Flashcards in Atoms & Lasers Deck (56):

1

##
Monochromaticity

Directionality

Brightness

Coherance

###
M - delta v << v, laser frequencey width much less than centre freq

D - highly directional: beam

B - spectrally bright

C - spatial (lateral) or temporal (longitudinal)

2

## Essential elements of laser

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1) gain medium that supports population inversion

2) Pump source that produces round trip gain greater than round trip loss

3) Resonant cavity that supports low loss modes

3

## Stimulated emission

###
Lasers require amplification by stimulated emission.

Want stimulated emission to prevail over spontaneous, since they scale with omega, harder to create lasers of higher frequencies

4

## Principle of detailed balance

### In equilibrium, the number of particles leaving a state by a particular route is the same as the number entering by the same route.

5

## 2 main classes of broadening

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Homogeneous - all atoms affected same

Inhomogeneous - atoms affected differently

6

## Homogeneous broadening

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Collisional (pressure) broadening: important in gas lasers, collisions deexcite atoms reducing the excited state lifetime - leads to broadening

Phonon broadening: important in solid state lasers, quantised vibrational modes: phonons. Temperature dependent

7

## Inhomogeneous broadening

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Doppler broadening: when moving atom emits or absorbs light there is doppler shift dependent on v, will be red or blue shifted

Amorphous crystal broadening: occurs in glass materials. Local inhomogeneity in glass, distribution of inhomogeneties is normal (gaussian). Emission lineshape is gaussian.

8

## Condition for gain

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Population inversion: N2>(g2/g1)N1

N* = N2-(g2/g1)N1 > 0

9

## Threshold condition

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Need net gain to get laser action. Define threshold condition:

round trip gain x round trip loss = 1

If gain x loss > 1 intensity grows

If gain x loss < 1 intensity decays

10

## Cavity basics: General cavity, losses, lifetime

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Gain medium at Brewster's angle to minimise losses

Can't be perfectly reflective as need photons out so light experiences round trip loss

When there is no gain, intensity will decay

11

## Good approx. for most good lasers

### Is(w) = hbarw/sigma(w)tau2

12

## Gain coefficient during osciallation

### g(wn) = gth(wn)

13

## Steady state

###
dI/dt = 0

gss(w) = gth

14

## Spatial hole burning

### For homogeneously broadened spectrum. As longitudinal laser mode develops, stimulated emission reduces whole gain profile - value of gain mode frequency is less in cavity. All atoms effected equal thus no further modes develop. Due to standing wave pattern in cavity gain varies, higher gain in regions of low intensity. Leads to wasted gain and is possible other modes develop feeing off this.

15

## Spectral hole burning

### Inhomogeneous, typical of gas lasers, pop in upper laser level only reduced at freq corresponding to laser cavity mode since different vel classes contribute to diff parts of gain spectrum. Gain depleted over freq width ~ natural linewidth of atom, reaching threshold at line centre. Dopler width of gas therefore broader than natural LW. Laser action can occur at series of equally space freq.

16

## Condition for laser oscillation

### g0(wn) = delta c / 2Lm

17

## Steady state inversion

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1) S2 > S1 - selective pumping

2) tau2 > tau1 - favourable lifetime ratio

3) g1>g2 - favourable degeneracy ratio

18

## Generic 3/4 level laser schemes

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Traditional: 3 level solid state laser, eg Ruby - Pump, fast decay, laser. NB traditional solid state lasers have high pumping threshold, need to pump N/2 out of GS to get inversion.

Gas laser: eg Ar+ - pump, laser, fast decay. NB Low QE

Solid state laser: dye lasers, eg Nd:YAG, 4 levels - pump, fast decay, laser, fast decay.

NB in 3 level schees, one transition is non-radiative due to parity.

4 level scheme best - Pth less for 4 level

19

## Quantum Efficiency

### QE = (E2-E1)/(E2-E0) = laser photon energy/pump photon energy = hbar w12/hbar w20

20

## Idealised 3 level laser

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N3 ~ 0

N1+N2 = N

-> at point of creating inversion N1=N2=N/2

21

## Idealised 4 level laser

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N0~N

N2 ~ (S03/Lambda21)N

N1 = N3 = 0

22

## Gas laser rates

### Dominated by radiative decay because atoms are isolated. Optical pumping not applicable to gas lasers - use particle pumping instead. A21 prop w^3, get larger ratio of lifetimes if w10 >> w12 - how they work by why QE is low.

23

##
Particle Pumping &

Adding species

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Used in gas lasers, usually electrons in gas discharge, electrons accelerated and collide inelastically with atoms.

Adding species to gas discharge can result in specific pumping to upper laser levels in case of He-Ne and CO2.

24

## Argon ion laser

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Isolated atom, degeneracies g1 = 4, g2 = 6

Lifetimes so favourable that a population inversion can be created if the pumping rate to the lower level is 22 times faster than to the upper level.

25

## Finesse

### Ratio of peak separation to peak width

26

## Fabry-Perot etalon

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Not used as laser cavity - difficult to align beam walkoff - use curved mirrors instead

Use to eliminate spectral hole burning

27

## Rayleigh range

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zR = (pi wo^2)/lambda

at z = zR beam is doubled

28

## Ray transfer matrices

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1) translation

2) reflection

3) thin lens

29

## Mode shapes of cavity

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Not used: plane parallel, symmetric confocal, symmetric concentric - on edge of stability and are sensitive to misalignment

Symmetric - waist at centre

Half symmetric R1 = infinity R2 = R

Symmetric confocal - R1 = R2 = Lc, common focus at Lc/2

30

## Mode volume

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V = pi wo^2 L can be used as upper limit for mode volume

Match R1 etc to gain medium - want it to be balance of efficient and stable

31

## Processes that give multimode behaviours

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Homogeneous - spatial hole burning

Inhomogeneous - spectral hole burning

Eliminate these by changing/adding to cavity

32

## Solution to spectral hole burning

### Introduce intracavity etalon. Angle allows tuning. Must satisfy two conditions (in notes)

33

## Solution to spatial hole burning

### Need to eliminate standing wave so mode propagates in only one direction. Achieved with ring cavity. Optical diode enforces directionality on the propagation.

34

## Grating

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1) Selects wavelength via angle - range set by resolving power

2) Forces an external cavity

35

## Repetition rate mode locked laser, pulse duration

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Determined by round trip cavity time - max when 1/2 delta w t = m pi

Puse duration determined by gain bandwidth of laser

36

## Q switching

### Q factor of cavity switched dynamically.

37

## Methods of mode locking & applications

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Active & Passive

1) Linear optical processes

2) Time resolved spectroscopy

3) Optical frequency comb

38

## Active mode locking

### Some form of intracavity shutter (open as pulse approaches, close after pulse passes eg). Mechanical shutter too slow. Use Acousto-Optic modulators or Electro-Optic modulators. Synchronous pumping of gain medium (modulator gain rather than loss). Still limited to pulses with delta tau > 10-50 micro s

39

## Passive mode locking 1.

### 1) Methods based on saturable absorber. SA exhibits strong absorbtion for low intensities but is highly transparent at high intensities as absorption saturates eg colliding pulse mode locking

40

## Passive mode locking 2.

### Methods based on optical Kerr effect - OKE leads to intensity dependent refractive inex. Usually negligable, but not for huge intensities in mode locked lasers. Gaussian beam profile gives radical variation in refractive index - a lense. Produces self focussing mode locking.

41

## Link between polarisation and electric field by suscelptibility

### P(t) = epsilon0 chi E(t)

42

## Second/third order effects

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2nd order effects enable second harmonic generation and sum and difference frequency mixing

Third order effects enable third harmonic generation and can lead to intensity-dependent refractive index

43

## Methods to avoid Doppler broadening

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1) Laser cooling - reduce delta w to less than linewidth

2) Crossed beam method - light source perpendicular to atom beam

3) Saturated absorption spectroscopy - probe interacts with atoms vz<0 such that Doppler shift brings into resonance, but populations not affected. Pump interacts with same |vz| but opposite sign. Saturates transition and transfers population. Scan laser into resonance - both laser beams interact with the same atoms with vz = 0..

44

## Optical frequency combs

### Output of mode-locked lser can be thought of as FC. Comb lines given by wn = delta wce + n delta w. Origin of offset is different phase and group velocities in laser cavity. If we know wce we know freq of all teeth.

45

## Measuring unknown frequency

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Beat unknown frequency against comb tooth.

w unknown = omega ce + n delta omega + omega beat

All freq on RHS are in rf/microwave domain and easily measured. Order no. of comb, n, can be easily found with standard wavemeter.

46

## Power eq

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3 level: P/V = hbar omega pump S13 N1

= hbar omega gamma N/2

47

## Gas laser 3 level why is Gamma20 ~ 0

### Parity

48

## Rayleigh range, beam waist, R

###
z_r = pi omega_0^2 / lamda

w = w_0(1+(z/z_R)^2)^1/2

R = (z^2 + z_R^2)/z

49

## Translation, reflection matrices and stable resonator condition

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1 L/neta

0 1

1 0

-1/f 1

0 < (1-L/R1)(1-L/R2) < 1

50

## Repetition rate, pulse duration

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tau rep = 2pi/delta omega = 2Lc/c

max when 1/2 delta omega t = m pi

Depends on cavity round trip time

delta tau = 2 pi/ N delta omega = tau rep / N

or = 2 pi / delta omega osc = 1/gain bandwidth

Depends on gain bandwidth

51

## Extra term if there is lasing

### sigma (n2 - g2/g1 n1) I/hbar omega

52

## Idealised 3 level

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N3 ~ 0

gamma 32 >> gamma 31

N1 = N2 = N/2

53

## Q switching details

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Initially high loss (low Q) cavity, pumping during this period means build up of population in upper laser level.

When pop inversion creates steady state switch cavity to low loss (high Q), radiation builds up and exponential grown leads to development of single giant pulse.

54

## Conditions in cavity

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w fsr > w osc/2

w fwhm < wn

55

## Coherance lenth and coherance time

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l = c/delta v

tau_c = 1/delta v

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