Lasers and Optical Pumping Questions and Answers

Answer: D

The transitions are (00°1) \(\rightarrow\) (02°0) and (00°1) \(\rightarrow\) (10°0).

The vibrational levels of CO\(_{2}\) are labelled (\(v_{1}v_{2}^{l}v_{3}\)) for the symmetric stretch, the bend and the asymmetric stretch. Nitrogen in the discharge excites the upper laser level, (00°1), one quantum of the asymmetric stretch. From it there are two laser transitions:

• to (10°0), the symmetric stretch: about 10.6 \(\mu\)m, the main line;
• to (02°0), the bending overtone: about 9.6 \(\mu\)m.

Option B pairs the same two transitions with the wavelengths in the opposite order to the question's (9.6 then 10.6). Options A and C describe the relaxation of the lower levels through the bending mode down to the ground state, which empties the lower level but is not the laser emission.

Answer: B

The coherence length is inversely proportional to the width of the spectral line.

The coherence time of a source is roughly the inverse of its frequency bandwidth, and the coherence length is the distance light travels in that time:

\[ \begin{aligned} L_{c} &= c\,\tau_{c} \approx \frac{c}{\Delta\nu} \\ &= \frac{\lambda^{2}}{\Delta\lambda} \end{aligned} \]

A laser's very narrow line therefore gives a long coherence length, metres or more, compared with micrometres for white light.

Direct proportionality to the line width has the relation upside down. The length of the active medium affects gain and mode spacing, not the coherence length directly, so neither option involving it is correct.

Answer: A

The laser transition takes place in Ne only.

In a He-Ne laser, the discharge excites helium atoms to metastable levels. Because these lie very close in energy to neon's 3s and 2s levels, collisions transfer the energy to neon, producing a population inversion in neon. The lasing transitions, such as 632.8 nm (3s to 2p), are all between neon levels.

Helium only pumps; it does not emit the laser light. So 'He only' and the two-stage options are wrong.

Answer: B

Laser emission is due to the \(E_{2} \to E_{1}\) transition.

Stimulated emission outweighs absorption on a transition only when the upper level is more populated than the lower one, a population inversion. Here \(N_{2} \gt N_{1}\), so the \(E_{2} \to E_{1}\) transition is inverted and can lase. This is the usual three-level scheme: atoms are pumped to \(E_{3}\), drop quickly to the metastable level \(E_{2}\), and lase to the ground level \(E_{1}\).

\(E_{3} \to E_{1}\) cannot lase because \(N_{3} \lt N_{1}\). \(E_{1} \to E_{3}\) is an upward transition, that is absorption (pumping), not emission, which rules out the options containing it.