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Flashcards in Atoms & Lasers Deck (56):


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)


Essential elements of laser

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


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


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.


2 main classes of broadening

Homogeneous - all atoms affected same
Inhomogeneous - atoms affected differently


Homogeneous broadening

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


Inhomogeneous broadening

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.


Condition for gain

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


Threshold condition

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


Cavity basics: General cavity, losses, lifetime

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


Good approx. for most good lasers

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


Gain coefficient during osciallation

g(wn) = gth(wn)


Steady state

dI/dt = 0
gss(w) = gth


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.


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.


Condition for laser oscillation

g0(wn) = delta c / 2Lm


Steady state inversion

1) S2 > S1 - selective pumping
2) tau2 > tau1 - favourable lifetime ratio
3) g1>g2 - favourable degeneracy ratio


Generic 3/4 level laser schemes

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


Quantum Efficiency

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


Idealised 3 level laser

N3 ~ 0
N1+N2 = N
-> at point of creating inversion N1=N2=N/2


Idealised 4 level laser

N2 ~ (S03/Lambda21)N
N1 = N3 = 0


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.


Particle Pumping &
Adding species

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.


Argon ion laser

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.



Ratio of peak separation to peak width


Fabry-Perot etalon

Not used as laser cavity - difficult to align beam walkoff - use curved mirrors instead
Use to eliminate spectral hole burning


Rayleigh range

zR = (pi wo^2)/lambda
at z = zR beam is doubled


Ray transfer matrices

1) translation
2) reflection
3) thin lens


Mode shapes of cavity

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


Mode volume

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


Processes that give multimode behaviours

Homogeneous - spatial hole burning
Inhomogeneous - spectral hole burning
Eliminate these by changing/adding to cavity


Solution to spectral hole burning

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


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.



1) Selects wavelength via angle - range set by resolving power
2) Forces an external cavity


Repetition rate mode locked laser, pulse duration

Determined by round trip cavity time - max when 1/2 delta w t = m pi
Puse duration determined by gain bandwidth of laser


Q switching

Q factor of cavity switched dynamically.


Methods of mode locking & applications

Active & Passive
1) Linear optical processes
2) Time resolved spectroscopy
3) Optical frequency comb


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


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


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.


Link between polarisation and electric field by suscelptibility

P(t) = epsilon0 chi E(t)


Second/third order effects

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


Methods to avoid Doppler broadening

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..


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.


Measuring unknown frequency

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.


Power eq

3 level: P/V = hbar omega pump S13 N1
= hbar omega gamma N/2


Gas laser 3 level why is Gamma20 ~ 0



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


Translation, reflection matrices and stable resonator condition

1 L/neta
0 1

1 0
-1/f 1

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


Repetition rate, pulse duration

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


Extra term if there is lasing

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


Idealised 3 level

N3 ~ 0
gamma 32 >> gamma 31
N1 = N2 = N/2


Q switching details

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.


Conditions in cavity

w fsr > w osc/2
w fwhm < wn


Coherance lenth and coherance time

l = c/delta v

tau_c = 1/delta v


Number of modes

delta omega_osc/ delta omega_n + 1