Gas Lasers

A gas laser is where four ideas from earlier in this chapter are forced to work together in one glowing tube. It needs a population inversion on a real atomic or molecular transition; it lives on stimulated emission, whose gain per unit length must out-run the losses; it almost always realises a four-level scheme, so a modest pump holds more atoms up than down; and it sits inside an optical resonator whose longitudinal and transverse modes decide the spectrum and beam. What makes the gas medium special is dilution: the active atoms fly past one another as an ideal gas at a fraction of an atmosphere, barely perturbing each other's levels, so the emission wavelength is set by the internal quantum structure of a single atom, ion, or molecule — not by any host lattice — and it is astonishingly sharp. Because the medium is thin and clean, the physics separates too. The wavelength is quantised by the level scheme; the linewidth is set almost entirely by the thermal Doppler motion of the emitters, a Gaussian a few gigahertz wide; and the pumping is done by an electrical discharge — a current of electrons that dumps energy into the gas by inelastic collisions, often through an intermediary that stores it and hands it off resonantly. Three families run the show: neutral-atom lasers (helium–neon), ion lasers (argon-ion), and molecular lasers (CO₂). The same handful of equations — Doppler width, gain, threshold, mode spacing, quantum defect — describes them all, and the numbers explain why a red He–Ne is feeble but perfect while a CO₂ laser cuts steel.

Key takeaways

A gas laser amplifies light in a dilute gas or vapour — neutral atoms, ions, or molecules — pumped almost always by an electrical discharge whose energetic electrons collisionally excite the active species, often via an energy-transfer intermediary.
Helium–neon is the archetype: helium metastables store discharge energy and transfer it near-resonantly to neon, which lases at 632.8 nm on a four-level scheme; a typical tube emits only milliwatts, but with superb beam quality.
Argon-ion lasers excite Ar⁺ for high-power visible lines (488.0, 514.5 nm); CO₂ lasers use vibrational–rotational transitions near 10.6 μm at up to ≈20% wall-plug efficiency.
Because the medium is dilute, the line is Doppler-broadened (inhomogeneous) to a few GHz, so several longitudinal modes — spaced by the free spectral range c/2L — usually oscillate at once.
The wavelength is fixed by discrete levels; the efficiency by kinetics and the quantum defect — He–Ne wastes ≈90% of the excitation energy, CO₂ keeps ≈40%.
Key idea: in a gas laser the dilute, internally structured medium fixes the emission wavelength by discrete atomic, ionic, or molecular levels while Doppler motion sets the linewidth, and electrical-discharge pumping — usually via a resonant energy-transfer partner — supplies the population inversion.

The core insight

In a gas laser the gain medium is dilute and internally structured, so the emission wavelength is fixed by discrete atomic, ionic, or molecular levels while the linewidth is set by Doppler motion; electrical-discharge pumping, often through an energy-transfer intermediary, creates the required population inversion.

Where this lives today

The helium–neon laser still turns up wherever a cheap, stable, near-diffraction-limited red beam is wanted: in survey instruments and laser levels, in the reference arm of metrology interferometers, and historically in barcode scanners and the alignment of machines like accelerators. Iodine-stabilised He–Ne lasers, locked to a hyperfine saturated-absorption feature, remain a recommended practical realisation of the metre — a portable length standard traceable to the SI second. At the high-power end the CO₂ laser is the industrial workhorse: sealed and flowing-gas versions from tens of watts to many kilowatts cut, weld, and engrave metals, acrylics, wood, and textiles, while medical CO₂ lasers exploit water's 10.6 μm absorption for tissue ablation. Argon-ion lasers — once the standard pump for dye and Ti:sapphire systems and the source in confocal microscopes — have largely yielded to diode-pumped and semiconductor sources, but the physics they pioneered, from resonant energy transfer to Doppler-limited mode structure, is exactly what every modern laser designer still reasons with.

The physical picture

Picture a low-pressure tube as a swarm of independent atoms drifting in the dark. Strike a discharge across it and the light electrons, not the heavy atoms, soak up energy from the field: a hot electron gas rattling inside a cool neutral gas. Every so often an electron slams into an atom and lands it in a specific excited level. If that level is metastable — forbidden to radiate quickly — the atom hoards the energy. Now bring in a second species whose upper laser level sits at almost the same height: when a metastable atom collides with it, the energy hops across near-resonantly, filling the upper laser level while leaving the lower one nearly empty. That is population inversion bought cheaply, and it is the whole secret of the helium–neon laser — helium collects, neon lases.

Figure

Helium–neon kinetics: an electron discharge pumps He to the 2³S₁ and 2¹S₀ metastables, which transfer energy near-resonantly with ΔE ≈ 0.05 eV to the Ne 3s₂ and 2s₂ levels; the 3s₂ → 2p₄ drop emits the 632.8 nm red line, then fast spontaneous decay to 1s and wall collisions empty the lower level

Because the atoms scarcely interact, each radiates its clean natural line — but they are moving. An atom drifting toward you emits a slightly higher frequency, one drifting away a lower one, and the Maxwell–Boltzmann spread of velocities smears the line into a Gaussian a few gigahertz wide. This is inhomogeneous (Doppler) broadening: different atoms sit at different places under the curve according to their speed. The resonator then acts as a comb, picking out only the frequencies that fit an integer number of half-wavelengths between the mirrors — the longitudinal modes, spaced by c/2L. Whichever comb teeth fall under the gain curve and clear the loss line oscillate; for an ordinary He–Ne that is a few at once, which is why it is bright and red but not single-frequency.

Figure

Doppler gain curve and cavity modes for a 30 cm He–Ne tube: the neon gain is a Gaussian of FWHM Δν_D ≈ 1.5 GHz, the longitudinal modes are combed at spacing Δν_FSR = c/2L = 500 MHz, and only the three modes rising above the threshold line oscillate

Efficiency, though, is decided by the kinetics and geometry of the level ladder, not by optics. In CO₂ the nitrogen molecule plays helium's role: N₂ vibrations are nearly resonant with the CO₂ upper vibrational level, so a discharge full of vibrationally hot N₂ pumps CO₂ superbly. And the CO₂ laser transition connects two vibrational levels only a fraction of an electron-volt apart, so the photon keeps a large slice of the energy invested — the quantum defect is tiny. That single fact is why CO₂ lasers reach wall-plug efficiencies near 20% while He–Ne languishes below 0.1%.

The core equations

At low pressure the dominant line-broadening mechanism is the thermal motion of the emitters, so the gain bandwidth follows from the Maxwell velocity distribution and the linear Doppler shift. The result is a Gaussian whose FWHM grows with temperature and shrinks with emitter mass — the key number for predicting how many cavity modes oscillate.

\Delta\nu_D = \frac{\nu_0}{c}\sqrt{\frac{8\,k_B T \ln 2}{M}} \qquad (1)

where: $\Delta\nu_D$ — FWHM of the Doppler-broadened line; $\nu_0$ — line-centre transition frequency; $c$ — speed of light; $k_B$ — Boltzmann constant; $T$ — gas temperature; $M$ — emitter mass. Physical reading: lighter, hotter emitters move faster, so their lines are broader; for neon on the red line at a few hundred kelvin this is about 1.5 GHz — a thousand times the natural linewidth. The inversion in a helium–neon laser is not made by electron impact on neon; it is delivered by a collision of the second kind, in which an excited helium atom de-excites and simultaneously excites a neon atom whose level lies at almost the same energy. The near-resonance of the reaction below is why the specific He/Ne mixture matters.

\mathrm{He}^*(2\,^3S_1,\ 2\,^1S_0) + \mathrm{Ne} \;\rightarrow\; \mathrm{He} + \mathrm{Ne}^* + \Delta E \qquad (2)

where: $\mathrm{He}^*$ — metastable helium in the $2\,^3S_1$ (19.82 eV) or $2\,^1S_0$ (20.61 eV) state; $\mathrm{Ne}^*$ — neon raised to its $3s$ or $2s$ upper laser levels; $\Delta E$ — the small (≈0.05 eV) mismatch, carried off as kinetic energy. Physical reading: the metastables are long-lived reservoirs that make the transfer efficient; only levels within about $k_B T$ of resonance are filled, which selects the neon upper levels so cleanly. Whether that inversion amplifies light is decided by the gain coefficient, the fractional growth of intensity per unit length. It scales with inversion density and lineshape — and because the lineshape is normalised, a broader line means lower peak gain for the same inverted atoms.

g(\nu) = \frac{\lambda^2}{8\pi n^2}\,\frac{A_{21}}{1}\,\Delta N\,\hat g(\nu) \qquad (3)

where: $g(\nu)$ — gain per unit length; $\lambda$ — vacuum wavelength; $n$ — refractive index (≈1 in a gas); $A_{21}$ — spontaneous emission rate; $\Delta N = N_2 - (g_2/g_1)N_1$ — inversion density; $\hat g(\nu)$ — normalised lineshape (Doppler Gaussian, peaking at $\hat g(\nu_0)\approx 1/\Delta\nu_D$ ). Physical reading: gain is bought with inversion but diluted by bandwidth — which is why narrow-line, long-lifetime gas transitions reach threshold most easily. Oscillation begins only when a wave, after a full round trip, returns at least as strong as it left. Balancing round-trip gain against internal loss and output-mirror loss gives the threshold gain — the value $g(\nu_0)$ must reach to lase.

g_{\text{th}} = \alpha_{\text{loss}} + \frac{1}{2L}\ln\!\frac{1}{R_1 R_2} \qquad (4)

where: $g_{\text{th}}$ — gain needed to oscillate; $\alpha_{\text{loss}}$ — distributed internal loss per unit length; $L$ — cavity length; $R_1,R_2$ — mirror power reflectivities. Physical reading: the logarithm is the output coupling; He–Ne gain is so feeble ( $g_{\text{th}}\sim10^{-3}\,\text{cm}^{-1}$ ) that tubes are long and mirrors reflect above 99%. The resonator only supports frequencies that fit a whole number of half-wavelengths between the mirrors. Adjacent longitudinal modes are equally spaced by the free spectral range — the quantity that tells us how many modes crowd under the gain curve.

\Delta\nu_{\text{FSR}} = \frac{c}{2L} \qquad (5)

where: $\Delta\nu_{\text{FSR}}$ — free spectral range, the spacing of adjacent cavity modes; $c$ — speed of light; $L$ — cavity length. Physical reading: a longer cavity packs the modes closer — a 30 cm tube spaces them by 500 MHz, a 1 m tube by 150 MHz. Dividing the Doppler bandwidth by this spacing, $N_{\text{modes}}\approx\Delta\nu_D/\Delta\nu_{\text{FSR}}=2L\Delta\nu_D/c$ , counts how many modes oscillate — only when that ratio drops below one (short cavity or intracavity etalon) is the laser single-frequency. Finally, the ceiling on efficiency is set by how much of the pump energy the photon recovers. This quantum-defect efficiency, quite apart from discharge and coupling losses, already separates the molecular lasers from the atomic ones by a wide margin.

\eta_q = \frac{h\nu_{\text{laser}}}{E_{\text{pump}}} \qquad (6)

where: $\eta_q$ — quantum (defect) efficiency; $h\nu_{\text{laser}}$ — emitted photon energy; $E_{\text{pump}}$ — energy invested to reach the upper laser level. Physical reading: CO₂ recovers ≈40% because its levels are close; He–Ne recovers under 10% because the neon upper level sits ≈20 eV up while its photon is worth only 1.96 eV.

Derivation AThe Doppler-broadened lineshape and its width

The goal here is to show, from first principles, why a low-pressure gas line is a Gaussian and to pin down its width — equation (1). We start from two ingredients: the first-order Doppler shift that ties an atom's emission frequency to its line-of-sight velocity, and the Maxwell–Boltzmann distribution of that velocity component. Folding one into the other converts a velocity distribution into a frequency distribution, and reading off the FWHM delivers the factor $\sqrt{8\ln 2}$ that separates a FWHM from a bare standard deviation.

Step 1. An atom whose velocity component toward the observer is $v_z$ emits, in the lab frame, at $\nu = \nu_0\,(1 + v_z/c)$ . Why: the atoms move far slower than light, so only the linear term of the relativistic Doppler formula survives, giving a clean one-to-one map between $v_z$ and the shift $\nu-\nu_0$ .

Step 2. In thermal equilibrium the single velocity component is Gaussian, $P(v_z)\,\mathrm{d}v_z \propto \exp[-M v_z^2/(2k_B T)]\,\mathrm{d}v_z$ . Why: one component of the Maxwell–Boltzmann distribution is exactly a normal distribution of variance $k_B T/M$ — the only statistical input the derivation needs.

Step 3. Substitute $v_z = c\,(\nu-\nu_0)/\nu_0$ into $P(v_z)$ to get $I(\nu)\propto \exp[-Mc^2(\nu-\nu_0)^2/(2k_B T\,\nu_0^2)]$ . Why: because the map from $v_z$ to $\nu$ is linear, the Gaussian in velocity becomes a Gaussian in frequency without distortion — each atom sits at the frequency its own speed dictates.

Step 4. Read off the width. A Gaussian $\exp[-(\nu-\nu_0)^2/2\sigma^2]$ has FWHM $=\sqrt{8\ln 2}\,\sigma$ ; here $\sigma = (\nu_0/c)\sqrt{k_B T/M}$ , so $\Delta\nu_D = (\nu_0/c)\sqrt{8 k_B T\ln 2 / M}$ . Why: half maximum occurs where the exponent equals $-\ln 2$ , and doubling that offset gives the $\sqrt{8\ln 2}\approx2.355$ factor that turns $\sigma$ into the quoted width. *As a check: with $M=20\,u$ , $T=400\,\text{K}$ , and $\nu_0=c/632.8\,\text{nm}$ , equation (1) gives $\Delta\nu_D=1.52\,\text{GHz}$ — the standard value for the neon red line.*

Go deeper · Derivation B · 1 minThe threshold gain from round-trip cavity balance

Derivation BThe threshold gain from round-trip cavity balance

The aim is to derive equation (4) — the gain a gas laser must supply to oscillate — by demanding that the intracavity field reproduce itself after one complete round trip. This is the central stability condition in laser physics: below it the field decays as spontaneous emission, at it round-trip gain exactly cancels round-trip loss, and above it the field grows until saturation clamps the gain back to threshold. The bookkeeping splits the loss into distributed scatter inside the tube and useful coupling out through the mirror.

Step 1. Follow the field through one round trip of length $2L$ : it is amplified by $e^{2gL}$ , attenuated by internal loss $e^{-2\alpha_{\text{loss}}L}$ , and reflected at each mirror by $R_1$ and $R_2$ . Steady state demands $R_1 R_2\,e^{(2g-2\alpha_{\text{loss}})L}=1$ . Why: a self-consistent oscillation must return to the same amplitude and phase after every round trip, so the product of all per-trip factors is exactly unity — less decays, more grows.

Step 2. Take the natural logarithm: $2gL = 2\alpha_{\text{loss}}L + \ln(1/R_1 R_2)$ . Why: the logarithm converts the multiplicative round-trip condition into an additive loss budget, and the mirror term $\ln(1/R_1R_2)$ is the fraction of light lost at the ends.

Step 3. Divide by $2L$ to isolate the required gain, $g_{\text{th}} = \alpha_{\text{loss}} + (1/2L)\ln(1/R_1R_2)$ . Why: sharing the mirror loss over the round-trip length shows why a long tube helps — it spreads a fixed output-coupling loss over more amplifying medium, lowering the gain each centimetre must provide. *As a check: $[g_{\text{th}}]=\text{m}^{-1}$ dimensionally; for $L=30\,\text{cm}$ , a perfect back mirror, and $R_2=0.99$ , $g_{\text{th}}=(1/0.6)\ln(1/0.99)\approx1.7\times10^{-4}\,\text{cm}^{-1}$ , consistent with the low single-pass gain of He–Ne. Equating this to the line-centre gain of equation (3) gives the required inversion $\Delta N_{\text{th}}=(8\pi n^2\tau_{sp}\Delta\nu/\lambda^2)\,g_{\text{th}}$ , which grows with the Doppler width — a broad line dilutes the peak gain and raises threshold.*

Limiting cases

Case	Result	Meaning
Low-pressure neutral-atom (He–Ne)	$p\sim1\,\text{Torr},\ \lambda=632.8\,\text{nm}$	Milliwatt CW, near-diffraction-limited beam; gain only a few percent per pass, so long tubes and $R\gtrsim0.99$ mirrors are essential.
High-current ion (Ar⁺)	$j\gg100\,\text{A cm}^{-2},\ \lambda=488.0,\,514.5\,\text{nm}$	Watts of visible CW; the discharge must both ionise and excite, so it is power-hungry and water-cooled.
Molecular vibrational (CO₂)	$\lambda=10.6\,\mu\text{m},\ \eta\lesssim0.2$	Highest efficiency and multi-kilowatt power; tiny quantum defect and N₂/He kinetics; the workhorse of industrial cutting.
Doppler-limited linewidth	$\Delta\nu_D=\dfrac{\nu_0}{c}\sqrt{\dfrac{8k_BT\ln2}{M}}$	Inhomogeneous broadening dominates at low pressure — GHz bandwidths that enable Lamb-dip stabilisation.
Single longitudinal mode	$\dfrac{2L\Delta\nu_D}{c}\lesssim1$	A short cavity or intracavity etalon leaves one mode under the gain curve — the route to a reference laser.

Worked examples

1 · The neon gain width and mode count (confidence builder)

A helium–neon tube 30 cm long runs on the 632.8 nm neon line with a discharge temperature of about 400 K. Find the Doppler gain bandwidth, the cavity mode spacing, and how many longitudinal modes oscillate.

Step 1. Line-centre frequency: $\nu_0 = c/\lambda = (2.998\times10^8)/(632.8\times10^{-9}) = 4.74\times10^{14}\,\text{Hz}$ ; neon's mass $M = 20\,u = 3.32\times10^{-26}\,\text{kg}$ .

Step 2. Velocity factor: $\sqrt{8k_BT\ln2/M} = \sqrt{(8)(1.381\times10^{-23})(400)(0.693)/(3.32\times10^{-26})} = 960\,\text{m/s}$ . Then $\Delta\nu_D = (\nu_0/c)\times960 = 1.52\times10^{9}\,\text{Hz}$ , i.e. Δν_D ≈ 1.5 GHz.

Step 3. Free spectral range for $L=0.30\,\text{m}$ : $\Delta\nu_{\text{FSR}} = c/2L = (2.998\times10^8)/0.60 = \textbf{500 MHz}$ .

Step 4. Mode count: $N_{\text{modes}} = \Delta\nu_D/\Delta\nu_{\text{FSR}} = 1.52\times10^{9}/5.0\times10^{8} = 3.0$ . About three longitudinal modes oscillate at once — which is why an ordinary He–Ne is not single-frequency without an intracavity etalon or a short cavity.

2 · Quantum defect — why CO₂ sips and He–Ne guzzles

Compare the quantum-defect efficiency of the 632.8 nm He–Ne line (neon upper level ≈20.66 eV above ground) with the 10.6 μm CO₂ line (upper vibrational level ≈0.291 eV above ground).

Step 1. Photon energies from $E = hc/\lambda$ with $hc = 1240\,\text{eV}\,\cdot\,\text{nm}$ . He–Ne: $E = 1240/632.8 = \mathbf{1.96\ eV}$ . CO₂: $E = 1240/10600 = \mathbf{0.117\ eV}$ .

Step 2. He–Ne quantum efficiency: $\eta_q = 1.96/20.66 = 0.095$ , so only about 9.5% of the energy sunk into lifting neon comes back as a photon — the rest is lost climbing 20 eV up.

Step 3. CO₂ quantum efficiency: $\eta_q = 0.117/0.291 = 0.40$ , so roughly 40% of the excitation energy exits as 10.6 μm light — over four times better, on levels sub-electron-volt apart.

Step 4. Fold in the rest of the chain — discharge efficiency, coupling, mode overlap — and the wall-plug numbers separate further still: CO₂ reaches ≈20% while He–Ne stays below 0.1%. Gas-laser efficiency is written into the level diagram before a single mirror is aligned.

Physics of the portrait

The gas laser is inseparable from the man who built the first one and then spent a career turning it into a scientific instrument — its birth was no lucky spark but deliberate engineering of a discharge's kinetics.

Origins · 1 minAli Javan and how this was discovered

Ali Javan

1926–2016 · inventor of the helium–neon gas laser

Ali Javan was an Iranian-American physicist who trained under Charles Townes at Columbia and carried Townes's maser thinking into optics. Where the earliest lasers used flashlamp-pumped ruby crystals firing in pulses, Javan reasoned that a gas discharge could pump continuously — given a level scheme that held more atoms up than down. His decisive insight was to let one gas do the collecting and another the lasing: helium metastables, efficiently excited by the discharge and almost exactly resonant with neon's upper levels, would hand their energy to neon by collisions of the second kind. Working at Bell Labs with William R. Bennett Jr. and Donald R. Herriott, he ran the first gas laser — and the first continuous-wave laser of any kind — in December 1960 on a neon infrared line at 1.15 μm; the visible 632.8 nm red line came shortly after, from White and Rigden in 1962. Javan later founded a laser-spectroscopy group at MIT, pioneering saturated-absorption and infrared frequency-measurement techniques and remeasuring the speed of light — work that fed into the 1983 redefinition of the metre. His helium–neon laser became, for a generation, the very image of a laser.

History

1960

— Javan, Bennett, and Herriott operate the first gas laser, a He–Ne at 1.15 μm, at Bell Labs

1962

— White and Rigden obtain laser action on the 632.8 nm visible red He–Ne line

1964

— Patel demonstrates the CO₂ molecular laser and Bridges the continuous argon-ion laser

1964

— Lamb's semiclassical theory of the optical maser predicts the Lamb dip

1983

— the metre is redefined via a fixed speed of light, built on stabilised-laser frequency measurements

Going further

Texts. Hecht, Optics, 5th ed., ch. 13 (Light sources and lasers) · Foot, Atomic Physics, ch. 1 and 7 · Loudon, The Quantum Theory of Light, 3rd ed., ch. 1 and 7 · Saleh & Teich, Fundamentals of Photonics, 3rd ed., ch. 15–16 (Laser amplifiers and lasers) · Demtröder, Laser Spectroscopy, Vol. 1, ch. 3 and 5 · Svelto, Principles of Lasers, 5th ed., ch. 10 (gas lasers). The key anchor values used throughout this article are: wavelengths He–Ne 632.8 nm, Ar⁺ 488.0 and 514.5 nm, CO₂ 10.6 μm; typical neon Doppler width ≈1.5 GHz (from equation (1) with $M=20\,u$ , $T\approx400\,\text{K}$ ); free spectral range $c/2L$ ; mode count from their ratio; threshold gain from the round-trip balance; threshold inversion from equating line-centre gain to threshold; quantum-defect efficiencies from the photon and level energies; CO₂ wall-plug efficiency ≈20%. The 1960/1962/1964 dates and the attribution to Javan, Bennett, and Herriott follow the primary Bell Labs literature.

Builds on. Population Inversion and Optical Gain · Stimulated Emission and the Gain Coefficient · Four-Level Laser Systems · Optical Resonators and Cavity Modes. Leads to. Laser Threshold Condition · Longitudinal Modes and Free Spectral Range · Cavity Q Factor and Photon Lifetime · Gaussian Beams.

Ask the tutor: Ask me why a 30 cm He–Ne runs on three modes while a stabilised reference laser is squeezed to one.

If neon does the lasing, why is helium in the tube at all?

Because neon on its own is a poor thing to pump: direct electron impact does not selectively fill neon's upper laser levels, so the inversion never builds. Helium solves this in two steps: its $2\,^3S_1$ and $2\,^1S_0$ metastables are excited efficiently by electron collisions and, being metastable, accumulate in large numbers. Those states sit within about 0.05 eV of neon's $3s$ and $2s$ upper levels, so a metastable-helium collision transfers energy resonantly, dropping the helium to ground and lifting the neon to its upper laser level. Helium is the pump; neon is merely the radiator.

Why is a helium neon laser so weak — only a milliwatt or two?

Two reasons, both structural. First, the gain is tiny: single-pass amplification is only a few percent, because the inversion density in a dilute gas is low and the Doppler line spreads it thinly across 1.5 GHz — forcing long tubes and mirrors above 99% just to reach threshold, which caps the power. Second, the quantum defect is brutal: the neon upper level sits about 20 eV up while the photon is worth only 1.96 eV, so under 10% of the excitation energy could ever emerge as light. The wonder of the He–Ne is not its power but its beam quality — clean, stable, nearly perfectly Gaussian.

What limits the He–Ne linewidth, and what is the Lamb dip?

At the pressures a He–Ne runs, the line is inhomogeneously broadened by the Doppler effect to about 1.5 GHz — far wider than the natural or collisional widths. That is the width of the gain curve, not of one oscillating mode, but it does mean several modes lase and the output is not intrinsically narrow. The Lamb dip beats this: run the laser single-mode and tune it toward line centre. The intracavity standing wave interacts with two velocity groups ( $\pm v_z$ ) except exactly at line centre, where both travelling waves talk to the same zero-velocity atoms and saturate the gain harder. The output power then shows a small dip precisely at line centre — a Doppler-free feature you can lock the frequency to.

Why 632.8 nm specifically, and not some other neon colour?

Neon has many laser lines — 1.15 μm and 3.39 μm in the infrared, several in the visible — all sharing the same helium-pumped upper levels, so which oscillates is decided by the mirrors and the gain competition. The 3.39 μm transition actually has the highest gain and shares its upper level with 632.8 nm, so a red He–Ne uses mirrors highly reflective at 632.8 nm but deliberately lossy at 3.39 μm to suppress the infrared and hand the inversion to the red. The famous red is thus a design choice: the cavity is engineered to make 632.8 nm win.

Why are CO₂ lasers infrared, and why so efficient?

CO₂ lases between two vibrational levels of the molecule rather than between electronic levels of an atom. Vibrational quanta are small — fractions of an electron-volt — so the photon lands at 10.6 μm in the mid-infrared. That small spacing is why it is efficient: the quantum defect is tiny, so the photon recovers ≈40% of the energy used to reach the upper level. Kinetics helps too — nitrogen in the mix, vibrationally excited by the discharge, is nearly resonant with the CO₂ upper level and pumps it effectively, while helium cools and empties the lower levels. The combination gives wall-plug efficiencies near 20%, the highest of any gas laser.

How is pumping an argon-ion laser different from a neutral-atom laser?

Fundamentally harder. In He–Ne the discharge only excites neutral atoms, and it borrows helium to do it gently. In an argon-ion laser the lasing species is Ar⁺, so the discharge must first strip an electron off argon (about 15.8 eV) and then excite the ion a further ≈20 eV — often through multiple collisions in a dense, hot plasma. That demands enormous current densities (hundreds of amperes per square centimetre) in a narrow bore, so argon-ion tubes run hot, need water cooling, and burn kilowatts to deliver a few watts. The payoff is high continuous-wave power at 488.0 and 514.5 nm with excellent beam quality — but the efficiency is dismal, which is why diodes have displaced them.