Lasers Flashcards
What are the key properties of laser light
collimation
monochromaticity
coherence
How can a laser beam be considered collimated
despite natural divergence due to diffraction, they can be considered well collimated
what is the far field diffraction angle for a laser
wavelength/beam diameter
How can a laser beam be considered monochromatic
spectrally pure would comprise of a single optical frequency
what is choherence length of a laser
the distance over which interference fringes are still visible lc=tc*c
what relates the coherence time to the coherence length
the speed of light
how can coherence time be related to optical bandwidth of a laser
spread of optical frequencies is Ξπ = 1/π‘π
what is spatial coherence for a laser and how can it be measured
points across the beam are coherent, measured using youngβs slits
what are the three basic elements needed to make a laser
gain medium
resonator
pump
what is the role of the gain medium in a laser
to amplify the light
what is the role of the resonator in a laser
to provide optical feedback
what is the role of the pump in a laser
to provide the energy for the amplification
what are the three mechanisms by which the population (N) of electrons may move between states
spontaneous emission
stimulated absorption
stimulated emission
describe spontaneous emission
electron in upper state spontaneously relaxes down to lower state and emits a photon
the emission of the photon is an incoherent process
what is the state lifetime
the average lifetime an electron will remain in one state before relaxing
describe stimulated absorption
an incoming photon absorbed and excites the electron from a lower to an upper state
describe stimulated emission
an incoming photon causes an electron in an upper state to relax to the lower state, emitting a second photon which has exactly the same frequency as the fist and the same phase
this is the key to laser action
what is the energy difference between states
E2-E1=hv
what are the einstein relations
g1B12=g2B21 (g is degeneracy)
A21/B21 = (8ππ3βπ)/π^3
what is beers law which relates the intensity at a frequency v to the absorption coefficient πΌ
Iv(z) = Iv(z=0)exp (βπΌπ§ )
what happens if the absorption coefficient is negative
amplification
what happens if the absorption coefficient is positive
incoming light absorbed
what happens to the beam as it masses through the gain medium
it loses energy through absorption to level 1 atoms but gains energy through stimulated emission from level 2
what is a general requirement for lasing
a population inversion g2/g1(N1)<N2 which gives a negative πΌ
what is the small signal gain coefficient
πΎ = (π2 β (π1)π2/π1)(π΅21βππ/π)
What happens once a population inversion is established
gain medium will amplify the input signal
what is optical feedback
by reflecting the light back and forth an intense beam of radiation can be generated
this creates a laser oscillator
why would a very small gain not be enough to establish a laser
gain needs to overcome the stimulated emission loss and the optical system losses
what is the threshold inversion
the necessary population inversion needed to satisfy the threshold gain
How can we create a population inversion
pumping
why can we not achieve inversion in a 2 state model
illuminating the system with light of a frequency to take electrons from E1 to E2 has an equal probability of stimulating the population down from 2 to 1
so at best the 2 level system is transparent to incoming photons - which happens at very strong pumping (bleached)
What is the process of achieving optical gain in a three level laser
- pump from 1 to 3
- decay from 3 to 2 is non radiative. In a good laser medium, the lifetime in 3 is short and all population rapidly decays to 2
- stimulated emission from 2 to 1. Ideally lifetime of 2 is long to allow the population to grow to create inversion wrt 1
- once this happens stimulated emission will give optical gain
why do we need to actively pump atoms into 3
in thermal equilibrium the majority of the population will stay in 1
what is the population inversion condition (3-level)
N2>=Ntotal/2
What do you multiply the threshold inversion condition by to find the pump rate (3-level)
1/the life time of 2
because 2 also decays to 1 by spontaneous emission
What is the process of achieving optical gain for a 4 level laser
- pump from 1 to 4
- non radiative decay from 4 to 3 (lifetime of 4 should be short)
- stimulated emission from 3 to 2 (lifetime of 3 should be long enough to build up population inversion wrt 2)
- non radiative decay from 2 to 1
why is a population inversion easier to maintain in a 4-level laser
the lower laser state is not the ground state in the 4 level laser
what happens under thermal eq in the 4 level laser
most of the population in 1, the lower laser level 2 is empty
even for small populations in 3 there can be a population inversion
what is the pump rate for a 4 level laser
R=Nthresh(1/π3)
What are some system losses that must be overcome to achieve laser action
transmission of mirrors
absorption and scattering by mirrors
unwanted absorption by the laser gain medium
scattering by optical imperfections
diffraction losses
what is the effective gain coefficient
πΎπππ = πΎ β πΎπππ π where πΎπππ π encompasses all system losses except mirror loss
What is the threshold inversion
Ξππ‘β = (8ππ^3π^2π2)/π^3π‘π
what are pulsed lasers
the pump power needed to attain threshold can be achieved for a short time
what are continuous wave lasers
the inversion can be maintained indefinitely and the output is continuous
