain medium, profile related to transition lifetime.
72
When does a frequency resonate in the cavity?
If there is low cavity loss i.e. if the frequency overlaps with a cavity mode.
73
What are the laser threshold conditions?
If the round trip gain is greater than the loss.
74
What is spatial hole burning?
Population inversion is more depleted near the peaks of the mode's standing wave pattern.
75
When do we get multimode oscillation of the laser?
The unused regions of population inversion can be used to feed other modes and these modes can reach threshold for cavity oscillation.
76
What is the paraxial regime?
When all light rays travel at small angles with respect to the optical axis.
77
When do we get free space propagation of a ray?
When the distance from the axis increases and the slope stays the same.
78
What is the unfolded cavity?
A series of lenses of the same focal length separated by cavity length.
This is equivalent to tranmission through a cavity.
79
What is the result of eigenvectors of a matrix forming a complete basis?
any ray vector in the resonator can be written as a superposition of eigenrays.
80
What is a stable cavity?
One in which light is not lost from the edges of the mirrors e.g. light is stored/trapped in the cavity.
81
What is the consequence of a stable cavity?
No ray can go arbitrarily far from the optical axis.
82
What is an unstable cavity?
The rays get exponentially further from optical axis with number of roundtrips eventually missing the mirror and escaping the cavity.
83
What are the two assumptions used to describe cavity stability?
1. That all rays are paraxial
2. That the mirror size is very large
84
How can we quantify the loss/energy storage in a cavity?
Using the photon lifetime and quality factor.
85
What is the quality factor of the cavity?
The quality factor is a measure of the energy storage versus energy loss.
86
How does the quality factor effect the linewidth of a cavity?
A narrow resonance will have a higher quality factor than a broader resonance.
87
What is the simplest mode of a stable resonator?
The gaussian beam or TEM00 mode.
88
What are the 5 terms that describe a gaussian laser beam?
1. Propagation term
2. Power normalisation term
3. Gaussian term
4. Describes curvature of the phase fronts
5.Effects of a phase shift relative to the phase of a uniform plane wave which the gaussian beam experiences upon propagation
89
When is the spot size the smallest
At the beam waist. Where the spot size is the waist size.
90
When is the beam the brightest?
At the waist
91
What is the Rayleigh range?
How far away from the waist the beam has expanded to have a spot size sqrt(2) times larger than the waist.
92
What criteria must cavity mirrors meet?
Cavity mirrors must match the phase front curvature of the beam.
93
What is non linear optics?
The study of the behaviour of light in non linear media i.e when the polarisation density in the medium has a non linear response to the electric field of the light.
94
What type of electric fields do we need to observe non linear effects?
Typically need high electric fields to observe non linear effects.
95
What do non linear processes enable?
Changes to be made to the wavelength of light
96
What are some examples of non linear frequency conversion?
Second harmonic generation
Third harmonic generation
Sum/difference frequency generation
Optical parametric oscillations
97
What is second harmonic generation?
The doubling of the frequency or halving of the wavelength of light
98
What is sum/difference frequency generation?
output light with the sum/difference of two input frequencies
99
What is optical parametric oscillation?
It converts light at one frequency into two output waves of lower frequency using a cavity plus a non linear crystal
100
What are some applications of nonlinear effects?
1. Optical kerr effect
2. Super-continuum generation
3. Raman amplification
101
What are the light sources used in non-linear processes?
1. A diode pump solid-state laser
2. Optical parametric oscillator
3. Supercontinuum source
102
What is super continuum generation?
Pulsed laser light that passes through a non linear process creates broad band laser light while maintaining spatial coherence
103
What is Raman amplification
Stimulated Raman scattering in which photon energy is changed by interaction with material
104
What is the origin of the refractive index
Propagating light distorts the electron cloud at the optical frequency. Electrons act like harmonic oscillators with resonant frequency. Such that the electron has oscillating motion.
105
What is the effect of the oscillating electrons?
They emit a co-propagating electric field whose effect is to retard the phase of the light wave
106
How do different wavelengths respond to different refractive indices?
Red light is bent less than blue.
107
What do we need to account for in a complete model of refractive index?
1. Several different atomic resonances
2. Damping - the electron oscillation is not lossless
108
Why does refractive index vary in a complicated manner with frequency?
Generally refractive index increases with frequency. Absorption occurs when ω ~ ωk. Close to resonances, in the absorption bands, index decreases with frequency. This is known as anomalous dispersion.
109
Refractive index arises from
- Polarisability of electron clouds/atoms
- Subsequent re-radiation from oscillating dipoles - causing dispersion, absorption bands.
110
What is an isotropic crystal?
One where the refractive index is the same in all directions.
111
Describe anisotropic crystals.
The spring constant and susceptibility varies with direction in the crystal / direction of polarisation of the light.
This results in birefringence.
112
What is birefringence?
Propagation speed varies with polarisation relative to crystal structure.
Refractive index depends on the polarisation of light.
113
What is calcite?
Calcite has an exceptionally high birefringence due to carbonate groups lying in parallel planes. It has inversion symmetry.
114
What did Bragg reveal when he analysed calcite?
When the electric field is in the plane of the triangle of oxygen atoms, the external field and the field from the other atoms in the triangle act in the same direction, polarising each atom more strongly.
115
What is uniaxial birefringence?
There is an optic axis in the crystal which defines the optical anisotropy. The refractive index depends on the orientation of the electric field and the optic axis.
116
What are the two principle refractive indexes
1. The ordinary refractive index
2. The extraordinary refractive index
117
What is the ordinary refractive index?
When the electric field is perpendicular to the optic axis
118
What is the extraordinary refractive index?
When the electric field is parallel to the optic axis.
119
What is the principle section?
The plane is defined by the optic axis and ray
120
When do we get double refraction?
When different refractive indices cause the rays to take different paths through the crystal.
121
What is walk off?
The deviation of the e-ray path from the o-ray path is called the walk-off.
122
What is a uniaxial crystal?
Atoms are arranged symmetrically about the optic axis
123
What is the electron cloud?
The electron cloud has different spring constants if distorted parallel or perpendicular to the optic axis
124
What is an o-ray?
The electric field is orthogonal to the optic axis. The light acts as in an isotropic medium. The speed of light is v(perp)
125
What is the e-ray?
The electric field is partly parallel to the optic axis. The speed of light depends on propagation direction. If propagating orthogonal to the optic axis the speed of light is v(parallel).
126
What does optical non linearity generate?
Harmonic distortion
127
What happens to light in free space?
Light does not interact with light (photons are bosons)
128
Describe the interaction of light in matter?
Light can interact with light via interaction with medium
129
How can we model the distorted electron cloud
Model as a harmonic oscillator - electron bound in a potential well.
130
What can be said about the higher order terms of the anharmonic potential
Higher order terms represent deviations from the potential well being a perfect parabola.
131
How is the potential modelled?
As an anharmonic for large displacement.
132
What happens when we have 2nd order harmonic distortion?
We get the original frequency, the second harmonic and also a zeroth order term - an offset to the curve.
133
What does polarisation vary non linearly with?
Field
134
How strong a field is required to see significant non linear effects?
Significant non linearity expected when E is comparable to electric field experienced by electrons in crystals.
This can be generated using a laser.
135
When was second harmonic generation first demonstrated?
In 1961 with a ruby laser
136
What is second harmonic generation?
As light of frequency ω1 propagates through crystal it loses energy by conversion into light of frequency 2ω1.
137
How does phase mismatch arise in second harmonic generation?
Second harmonic is generated in phase with the pump beam at all z but the refractive index varies with ω so the second harmonic experiences different index to the pump. This results in phase mismatch.
138
What is phase mismatching?
When we get different propagation and phase evolution on propagation through the crystal. This results in destructive interference between waves generated at different points in the crystal.
139
Why do we want phase matching?
Phase matching ensures the intensity grows as it propagates through the crystal.
140
Describe phase matching vs no phase matching?
Phase matching when Δk = 0 all the phase contributions add coherently.
No phase matching when Δk ≠ 0, the contributions from each point in the crystal interfere destructively, resulting in a phase shift.
141
How do we achieve phase matching?
For a positive birefringent material, we vary the propagation angle to alter the effective refractive index until it matches the generated second harmonic refractive index.
For a negative birefringent material, we use the o(ω)o(ω) -> e(2ω) process.
142
How do we achieve type II phase matching?
For positive birefringence: the polarisation component perpendicular to the optic axis combined with the polarisation component parallel to the optic axis creates an ordinary wave at the second harmonic.
143
How are both types of phase matching achieved?
By angle tuning - using propagation direction and birefringence to ensure refractive indices at both frequencies are matched.
144
What are the drawbacks of phase matching?
1. Angle tuning is very sensitive
2. Difficult to align
3. Limited range of crystal materials
4. Walk-off between fundamental and second harmonic beam.
145
What happens as a result of walk off?
Angular separation of the o-ray and e-ray beans as they propagate through crystal
146
What does walk off limit?
The range over which beams overlap within the crystal. This prevents the constructive interference of the phase matched beams. When the o and e beams no longer overlap no type II SHG can take place.
147
What is non critical phase matching?
When we do not use angle tuning so we do not get walk off. The crystal properties must yield phase matching using temperature tuning.
148
What is Quasi phase matching?
Making SHG crystal out of short lengths of ~ Lc/2. Invert d(eff) axis in alternating sections. This effectively stops complete destructive interference occurring.
149
How do we get significant SHG?
-Make the crystal as long as possible as more interaction length leads to more SH light.
-Focus the pump beam to as small a spot as possible
150
What limits the focus of the beam?
A gaussian laser beam focus is limited by diffraction so if we focus tighter, the beam diverges more.
151
What do guided wave structures allow?
Guided wave structures can allow efficiency proportional to L^2. Such that the beam in waveguide will not diverge, so interaction area remains constant along the fibre.
152
How do we get high conversion efficiency?
High intensity within cavity and multiple passes of pump photons through the non linear crystal.
153
What is down conversion?
Generation of ω3 = ω1 - ω2. known as difference frequency generation. Where a bystander photons catalyse the process.
154
How do we generate the third harmonic?
Need huge electric fields to get a significant effect. So we generate the second harmonic and sum the second harmonic with pump light to get the third harmonic.
155
What are optical parametric oscillators?
devices which convert an input laser wave into two output waves of lower frequency known as the signal and idler.
156
Describe the frequencies of signal and idler waves?
By convention, the higher frequency is the signal, the lower the idler.
157
What is optical parametric amplification?
Describes the interaction between pump, signal and idler photon.
A non-linear interaction of pump and signal can generate the difference frequency or the idler beam. Conservation of energy ensures a photon at the signal frequency is generated. The growth rate for the signal amplitude is proportional to the pump amplitude, but also to the signal amplitude.
158
How does the optical parametric amplification process start?
In the presence of an intense pump the random spontaneous generation of an appropriate signal/idler photon in the crystal can start the process.
159
How is the amplification at the signal and idler frequencies determined?
It is determined by phase matching and energy conservation.
160
How can we achieve optical parametric oscillator?
Using an optical amplifier (OPA) which is inserted into a resonant cavity.
161
What is optical frequency conversion?
Three-wave mixing: up-conversion or down-conversion.
162
Describe the components of an OPO system?
Three components
1. Light Source
2. Frequency Tripler
- light is frequency doubled and mixed with light to produce the third harmonic
3. Singly resonant OPO
163
What is the Kerr effect?
The kerr effect makes material act as a uniaxial positive birefringent material.
164
Describe the Kerr effect in nonlinear crystals
A DC field shifts the equilibrium position of atomic electron cloud potential.
165
Describe a Kerr cell.
A material is held in cell, with electrodes to apply high voltage - adjusting the voltage makes the material more or less birefringent.
Polarisers aligned at +45 and -45 degrees to E.
As E increases, birefringence changes polarisation of the light, and producing a component that will be transmitted by the analyser.
166
What does the Kerr effect arise from?
the third order nonlinear susceptibility
167
What is the pockels effect?
Directional linear variation in refractive index under applied electric field. Electric field is applied along the same axis as light propagation.
168
What is a pockels cell?
Sandwich cell of material between crossed polarisers.
The phase retardation varies linearly with applied voltage.
169
Where does the pockles effect occur?
In non-centrosymmetric crystals (these are solids not liquids)
170
What are the electro-optic modulators?
a pockles cell and kerr cell
171
What are the applications of electro-optic modulators?
High intensity pulsed lasers
172
How can we generate high intensity pulsed lasers?
Using Q-switching and cavity dumping.
173
How does Q-switching work?
1. Quality factor of cavity is initially low. An electro-optic switch is used to prevent feedback. The pumping stores energy, increasing population inversion.
2. Quality factor of cavity is switched to high. The mirror is switched to reflective the energy stored in population inversion emitted as a single intense pulse.
3. Switch to low Quality factor cavity.
174
What are the Q-switching methods?
1. Rotating end mirror - pick rotation speed to produce pulses
2. Use a pockels cell as a switch - control it electrically
3. Saturable absorber: light excites electrons to an upper state with long lifetime.
175
What is cavity dumping?
Can store laser energy in the cavity by having it very high Q with 100% reflective mirrors. Switching then used to allow beam to exit cavity - dumping the power in a laser pulse.
1. The light coupled out of resonator
2. E-O modulator switched so light is retained in resonator
3. E-O modulator switches light out
176
Describe the Q-switching versus cavity damping?
Q-switching: Store energy in population inversion
Cavity dumping: Store energy optically in circulating light
Lasers and non-linear optics
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