Laser Linewidth and Gain Saturation

Question 1

Why can we not consider laser output to be at a single frequency

Answer 1

atoms absorb and emit photons over a narrow band of neighboring frequencies given by the lineshape function g(v)

Question 2

What causes the line broadening effect in gases

Answer 2

doppler broadening, pressure broadening, natural lifetime, observation time

Question 3

what causes the line broadening effect in solids

Answer 3

lattice vibrations, phonon interactions, natural lifetime

Question 4

what are the two categories of line broadening

Answer 4

inhomogeneous and homogeneous

Question 5

What is an example of inhomogeneous broadening

Answer 5

Doppler broadening in gases

Question 6

describe doppler broadening in gases

Answer 6

the atoms in the gain medium move with thermal velocity
when a photon is emitted, its emission frequency will be doppler shifted
each atom has a specific velocity and therefore contributes to a specific delta frequency
𝛿𝜈 = 𝜈0(v𝑥/𝑐)
the lineshape of doppler broadening is exactly the same as the velocity distribution (gaussian)
each frequency within the lineshape always corresponds to an individual subgroup of atoms

Question 7

What does inhomogeneous broadening look like for solids

Answer 7

different atoms are found in slightly different lattice sites so they see different perturbing fields

Question 8

what gives rise to homogeneous braodening

Answer 8

the natural lifetime of atomic states

Question 9

How do we understand homogeneous broadening

Answer 9

the uncertainty principle Δ𝐸Δt ≈ ℎ

Question 10

Describe homogeneous broadening for a laser

Answer 10

the lifetime of the upper laser transition is related to the uncertainty in the energy of this state
by relating the energy uncertainty to frequency we find Δ𝜈 ≈ 1/𝜏2
with the homogeneous linewidth, no distinction can be made between different atoms - they are all broadened by the same amount

Question 11

How can the linewidth broadening be effected

Answer 11

reducing delta t by pressure broadening (atom collisions) and power broadening (rapid stimulated emission)

Question 12

What types of broadening effect all transitions

Answer 12

inhomogeneous (brownian induced doppler shifts)
homogeneous (spontaneous emission lifetime)

Question 13

what is implied from the doppler broadening in an inhomogeneous system (𝜈𝑖𝑛ℎ𝑜𝑚𝑜 ∝ 𝜈0)

Answer 13

IR transitions are long lived and Doppler broadening is very significant, while UV transitions are short lived and natural linewidth dominates

Question 14

In both broadening cases, 𝑔(𝜈)𝑖𝑛ℎ𝑜𝑚𝑜𝑔 and 𝑔(𝜈)ℎ𝑜𝑚𝑜𝑔 what is the limit on g(v) and what is the most likely transition frequency

Answer 14

g(v)<1 and v=v0 is the most likely

Question 15

What effect will including the lineshape function into our expression for gain have

Answer 15

reduced probability of a photon causing stimulated emission

Question 16

where does the maximum gain occur

Answer 16

on the line centre

Question 17

where is the minimum threshold

Answer 17

the line centre

Question 18

how can the threshold population Nth be reduced

Answer 18

• use a good resonator with large tc
• use a transition with narrow linewidth (small deltav) which will emit at the right frequency
• using a low frequency transition with a short upper state lifetime which implies a large B21 (but if t2 is too small it can become difficult to create a population inversion)

Question 19

What is the probability of a single atom undergoing stimulated emission

Answer 19

incident photon flux x cross section
(photon number densityccrosssection for stimulated emission)/no.photons

Question 20

what can the cross section allow us to do

Answer 20

rewrite many of the einstein coefficient equations in terms of the cross section 𝜎𝜈

Question 21

when does the gain begin to saturate even if we continue to increase R

Answer 21

once the pump excitation rate is insufficient to support continuous growth of the stimulated emission

Question 22

to build up radiation within the resonator from an initial low level of spontaneous emission, what must the round trip net gain be, and how does the optical field Iv grow

Answer 22

round trip net gain must be >1
optical field grows exponentially

Question 23

what is the steady state condition

Answer 23

Iv = constant so the gain = 1
the stimulated emission is just sufficient to offset the pumping and maintain the inversion at the threshold value

Question 24

what happens to the rate of stimulated emission as Iv increases

Answer 24

the rate of stimulated emission increases, hence the population inversion reduces

Question 25

how should the upper and lower state lifetimes be related for a population inversion

Answer 25

t1«t2 such that the population inversion takes a positive value

Question 26

what is the formula for the initial population inversion at Iv=0

Answer 26

deltaN=Rt2

Question 27

how do you define the saturation intensity

Answer 27

Isat = hv/t2𝜎𝜈

Question 28

what happens to the population inversion and emission rates when the intensity is at the saturation intensity

Answer 28

the population inversion is half the initial population inversion
the rate of spontaneous emission = rate of stimulated emission

Question 29

what is the saturation intensity

Answer 29

a measure of the amount of power per unit cross sectional area that can be extracted from a practical laser system

Question 30

under steady state conditions what happens when the gain in the gain medium becomes saturated

Answer 30

the gain will decrease to the point where the gain = cavity losses

Question 31

does the saturation intensity depend on the pumping rate?

Answer 31

no, because cross section and upper state lifetime don’t depend on these

Question 32

what is the effect of pumping the system harder

Answer 32

more small signal gain