Lasers

Question 1

What are the key properties of laser light

Answer 1

collimation
monochromaticity
coherence

Question 2

How can a laser beam be considered collimated

Answer 2

despite natural divergence due to diffraction, they can be considered well collimated

Question 3

what is the far field diffraction angle for a laser

Answer 3

wavelength/beam diameter

Question 4

How can a laser beam be considered monochromatic

Answer 4

spectrally pure would comprise of a single optical frequency

Question 5

what is choherence length of a laser

Answer 5

the distance over which interference fringes are still visible lc=tc*c

Question 6

what relates the coherence time to the coherence length

Answer 6

the speed of light

Question 7

how can coherence time be related to optical bandwidth of a laser

Answer 7

spread of optical frequencies is Δ𝜈 = 1/𝑡𝑐

Question 8

what is spatial coherence for a laser and how can it be measured

Answer 8

points across the beam are coherent, measured using young’s slits

Question 9

what are the three basic elements needed to make a laser

Answer 9

gain medium
resonator
pump

Question 10

what is the role of the gain medium in a laser

Answer 10

to amplify the light

Question 11

what is the role of the resonator in a laser

Answer 11

to provide optical feedback

Question 12

what is the role of the pump in a laser

Answer 12

to provide the energy for the amplification

Question 13

what are the three mechanisms by which the population (N) of electrons may move between states

Answer 13

spontaneous emission
stimulated absorption
stimulated emission

Question 14

describe spontaneous emission

Answer 14

electron in upper state spontaneously relaxes down to lower state and emits a photon
the emission of the photon is an incoherent process

Question 15

what is the state lifetime

Answer 15

the average lifetime an electron will remain in one state before relaxing

Question 16

describe stimulated absorption

Answer 16

an incoming photon absorbed and excites the electron from a lower to an upper state

Question 17

describe stimulated emission

Answer 17

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

Question 18

what is the energy difference between states

Answer 18

E2-E1=hv

Question 19

what are the einstein relations

Answer 19

g1B12=g2B21 (g is degeneracy)
A21/B21 = (8𝜋𝑛3ℎ𝜈)/𝑐^3

Question 20

what is beers law which relates the intensity at a frequency v to the absorption coefficient 𝛼

Answer 20

Iv(z) = Iv(z=0)exp (−𝛼𝑧 )

Question 21

what happens if the absorption coefficient is negative

Answer 21

amplification

Question 22

what happens if the absorption coefficient is positive

Answer 22

incoming light absorbed

Question 23

what happens to the beam as it masses through the gain medium

Answer 23

it loses energy through absorption to level 1 atoms but gains energy through stimulated emission from level 2

Question 24

what is a general requirement for lasing

Answer 24

a population inversion g2/g1(N1)<N2 which gives a negative 𝛼

Question 25

what is the small signal gain coefficient

Answer 25

𝛾 = (𝑁2 − (𝑁1)𝑔2/𝑔1)(𝐵21ℎ𝜈𝑛/𝑐)

Question 26

What happens once a population inversion is established

Answer 26

gain medium will amplify the input signal

Question 27

what is optical feedback

Answer 27

by reflecting the light back and forth an intense beam of radiation can be generated
this creates a laser oscillator

Question 28

why would a very small gain not be enough to establish a laser

Answer 28

gain needs to overcome the stimulated emission loss and the optical system losses

Question 29

what is the threshold inversion

Answer 29

the necessary population inversion needed to satisfy the threshold gain

Question 30

How can we create a population inversion

Answer 30

pumping

Question 31

why can we not achieve inversion in a 2 state model

Answer 31

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)

Question 32

What is the process of achieving optical gain in a three level laser

Answer 32

• 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

Question 33

why do we need to actively pump atoms into 3

Answer 33

in thermal equilibrium the majority of the population will stay in 1

Question 34

what is the population inversion condition (3-level)

Answer 34

N2>=Ntotal/2

Question 35

What do you multiply the threshold inversion condition by to find the pump rate (3-level)

Answer 35

1/the life time of 2
because 2 also decays to 1 by spontaneous emission

Question 36

What is the process of achieving optical gain for a 4 level laser

Answer 36

• 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

Question 37

why is a population inversion easier to maintain in a 4-level laser

Answer 37

the lower laser state is not the ground state in the 4 level laser

Question 38

what happens under thermal eq in the 4 level laser

Answer 38

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

Question 39

what is the pump rate for a 4 level laser

Answer 39

R=Nthresh(1/𝜏3)

Question 40

What are some system losses that must be overcome to achieve laser action

Answer 40

transmission of mirrors
absorption and scattering by mirrors
unwanted absorption by the laser gain medium
scattering by optical imperfections
diffraction losses

Question 41

what is the effective gain coefficient

Answer 41

𝛾𝑒𝑓𝑓 = 𝛾 − 𝛾𝑙𝑜𝑠𝑠 where 𝛾𝑙𝑜𝑠𝑠 encompasses all system losses except mirror loss

Question 42

What is the threshold inversion

Answer 42

Δ𝑁𝑡ℎ = (8𝜋𝑛^3𝜈^2𝜏2)/𝑐^3𝑡𝑐

Question 43

what are pulsed lasers

Answer 43

the pump power needed to attain threshold can be achieved for a short time

Question 44

what are continuous wave lasers

Answer 44

the inversion can be maintained indefinitely and the output is continuous