Lasers

Question 1

How do you calculate the frequency range, Δν, from a corresponding range of wavelengths Δλ?

Answer 1

Differentiate ν = c/λ with appropriate approximations, to get Δν = c * Δλ / λ^2

Question 2

What are the two types of emission in lasers?

Answer 2

Spontaneous and stimulated.

Question 3

What does LASER stand for?

Answer 3

Light Amplification by the Stimulated Emission of Radiation.

Question 4

Which type of emission produces coherent light?

Answer 4

Stimulated.

Question 5

How does stimulated emission occur?

Answer 5

A passing photon triggers the emission of an exact copy when an excited atom matches the energy of the photon - same phases & direction

Question 6

Name the parts of a laser

Answer 6

• power supply
• gain material
• resonator mirrors

Question 7

What is the simplest model of laser system? What is its drawback?

Answer 7

Two-level system, cannot achieve population inversion.

Question 8

Equation for the rate of absorption?

Answer 8

dN1/dt = - B * ρ(ν)* N1
B = probability a photon will cause a 1 -> 2 transition
ρ(ν) = photon density at frequency ν

Question 9

Equations for the rates of emission?

Answer 9

Spontaneous: dN2/dt = - A(21)N2
Stimulated: dN1/dt = - B * ρ(ν) * N2

Total emission = sum of spontaneous + stimulated

Question 10

What are the Einstein equations?

Answer 10

Equations for the emission and absorption rates in lasers

Question 11

What are the Einstein coefficients?

Answer 11

The coefficients B12, B21, and A21 in the Einstein equations.

Question 12

Equation for the ratio R of stimulated and spontaneous emissions?

Answer 12

R = e^(hν/k{B}T) - 1

Question 13

What is population inversion?

Answer 13

When N2 > N1`

Question 14

Which transition in a three level system is the fast one?

Answer 14

N2 -> N3

Question 15

Equation for the maximum efficiency of a three-level laser?

Answer 15

η{max} = λ[absorbed] / λ[emitted]

Question 16

What is the equation for the intensity of a signal going through a gain medium?

Answer 16

I = I{o} * e^(α*x)

Question 17

What is the laser threshold and its equation?

Answer 17

The laser threshold is the condition where I2 = I1 through the gain medium - there is no amplification. Occurs when R1 * R2 * e^(2αL) = 1

Question 18

What are the limitations of a three-level system?

Answer 18

• Laser transition ends in ground state
• Ground state is well populated
• Lasing transition can undergo absorption
• Emitted photons lost to re-absorption

Question 19

Name the transition sequence of an atom in a four level system

Answer 19

N1 -> absorption -> N2 -> non-radiative transmission -> N3 -> emission -> N4 -> fast non-radiative transmission -> N1

Question 20

What is a doped gain material?

Answer 20

A crystalline/glass matrix with a dopant that provides it with excitable electrons, denoted dopant:matrix

Question 21

What is the resonance condition?

Answer 21

When the wave in the laser is a standing wave, at m * λ{m} = 2 * L{opt}

Question 22

What is the optical length of a standing wave cavity?

Answer 22

L{opt} = n * L
n = refractive length 
L = physical length of resonator

Question 23

The spacing between two adjacent resonator modes is…

Answer 23

… the free spectral range, delta nu. Given by: Δν= c / 2*L{opt}

Question 24

What types of gain materials exist?

Answer 24

• solid state gain media
• liquid gain media (dye lasers)
• gaseous gain media
• semiconductor gain media