Understanding Lasers: Chapter 14 Quiz

Source: Jeff Hecht, Understanding Lasers: An Entry-Level Guide, fourth edition (2019), Chapter 14 quiz, printed pages 540–542. The questions are paraphrased.

Quick answers

Question

Answer

1

c

2

a

3

a

4

d

5

b

6

c, surface plasmons

7

a, \(1\ \mathrm{mJ}\)

8

No listed answer; characteristic size about \(1\ \mathrm{\mu m}\)

9

e, \(0.170\ \mathrm{mrad}\)

10

a, about \(6\ \mathrm{mm}\)

Worked reasoning

  1. Doppler-free spectroscopy: c. Counterpropagating beams address atoms with opposite Doppler shifts. Selecting the common response cancels first-order Doppler broadening without physically stopping every atom.

  2. Frequency-comb source: a. A periodic train of phase-coherent short pulses has a Fourier spectrum of evenly spaced narrow frequency teeth.

  3. Laser cooling: a. Properly detuned light is preferentially absorbed by atoms moving toward a beam. Repeated absorption and random re-emission remove net momentum and kinetic energy.

  4. Bose–Einstein condensate: d. Below the critical temperature, a macroscopic fraction of bosonic atoms occupies the same lowest quantum state.

  5. Gravitational-wave detection: b. Long laser interferometers compare optical path lengths to detect extraordinarily small relative motions of suspended end mirrors.

  6. Subwavelength nanolaser: c. Surface plasmons are collective electron oscillations confined near a metal–dielectric boundary and can support optical modes smaller than the free-space diffraction volume.

    Important

    Answer-key discrepancy

    The printed key selects b, but Section 14.8 explains that quantum-dot lasers are larger devices whose active layers contain one or more dots; they are not made by forcing a single electron to oscillate. Section 14.8.3 explicitly identifies surface-plasmon devices as capable of operating in less than a cubic wavelength, so c is supported by the chapter itself.

  7. Petawatt for one attosecond: a.

    \[E=P\Delta t=(10^{15}\ \mathrm W)(10^{-18}\ \mathrm s) =10^{-3}\ \mathrm J=1\ \mathrm{mJ}.\]

  8. Spot for :math:`10^{23}mathrm{W/cm^2}`: no listed answer. Required area is

    \[A=\frac{P}{I}=\frac{10^{15}\ \mathrm W} {10^{23}\ \mathrm{W/cm^2}} =10^{-8}\ \mathrm{cm^2}.\]

    A square spot would have width \(\sqrt A=10^{-4}\ \mathrm{cm}=1\ \mathrm{\mu m}\); an equal-area circular spot would have diameter \(1.13\ \mathrm{\mu m}\).

    Important

    Answer-key discrepancy

    None of the choices is near \(1\ \mathrm{\mu m}\). The printed key selects e, \(0.03\ \mathrm{mm}\), which would produce only about \(10^{20}\ \mathrm{W/cm^2}\) for a one-petawatt beam. The key and the stated \(10^{23}\ \mathrm{W/cm^2}\) cannot both be correct.

  9. Mars-to-Earth divergence: e. To cover Earth’s diameter at distance \(L\),

    \[\theta\approx\frac{D_E}{L} =\frac{12{,}800\ \mathrm{km}}{75\times10^6\ \mathrm{km}} =1.71\times10^{-4}\ \mathrm{rad}=0.171\ \mathrm{mrad}.\]

  10. Diffraction-limited mirror: a.

    \[D\approx\frac{\lambda}{\theta} =\frac{1.0\times10^{-6}\ \mathrm m}{1.71\times10^{-4}} =5.85\times10^{-3}\ \mathrm m\approx6\ \mathrm{mm}.\]

    Substitution back into \(\theta\approx\lambda/D\) returns the required \(0.17\ \mathrm{mrad}\) divergence.