Photonics Exam Deck

Question 1

Topic 2: The real and imaginary parts of the complex relative permittivity of a material at a wavelength of 0.65 µm are 19.72 and 2.56, respectively. Find the complex refractive index. What is the power loss coefficient?

Answer 1

Question 2

Topic 2: Snell’s Law and evanescent wave form

Answer 2

Note how the equation for cosθ_t s changed with the deduction that the square root will be negative knowing that the incidence angle is greater than the critical angle.

Also note how the propagation constant can take more than direction. Direction of oscillation of the e-field, y, is zero in this case.

Question 3

Topic 3: Could Al_0.5Ga_0.5As be used for the active layer of an LED? Give your reasons.

Answer 3

No – this composition of AlGaAs does not have a direct bandgap, since x > 0.43.

Question 4

Topic 3: . What are the advantages of using a quaternary alloy such as InGaAsP?

Answer 4

The InGaAsP system allows alloys with a wide range of compositions and a wide range of bandgap energies to be grown. Using a quaternary alloy allows independent control of 𝐸𝑔 and the lattice constant (making it possible to lattice match to InP substrates, for instance).

Question 5

Topic 4: What are the essential conditions for lasing to occur?

Answer 5

For lasing, we need gain and feedback. Gain is obtained when there is net stimulated emission, which requires population inversion. Feedback can be provided by, for example, placing the gain medium in a Fabry-Perot etalon

Question 6

Topic 4:

(a) If the laser in the previous question operates at a wavelength of 1300 nm, find the number of wavelengths in a round trip of the cavity (i.e. find the integer ). Assume a refractive index of 3.5.
(b) What is the longitudinal mode spacing in nm?

Do b) - what do you need to remember?

Answer 6

Differentiate f = c/𝜆

Question 7

Topic 4: The threshold current of a semiconductor laser is 20 mA and its slope efficiency is 0.3 W.A^-1 . What is the output power at a drive current of 70 mA?

Answer 7

The output power will be approximately zero at the threshold drive current, then will increase linearly with the additional current above threshold, with the slope give by the slope efficiency. Drive current of 70 mA is 50 mA above threshold, so the output power at 70 mA will be 70 × 0.3 = 𝟐𝟏 mW.

Question 8

Topic 4: The lecture notes show the LI plots for a laser at 0, 25 and 50 C. Estimate the characteristic temperature of this laser.

Answer 8

Estimating the threshold currents at 0°C and 50°C to be 47 mA and 62 mA respectively, we can find 𝑇0 as follows:

Using a rearranged form of the attached equation (with T₁ an T₂ representing the threshold currents).

𝑇0 = (50 − 0) / ln ( 62 / 47) = 𝟏𝟖𝟎 K

Question 9

Topic 4: Explain why a three-level system is required to achieve population inversion in an optically pumped solid-state laser. What additional advantage is provided by using a four-level system?

Answer 9

• 2 level system
  
  • for rate of absorption from level 1 to level 2 and rate of stimulated emission from level 2 to level 1, the Einstein B coefficients are the same
  • processes are equally likely, prevent 𝑁2 becoming greater than 𝑁₁
  • not actually possible to achieve population inversion
• 3 level system
  
  • pumping occurs to a higher energy state E₃, from which the particles rapidly decay to a relatively long-lived (metastable) state E₂
  • population inversion can be achieved between E₂ and E₁
  • Problem:
    
    • takes time to achieve the population inversion – at least half the particles originally in state E₁ must be pumped to E₂ via E₃
    • Thus lasing cannot begin immediately once pumping starts.
• 4-level system
  
  • Avoids problem of 3-level system,
    
    • pumping from a ground state E₀ which has a lower energy than E₁.
    • If E₁ is initially nearly empty, then as soon as particles are pumped to E₂ via E₃, population inversion is achieved and lasing can occur.
    • To maintain population inversion, particles in energy state E₁ need to rapidly decay back to the ground state E₀
      
      • _​ So that the number of particles in E₁ is kept low

Question 10

Topic 4: Using diagrams, explain the main differences between an LED and a semiconductor laser in terms of (a) their light-current characteristics, and (b) their output spectra.

Answer 10

• (a)
  
  • The light output from an LED is just due to spontaneous emission, so will increase approximately linearly with drive current (but probably curving slightly down, particularly at high drive currents).
  • Lasers emit spontaneous photons below threshold, but once the threshold current is reached, stimulated emission dominates, and the light output increases linearly from the threshold current.
• (b)
  
  • The spectrum of an LED will be quite broad (maybe 20 nm full-width at half maximum), because spontaneous emission can occur from a range of energies in the conduction band (and, to a lesser extent, to a range of energies in the valence band).
  • Lasers (specifically Fabry-Perot lasers) will emit in one or a few narrow spectral lines. Although stimulated emission can occur at a range of wavelengths, due to the distribution of energy states within the conduction and valence bands (so similar to the range of spontaneous emission in an LED), the lasing threshold will be reached first close to the peak emission wavelength, and once reached, the carrier density will be clamped, preventing other modes from reaching threshold. Thus, only one longitudinal cavity mode (corresponding to the round-trip gain and phase conditions being met) should lase.
    
    • In practice, the carrier density may not be completely clamped above threshold, allowing other modes to lase.

Question 11

Topic 4: What do you need to remember about applying the power conversion efficiency equation to semiconductor lasers?

Answer 11

They might ive you the output power but you need to remember that there are two facets, and both facets give the same output.

Thus output power in the PCE equation should be 2x

Question 12

Topic 4: A buried heterostructure semiconductor laser emitting at a wavelength of 1550 nm is 400 µm long and has a waveguide cross-section area of 0.3 µm x 1 µm. Both facets have a reflectance of 30%. Find the threshold carrier density if the power loss coefficient, 𝜶, is 20 cm^-1 , and the gain coefficient is given by 𝒈(𝑵) = 𝟐 × 𝟏𝟎^−𝟏𝟔(𝑵 − 𝟏. 𝟓 × 𝟏𝟎^𝟏𝟖) cm^-1 (where 𝑵 is the number of carriers per cm³ ). Estimate the photon density in the laser cavity when the output power Drive Threshold current Output Power Laser LED Wavelength Output Power Laser LED from each facet is 5 mW (assume a refractive index of 3.5). How many photons are there in the laser cavity?

Answer 12

Question 13

Topic 4: A 1.55 µm laser with a cavity length of 600 µm lases with a multi-longitudinal-mode spectrum with full width at half maximum (FWHM) of 2 nm. Estimate the number of cavity modes in the laser spectrum. (Assume a refractive index of 3.5.)

Answer 13

The mode spacing in frequency is Δ𝑓 = 𝑐/(2𝑛𝐿) = 71.4 GHz = 0.57 nm (1 nm = 125 GHz at 𝜆 = 1.55 µm). Assuming a roughly triangular spectrum, the total width is 4 nm. So there are approximately 4/0.57 = 7 lasing modes

Question 14

Topic 4: Explain the advantages of index guiding (as in a buried heterostructure laser) over gain guiding (as in a simple stripe contact laser).

Answer 14

• In a buried heterostructure, the stripe of active material is surrounded on all sides by lower refractive index material, forming a dielectric waveguide. The index guiding ensures the light is tightly confined in the active material, and that the mode distribution doesn’t change as the drive current is varied. The buried heterostructure also has a well-defined active region, through which the injected current flows uniformly. Altogether, these factors result in lower threshold current and higher slope efficiency, and enable stable emission to higher output powers.
• In a gain guided laser, the active region width depends on the area through which the current flows, since this is where there will be optical gain (hence gain guiding). The current spreads out below the strip contact, meaning that the gain region under the stripe is wider than the stripe, and the current density varies laterally under the stripe, so the active region width is not very well defined. As a result, the threshold current will be higher than would be calculated based on the stripe width, and efficiency is lower. The carriers injected into the gain region cause a small change in refractive index, which provides some weak index guiding, but this will vary with drive current, which can lead to instability in the operation of the laser.

Question 15

Topic 6: A semiconductor heterostructure waveguide has 𝒏_𝟏 = 3.50 and 𝒏_𝟐 = 𝟑. 𝟒𝟗. What is the maximum waveguide width for single-mode operation at a wavelength of 0.85 µm?

Answer 15

Question 16

Topic 6: By considering the graphical method of solving for the modes of the symmetrical slab waveguide, estimate the number of modes in terms of the V parameter. Hence estimate the number of modes that can be supported by a 50 µm wide slab waveguide with 𝒏_𝟏 = 𝟏. 𝟒𝟓𝟎 and 𝒏_𝟐 = 1.435 at a wavelength of 1 µm.

Answer 16

Question 17

Topic 7: What is the bit period for a 6.25 Gb/s OOK RZ signal? If the pulse width is 𝑻_𝒃/𝟒, at what frequency from the carrier is the first null in the spectrum?

Answer 17

𝑇_𝑏 = 1/𝑅_𝑏 = 160 ps. Pulse width = 40 ps. First null in spectrum is at 1/(pulse width) = 25 GHz.

Question 18

Topic 7: Calculate the loss and output power after 100 km of standard fibre at wavelengths of 1.55 µm and 1.3 µm. Assume Pin= 5 mW.

Answer 18

5 mW = 7 dBm.

At 1.55 μm, loss = 0.2 dB/km x 100 km = 20 dB; output power = -13 dBm (0.05 mW).

At 1.3 μm, loss = 0.5 dB/km x 100 km = 50 dB; output power = -43 dBm (0.05 μW).

Question 19

Topic 7: A 10 Gb/s optical communications system operates at a wavelength of 1.55 µm. Estimate the width of a pulse representing an isolated binary “1” after 100 km of standard fibre if raised cosine pulse shaping with 𝜶 = 0.8 is used.

Answer 19

Assume the bandwidth of the signal is limited to 20 GHz (i.e. the central lobe of the spectrum).

At 1.55 μm, 1 nm = 125 nm, so Δ𝜆 = 20/125 = 0.16 nm.

Δ𝑡 = 𝐿. Δ𝜆.𝐷 =100 x 0.16 x 17 = 272 ps. Assuming this spreading adds to the original pulse, the pulse width after 100 km is 372 ps.

Question 20

Topic 7: Look over the rest of the questions!

Answer 20

Question 21

Explain the terms direct and indirect bandgap semiconductor with the aid of diagrams. Which type Should be used ‘as the active region of a light-emitting diode (LED)? State the reasons for your answer.

Answer 21

In a direct band gap semiconductor, the top of the valence band and the bottom of the conduction band occur at the same value of momentum.

In an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different value of momentum to the minimum in the conduction band energy.

Question 22

An LED is fabricated from the semiconductor layer structure illustrated in Figure 1.1:

Answer 22

b) The LED will emit light close to the bandgap wavelength of GaAs, i.e. at about 870 nm.
c) The advantages are: good carrier confinement; high injection efficiency; no re-absorption losses in AlGaAs; produces a guided wave structure because refractive index of AlGaAs is less than that of GaAs.

Question 23

Define the terms internal and external quantum efficiency for light generation in a semiconductor p-n junction. What factors determine each of these efficiencies?

Answer 23

• The internal quantum efficiency is the ratio of the radiative recombination rate to the sum of the radiative and non-radiative recombination rates.
  
  • Depends on the radiative and non-radiative carrier lifetimes
    
    • Determined by factors such as:
      
      • is material direct or indirect bandgap,
      • carrier injection level
      • doping concentration
      • impurity concentration
      • crystal defects (e.g. at hetero-interfaces).
• The external quantum efficiency is the ratio of the number of photons emitted to the number of carriers crossing the junction.
  
  • Depends on internal quantum efficiency,
  • Depends on factors that determine whether the generated photons are absorbed before they are emitted (e.g. half will be lost into substrate, absorption in capping layers, reflection from semiconductor-air interface, total internal reflection at some angles).

Question 24

With the aid of a schematic diagram, briefly describe the three main band-to-band electronic transitions that you might expect to occur in a simple two-level energy system. Your schematics should clearly indicate which processes require an incoming radiation wave.

Answer 24

• a)
  
  • Absorption of photons, where a photon excites a system from a lower energy state (𝐸₁ in the diagram) to a higher energy state (𝐸₂), e.g. a photon excites an electron from the valence band to the conduction band in a semiconductor.
• b)
  
  • Spontaneous emission, where a system moves randomly from a higher to a lower energy state (i.e. 𝐸₂ to 𝐸₁ in the diagram), giving off a photon in the process (an example is an EHP recombining in a semiconductor).
• c)
  
  • stimulated emission, involves an incoming photon causing (stimulating) a system in a higher energy state to lose energy and give off a new photon, without the original photon being absorbed. Photon generated in this stimulated emission process is identical to the incoming photon, that is, it has the same frequency (energy), phase, and direction as the incoming photon.

Question 25

Show that one of the conditions for lasing to occur in a cavity formed by two parallel reflectors leads to the requirement that the gain in the laser cavity is given by:

Answer 25

Question 26

State, giving your reasons, whether you would expect the threshold current of a semiconductor laser to increase or decrease if: (i) The length of the laser cavity is increased. [2 marks] (ii) Coatings of dielectric material are deposited on the laser facets to reduce their reflectivity [2 marks]

Answer 26

(i) If 𝐿 is increased, the threshold gain is reduced, and the threshold current density will be reduced, but less, in proportion, than the length, because of the form of the gain vs carrier density relationship. But the threshold current depends on the length in direct proportion. Therefore, the overall effect will be to increase the threshold current.
(ii) If 𝑅 is reduced, the threshold gain is increased. Hence the carrier and current densities at threshold will be higher, and the threshold current will be increased.

Question 27

The threshold current of a semiconductor laser is 20 mA at an operating temperature of 20ºC. If the laser has a characteristic temperature 𝑇₀ of 100K, what will the threshold current be at 75ºC?

Answer 27

Question 28

How do you conert dBm to watts

Answer 28

dBm= 10log(p1/.001)

remember not to conver dBm to ‘dB’, just plug into the equation as is.

Question 29

What are the design guidelines for a pin photodiode with respect to bandwidth?

What areas are of concern?

Answer 29

• thin p-layer → diffusion time 𝑡_𝑑<< 1/B
• intrinsic layer width → drift time 𝑡_𝑐< 1 / (2B)
• junction capacitance (PD area) → 𝑡_RC< 1 / (2πB)
• Note: there is a trade-off between junction capacitance (𝑡_RC) and drift time (t_c)

Question 30

Q-parameter

Answer 30

Question 31

NRZ

Answer 31

Question 32

Calculate the carrier drift time given that the length of the depletion region is 10 μm and the mobility is 0.85 m²V^-1s^-1 for a bias voltage of 3 V. What -3-dB bandwidth does this drift time correspond to? What other factors will affect the bandwidth of the pin photodiode?

[9 marks]

Answer 32

Question 33

Sketch and carefully label a diagram showing the structure of a pin photodiode. Explain the function of each labeled part and indicate where the absorption of photons should occur for optimum detection efficiency.

[8 marks]

Answer 33

Question 34

State what the symbols w and (J represent, and explain what is meant by the terms phase velocity and group velocity.

Answer 34

Question 35

Light-emitting diodes (LEDs) and semiconductor lasers are usually fabricated from III-V semiconductor alloys. Explain what is meant by a III-V semiconductor alloy, and give an example of a III-V alloy system. What characteristics make these materials particularly well suited to photonic devices?

Answer 35

5(a) A semiconductor alloy is a mixture of two or more binary III-V alloys, such as GaAs and AlAs giving AlGaAs (other examples include GaAsP, InGaN, and InGaAsP).

These allow semiconductors to be grown with a range of direct bandgap energies that correspond to visible or near infra-red light. Changing the alloy composition allows the bandgap energy to be varied while the lattice constant is kept the same, allowing lattice-matched epitaxial growth on GaAs or InP substrates.

Question 36

Do b) ii)

Answer 36

Question 37

Longitudinal modes

Answer 37