🔦Laser physics simulator - population inversion, rate equations, cavity modes, Gaussian beams

How to use Laser physics simulator

1. 1On the Atoms & inversion tab pick a two-, three- or four-level scheme, set the pump rate and press Play to watch the populations, the inversion and the output photons.
2. 2On the Rate equations tab choose a laser preset or enter mirror reflectivities, cross-section and lifetime to get the threshold pump power and slope efficiency, then simulate turn-on or a Q-switched pulse.
3. 3On the Cavity & modes tab change the cavity length, gain linewidth and gain-to-loss ratio and count the modes above threshold.
4. 4On the Gaussian beam tab enter a waist and wavelength for the Rayleigh range, divergence and spot size at any distance, or get the mode waist straight from a two-mirror stable cavity.
5. 5On the Presets & safety tab compare common lasers and read what laser classes 1 to 4 mean.

FAQ

Why can't a two-level system lase?

When you pump two-level atoms with light, the pump excites ground-state atoms but also drives excited atoms back down by stimulated emission with the same probability, because the Einstein B coefficients for absorption and stimulated emission are equal. However hard you pump, the upper population can only approach the lower one, never exceed it, so there is no gain. Three- and four-level schemes separate the pump transition from the laser transition, which makes inversion possible.

Why does a four-level laser have a lower threshold than a three-level one?

In a three-level laser the lower laser level is the ground state, so more than half of all atoms must be moved up before there is any inversion. In a four-level laser the lower level sits above the ground state and empties quickly, so it is almost always empty and a small upper population already counts as inversion. That is why four-level lasers like Nd:YAG have a far lower threshold than ruby.

Why does the output start with a train of spikes?

When pumping starts, the inversion builds up past threshold while there are still very few photons in the cavity, so it overshoots. Once the photon number avalanches it drains the inversion below threshold, the photons die away, and the cycle repeats. These are relaxation oscillations, with a small-signal period of about 2π√(τ τc/(r−1)), and they damp towards the steady state.

How does Q-switching produce such high peak power?

While pumping, a shutter or an electro-optic or acousto-optic switch keeps the cavity loss high so the laser cannot oscillate, and the inversion builds far above the normal threshold. The loss is then dropped suddenly and the stored energy comes out as one short pulse within a few photon lifetimes. The tool solves n_i − n_f = ln(n_i/n_f) for the extraction efficiency, gives pulse energy, peak power and width, and checks them against a numerical integration.

How do I work out the mode spacing and the number of lasing modes?

Adjacent longitudinal modes are spaced by c/(2nL), about 500 MHz for a 30 cm He-Ne cavity. Only modes inside the band where gain exceeds the cavity loss can lase. A He-Ne with its 1.5 GHz Doppler linewidth usually runs on two or three modes, while a sub-millimetre diode laser has mode spacings of a hundred GHz or more. In homogeneously broadened media mode competition reduces the count further.