Understanding Lasers: Chapter 6 Quiz
Source: Jeff Hecht, Understanding Lasers: An Entry-Level Guide, fourth edition (2019), Chapter 6 quiz, printed pages 213–216. The questions are paraphrased.
Quick answers
Question |
Answer |
|---|---|
1 |
d in the printed key; b under the book’s taxonomy |
2 |
c |
3 |
d |
4 |
e |
5 |
d |
6 |
b |
7 |
e |
8 |
a |
9 |
d, mode locking |
10 |
b, about \(24\ \mathrm{fs}\) |
11 |
e, \(441\ \mathrm{ns}\) |
12 |
a, \(532\ \mathrm{nm}\) |
Worked reasoning
Excluded from the book’s solid-state-laser category: d. The neodymium-doped glass slab is actually a solid-state laser material, so the printed key’s selection of d appears inconsistent with both the chapter and standard terminology. A gallium-arsenide diode, b, is normally put in the separate semiconductor laser category used by this book.
Important
Answer-key discrepancy
The printed key says d, but b is the defensible answer under the book’s classification. The slab, fibre, ruby, and Nd:YVO4 choices are all solid-state gain media.
Dielectric: c. In this context it is a transparent, electrically insulating crystal. Dielectrics polarize in an electric field but do not conduct current like metals.
Not a diode-pump advantage: d. Diodes are efficient, wavelength matched, and easy to couple to fibres, but flashlamps can deliver much higher single-pulse energy.
Requirement for electrical pumping: e. Current must pass through the gain material, so electrical conductivity is essential.
Laser oscillator condition: d. A resonant cavity must have enough round-trip gain to replace internal loss and useful output coupling:
\[G_{\mathrm{rt}}\ge L_{\mathrm{internal}}+L_{\mathrm{output}}.\]Optical amplifier: b. Stimulated emission amplifies a signal in one or more passes without requiring resonant feedback.
Wavelength-multiplexed capacity: e. Every channel lying within the amplifier gain band can be amplified simultaneously, subject to saturation and gain-flatness limits.
Q switching: a. A low-cavity-Q state suppresses oscillation while the pump stores energy in the upper level. Switching to high Q releases that stored energy as a short, energetic pulse.
Shortest pulses: d. Mode locking fixes the phase relationship among many longitudinal modes, so they add into ultrashort pulses.
Transform-limited 40-nm-bandwidth pulse: b. First convert wavelength bandwidth near \(800\ \mathrm{nm}\) to frequency bandwidth:
\[\Delta\nu\approx\frac{c\,\Delta\lambda}{\lambda^2} =\frac{(2.998\times10^8)(40\times10^{-9})} {(800\times10^{-9})^2} =1.87\times10^{13}\ \mathrm{Hz}.\]For a transform-limited Gaussian pulse,
\[\Delta t\approx\frac{0.441}{\Delta\nu} =2.35\times10^{-14}\ \mathrm s\approx24\ \mathrm{fs}.\]One-megahertz bandwidth pulse: e. The same time-bandwidth product gives
\[\Delta t\approx\frac{0.441}{10^6\ \mathrm{Hz}} =4.41\times10^{-7}\ \mathrm s=441\ \mathrm{ns}.\]Frequency-doubled Nd:YAG: a. Doubling frequency halves wavelength: \(1064/2=532\ \mathrm{nm}\).