L20 · Carriers and gain media

Laser Medium Zoo

Compare ruby, helium–neon, neodymium YAG, carbon dioxide, KrF and dye. Test ground-state absorption, energy transfer, lower-state clearance and feedback in one consistent population ledger.

Time / upper lifetime $\text{—}$

Selected medium $\text{—}$

Representative wavelength $\text{—}$

Population model $\text{—}$

Ground fraction $\text{—}$

Pump or donor fraction $\text{—}$

Upper laser fraction $\text{—}$

Absorbing state fraction $\text{—}$

Population ledger total $\text{—}$

Upper minus absorbing fraction $\text{—}$

On-pump small-signal gain margin $\text{—}$

Instantaneous gain / loss $\text{—}$

Normalized cavity photons $\text{—}$

Normalized output rate $\text{—}$

Largest output in retained run $\text{—}$

Instantaneous route feed $\text{—}$

Representative pump compatibility $\text{—}$

Six representative media share a dimensionless ensemble, not a common physical device. Real names, representative wavelengths, pump routes and qualitative bandwidth character are sourced; every rate, transfer yield, loss, cavity gain and output value is an illustrative teaching choice. Time is normalized by an upper-state lifetime chosen separately for each medium, so equal horizontal times do not mean equal seconds. A ground reservoir feeds a pump or donor reservoir, then an upper laser reservoir. Ruby returns to the absorbing ground state; the other media use a fast lower reservoir. For KrF, that reservoir is a population-flow proxy for a repulsive continuum, not a bound lower level or a chemistry solver. He–Ne and carbon dioxide donor reservoirs stand for energy-transfer routes, not a conserved literal species count. The normalized population ledger conserves one effective ensemble. Pump type chooses the representative optical or discharge route; a mismatch sets that route to zero, not a claim that all alternative pumping is impossible. Pump pulses have a three-unit on window in a twelve-unit period. A common Lorentzian selected-mode factor uses detuning in units of one illustrative full width; it does not synthesize the actual multi-line spectrum or predict tuning range. Feedback blocking adds a large escape rate; the tiny single-channel spontaneous background remains. Lower-clearance controls change only the four-reservoir proxy and have no effect on ruby. Readouts and plots come from the same integrated populations and cavity photons. The small-signal margin is an independent unseeded steady reference, using the on-state pump for pulsed cases. Output is a normalized escape rate, not watts, efficiency or a material ranking. Chemical kinetics, gas flow, triplets, bleaching, thermal effects, actual cross-sections and real cavity design are omitted. Apparatus dimensions and visible colors are schematic.

Compare the mechanisms

These are representative transitions and qualitative properties. The simulation uses separate, illustrative normalized rates.

Ruby

$694.3\,\mathrm{nm}$

Optical bands → fast relaxation → chromium metastable state

Narrow electronic line

Often pulsed; ground-state absorption raises the pump burden

He–Ne

$632.8\,\mathrm{nm}$

Discharge → helium metastable atoms → collision transfer to neon

Narrow atomic gain line

Commonly continuous; gas mixture and lower-level removal matter

Nd:YAG

$1064\,\mathrm{nm}$

Optical absorption → relaxation → neodymium upper laser level

Narrow solid-state transition

Continuous or pulsed; the cavity and pump schedule decide

Carbon dioxide

$10600\,\mathrm{nm}$

Discharge → nitrogen vibration → resonant transfer to carbon dioxide

Many distinct vibrational–rotational lines

Continuous or pulsed; vibrational relaxation and gas cooling matter

KrF excimer

$248\,\mathrm{nm}$

Discharge chemistry → excited bound exciplex → repulsive lower continuum

Broad molecular band

Usually pulsed; formation, dissociation and gas chemistry limit cycling

Rhodamine 6G dye

$600\,\mathrm{nm}$

Optical pump → vibrational relaxation in excited singlet → emission band

Broad vibronic band; representative wavelength only

Continuous or pulsed; triplets, bleaching and flow matter

MIT: gain media and laser types, sections 7.2–7.3

Start with the essentials

Focus question: Which pump route and population bottleneck does each medium need?
One-sentence intuition: The absorbing state and its removal determine how pumping can build inversion.

Core mathematical model

One population ledger

n_g+n_d+n_u+n_\ell=1

The ensemble is effective and normalized; donor populations do not count real helium or nitrogen atoms.

A route with a transfer bottleneck

\begin{aligned}\dot n_d&=rn_g-k_dn_d\\F_u&=\eta_dk_dn_d\end{aligned}

A compatible source feeds the donor reservoir. Failed transfer returns to the ground reservoir.

The absorbing state changes the threshold

\Delta=\begin{cases}n_u-n_g&\text{ruby}\\n_u-n_\ell&\text{other proxies}\end{cases}

Ruby must overcome a populated ground state. A fast lower-state exit changes the population burden.

A selected mode, not a material spectrum

\begin{aligned}G&=8\Delta/(1+4\delta^2)\\\dot s&=(G-\kappa)s+\beta n_u\end{aligned}

Detuning is in units of the illustrative full gain width. This common line shape cannot reproduce actual multi-line media.

Removing feedback leaves a background

\begin{aligned}\kappa&=\kappa_i+\kappa_o+\kappa_{\rm block}\\p_{\rm out}&=\kappa_os\end{aligned}

Feedback blocking adds rapid escape; the small spontaneous channel remains. Output units are normalized.

Small-signal reference before depletion

M_0=8\Delta_0/(1+4\delta^2)-\kappa

The unseeded steady population gives an onset margin. Above threshold, the integrated field depletes it; pulsed operation is not a steady state.

Common difficulties

Gain is not yet oscillation

Typical misconceptionA pumped medium must lase.

Better mental modelThe selected mode must compensate all losses and maintain its population supply.

Read the model boundary

Typical misconceptionA teaching trace predicts a commercial device.

Better mental modelThe assumptions and chosen constants define a controlled mechanism experiment, not material certification.

Run the experiment

01
Compare the absorbing state
Run ruby and neodymium YAG at the same normalized pump.
What to observe: A populated ground state changes the inversion needed for gain.
02
Break the energy-transfer route
Choose helium–neon and turn on optical pumping.
What to observe: This representative discharge route receives no modeled feed.
03
Block lower-state removal
Run a four-reservoir medium with a large clearance slowdown.
What to observe: Lower-state accumulation suppresses inversion and output.
04
Separate pumping from oscillation
Compare continuous and pulsed pumping, then disconnect feedback.
What to observe: A pumped upper state is insufficient; the feedback and loss balance still decide.