Understanding Lasers: Chapter 10 Quiz

Source: Jeff Hecht, Understanding Lasers: An Entry-Level Guide, fourth edition (2019), Chapter 10 quiz, printed pages 395–398. The questions are paraphrased.

Quick answers

Question

Answer

1

b, direct-bandgap semiconductor

2

a, InGaAsP

3

c, 40% Ga, 10% Al, 50% As

4

d

5

b

6

e, all listed structures

7

d, VCSEL

8

a, InGaN diode

9

c, \(827\ \mathrm{nm}\)

10

d, distributed feedback

11

e, AlGaN

12

b, AlGaInP

13

e, VCSEL

14

d, stacked arrays

15

e, \(3.1\ \mathrm{eV}\)

Worked reasoning

  1. Efficient diode-laser material: b. A direct bandgap lets an electron and hole recombine while conserving crystal momentum and emitting a photon. Indirect-gap materials usually lose energy nonradiatively through phonons.

  2. Quaternary III–V compound: a. InGaAsP contains four elements, all drawn from periodic-table groups III and V. GaAlAs is ternary and GaAs is binary.

  3. Atomic fractions in Ga0.8Al0.2As: c. One formula unit contains \(0.8+0.2+1=2\) atoms in normalized proportions. Therefore

    \[x_{\mathrm{Ga}}=\frac{0.8}{2}=40\%,\quad x_{\mathrm{Al}}=\frac{0.2}{2}=10\%,\quad x_{\mathrm{As}}=\frac{1}{2}=50\%.\]

  4. Exciton: d. It is a bound electron–hole pair: the electron is excited relative to the filled valence band but has not recombined with the hole.

  5. Double-heterostructure advantage: b. Higher-bandgap layers confine injected carriers to the thin active layer, increasing the probability of radiative recombination. They also help confine the optical mode.

  6. Structures possible in GaAlAs: e. The material system supports Fabry–Perot and distributed-feedback edge emitters, VCSELs, and gain chips used in external cavities.

  7. Shortest cavity: d. A VCSEL cavity runs vertically through only a few micrometres of epitaxial material, much shorter than edge-emitter or free-space cavities.

  8. High-definition optical-disc source: a. InGaN diodes emit violet-blue light, whose shorter wavelength focuses to the small spot required for high-density Blu-ray data.

  9. Bandgap wavelength: c. Using \(E(\mathrm{eV})\lambda(\mathrm{nm})\approx1240\),

    \[\lambda=\frac{1240\ \mathrm{eV\,nm}}{1.5\ \mathrm{eV}} =827\ \mathrm{nm}.\]

  10. Single-longitudinal-mode diode: d. A distributed-feedback grating selects one cavity mode across the gain region.

  11. Shortest-wavelength family: e. Wide-bandgap AlGaN reaches farther into the ultraviolet than GaInN, AlGaInP, GaAlAs, or InGaAsP.

  12. Red pointer diode: b. AlGaInP is the standard material family for efficient visible-red diode emission.

  13. Low-threshold, efficient, good-beam source: e. VCSELs combine a tiny active volume with strong mirrors and a circular, low-divergence output mode.

  14. Maximum efficient power without beam-quality priority: d. Stacking multiple diode arrays combines many broad emitting stripes and scales total power, at the cost of poorer spatial quality.

  15. Energy of a 400-nm photon: e.

    \[E=\frac{1240\ \mathrm{eV\,nm}}{400\ \mathrm{nm}} =3.10\ \mathrm{eV}.\]

    Check: a shorter wavelength than \(1240\ \mathrm{nm}\) must have more than \(1\ \mathrm{eV}\) of energy.