Photonics - Topic 4

Question 1

What does laser stand for?

Answer 1

Light Amplification by Stimulated Emission of Radiation

Question 2

What is a laser?

Answer 2

• A source of coherent light
  
  • “Monochromatic” (single wavelength) – spectral coherence
  • Usually intense and highly directed – implies spatial coherence
  • Usually taken to mean an “optical oscillator”
    
    • Gain + feedback

Question 3

What is stimulated emission?

Answer 3

• Incoming photon stimulating a higher energy state to lose energy and give off a new photon,
  
  • original photon is not absorbed, thus system emits two photons
• The photon generated is identical to the incoming photon; same frequency (energy), phase, and direction as the incoming photon.
• Amplification of incoming optical, if stimulated emission is more likely than absorption.

Question 4

What does a 3 level system look like?

Answer 4

Question 5

What does a 4 level system look like?

Answer 5

Question 6

What are the main takeaways from einsteins coefficients?

Answer 6

B₁₂ = B₂₁

B₁₂ is the Einstein coefficient for absorption.

B₂₁ is the Einstein coefficient for stimulation

This tells us that absorption an stimulated emission are equally likely.

Also,

R₂₁ (stim) − R₁₂ (𝑎𝑏s) = B₂₁𝜌(f)(𝑁₂ − 𝑁₁)

which shows tha 𝑁₂ > 𝑁₁ for net stimulated emission, thus population inversion is required.

Question 7

What is population inversion?

Answer 7

The condition for stimulatd emission to dominate over absorption is that there must be more occupied states (electrons) at E₂ than at E₁. A 3/4 level system is required.

Question 8

Where does the gain of the laser come from?

Answer 8

The gain of the laser comes from having more stimulated emission than absorption.

Question 9

What does the Fabry-Perot cavity look like?

Answer 9

Question 10

How will the power vary across a feedback cavity such as Fabry-Perot?

Answer 10

𝑃(𝑧) = 𝑃₀e^{(𝑔 − 𝛼)z}

where g is the power gain coefficient

𝛼 is the power loss coefficient

Net gain (coefficient) is given by (𝑔 − 𝛼)

Question 11

What do we require for FP laser to function>?

Answer 11

unity round-trip gain

Question 12

Expression for the threshold gain of an FP laser?

Answer 12

• We normally interpret this as the balance between net stimulated gain (i.e. due to the excess of stimulated emission over absorption between energy levels) and loss
  
  • 𝛼 then accounts for scattering and other losses (but not absorption between lasing levels)
  • The second term on the RHS represents loss through the mirrors
• 𝑔_th is reduced if either L or R are increased

Question 13

Light output against pumping level plot

Answer 13

Below threshold, 𝑔 proportinal to 𝑁₂ − 𝑁₁

Once threshold is reached, 𝑁₂ − 𝑁₁ is clamped

Pumping above the threshold level results in additional stimulated emission which results in increased photon density within the cavity and increased light output power

Question 14

What are the conditions for the wavelengths or frequencies in FP laser?

Answer 14

λ_m = 2nL/m

f_m = mc/2nL

It is only at these wavelengths or frequencies that there will be an output.

Where m is the number of wavelengths in a round trip.

The spacing of the longitudinal modes is given as:

△f = c/2nL

Question 15

What do 𝑁₁ and 𝑁₂ symbolise?

Answer 15

the number of states per unit volume at 𝐸₁ and 𝐸_{<span>2</span>}

Question 16

Diagram of a Edge-emitting semiconductor laser

Answer 16

Question 17

Benefit of using a Heterostructure semiconductor lasers

Answer 17

• A double heterostructure can provide better carrier confinement than a homostructure.
  
  • Easier to reach the required threshold gain, i.e. it reduces threshold current.
• Difference in refractive index between the active region and wider bandgap cladding layers creates a waveguide, guiding the light along the cavity between the FP mirrors.
  
  • This helps confine the light to the active layer, which reduces the threshold gain.

Question 18

Buried heterostructure laser diode

Answer 18

• Improvement on the stripe contact laser is the buried heterostructure laser.
• Active region is surrounded by wider bandgap material in the lateral direction, as well as in the vertical direction.
  
  • This creates a rectangular waveguide which confines the light in both lateral and vertical directions.
• The current flow also confined to the active layer.
• Together, these improvements can considerably reduce the threshold current.

Question 19

Variation of gain with carrier density (𝑁, in m^-3 ), plot

Answer 19

Question 20

Eq: Dependence of on temperature

Answer 20

𝐼 = Ae^𝑇/𝑇₀

where 𝑇₀ is the characteristic temperature (in K)

Question 21

Semiconductor FP laser spectrum

Answer 21

• Fabry-Perot lasers can lase in several longitudinal modes simultaneously
• They may be single-longitudinal mode (typically at higher output power)
• Mode hops can occur as the current is increased. This is when the dominant mode can switches from one wavelength to another as current increases.
• Each longitudinal mode can have a very narrow linewidth (a few MHz)

Question 22

Semiconductor laser light-current characteristic: Effect of facet reflectance on LI

Answer 22

• Increasing R reduces 𝑔_th , so reduces 𝐽_th and 𝐼_th
• Increasing R reduces slope efficiency

Question 23

Semiconductor laser light-current characteristic: Effect of cavity length

Answer 23