L16 · Store energy, then release

Q-Switched Giant Pulse

Hold a cavity below threshold, open its loss gate, and resolve the resulting burst. Compare active timing with autonomous absorber bleaching and repeated operation.

Elapsed time $\text{—}$

Switch mechanism / gate state $\text{—}$

Effective active hold time $\text{—}$

Threshold-normalized inversion $\text{—}$

Instantaneous inversion threshold $\text{—}$

Upper-population energy $\text{—}$

Cavity optical energy $\text{—}$

Instantaneous useful power $\text{—}$

Strongest output in selected cycle $\text{—}$

Time of selected maximum $\text{—}$

Pulse full width at half maximum $\text{—}$

Output in one-percent pulse window $\text{—}$

Useful energy in selected cycle $\text{—}$

Total extracted energy $\text{—}$

Accumulated energy-balance residual $\text{—}$

Active trigger / passive window frequency $\text{—}$

L16

How can stored inversion become a giant pulse?

Passive absorber instead of active gate

b

0

Threshold-normalized pump

r

4

Requested storage time

t_h

200\,\mathrm{\mu s}

Active period / passive recording window

T_R

500\,\mathrm{\mu s}

Active gate opening duration

t_{\rm open}

20\,\mathrm{ns}

Open-cavity photon lifetime

\tau_p

10\,\mathrm{ns}

Closed-gate / unsaturated absorber loss

q_0

8

Absorber saturation energy

E_a

20\,\mathrm{\mu J}

Absorber recovery time

\tau_a

10\,\mathrm{\mu s}

Prepare the storage state, then complete a cycle. Compare pulse-window energy with the whole-cycle energy. In passive mode, storage and opening controls do not drive the absorber.

A spatially uniform four-level, single-mode, continuous-time energy model couples threshold-normalized inversion and cavity energy. The upper lifetime is two hundred microseconds and the illustrative threshold inversion energy is half a millijoule. Open-cavity photon lifetime is controlled in nanoseconds; seventy percent of its base escape rate is useful output and the rest is internal loss. Additional switch loss is expressed relative to that base escape rate, not as a mirror power percentage. A constant pump injects a threshold-normalized upper-population rate throughout storage and emission. An active gate closes at each cycle start, opens after the effective hold, and falls linearly over the selected opening time. Effective hold is capped at ninety percent of the period. In passive mode the absorber recovers and bleaches in proportion to the energy it actually absorbs; hold and opening controls are inactive, and period is only a recording-window length. A tiny deterministic mean spontaneous branch seeds the cavity while the remaining population decay is dissipated; this is not a random noise realization. Positive exact subflows for pump, escape, stimulated exchange and absorber bleaching are composed with adaptive step doubling. Their accumulated energy ledger conserves injected energy, inversion, cavity energy, useful output and dissipation. The strongest burst in the latest cycle is measured from its integrated trajectory: full width at half maximum requires two crossings; pulse energy integrates useful output between one-percent peak crossings. If either side is incomplete the window is unresolved. Cycle energy also includes later emission because the pump stays on; it is not pulse energy. Display repetition frequency refers to the active trigger; passive pulses choose their own timing. The axial apparatus is schematic, the active gate is a lumped loss port rather than a calibrated Pockels-cell or acousto-optic device, and the passive absorber is uniform. Diffraction, polarization, spatial hole burning, multimode beating, distributed gain, heating and quantum fluctuations are omitted. Marker fractions and logarithmic brightness are not detector data.

Start with the essentials

Focus question: How do storage, loss and switch timing determine the burst?
One-sentence intuition: The pulse grows while gain exceeds loss, then ends by depleting inversion. A passive absorber creates its own positive feedback by bleaching.

Core mathematical model

Population and cavity energy

\begin{aligned}\dot D&=\frac{r-D}{\tau_L}-\frac{DV}{\tau_p}\\\dot V&=\frac{(D-1-q)V}{\tau_p}+\frac{\beta D}{\tau_L}\end{aligned}

Both reservoirs use the same threshold energy. The spontaneous branch transfers a fraction of population decay into the cavity.

Closed storage and open release

\begin{aligned}D_{\rm th}(t)&=1+q(t)\\D(t)&\simeq r(1-e^{-t/\tau_L})\\r&<1+q_0\quad\text{for holdoff}\end{aligned}

The storage approximation assumes negligible stimulated depletion. Insufficient closed loss permits premature lasing.

Absorber recovery and bleaching

\begin{aligned}\dot q&=\frac{q_0-q}{\tau_a}-\frac{qE_0V}{E_a\tau_p}\\P_a&=\frac{qE_0V}{\tau_p}\end{aligned}

Bleaching is driven by absorbed cavity power. Passive timing follows the coupled equations rather than the active trigger.

Useful output and full energy balance

\begin{aligned}U&=E_0V,\quad E_g=E_0D\\P_{\rm out}&=\eta E_0V/\tau_p\\\frac{\dot E_g+\dot U}{E_0}&=\frac{r-(1-\beta)D}{\tau_L}\\&\quad-\frac{(1+q)V}{\tau_p}\end{aligned}

Output, base internal escape, switch absorption and non-mode population decay close the budget. Pump here is an ideal excitation-energy input, not wall power.

An isolated fast extraction limit

\begin{aligned}D_i-D_f&=\ln(D_i/D_f)\\V_{\rm peak}&=D_i-1-\ln D_i\end{aligned}

For a fully opened gate, negligible pump and decay during the burst, and a negligible seed, integration eliminates time. The peak occurs when inversion crosses the open threshold.

Measure a defined pulse window

\begin{aligned}\Delta t_{1/2}&=t_{+,1/2}-t_{-,1/2}\\E_{\rm pulse}&=\int_{t_{-,0.01}}^{t_{+,0.01}}P_{\rm out}(t)\,dt\\E_{\rm cycle}&=\int_{t_0}^{t_0+T_R}P_{\rm out}(t)\,dt\end{aligned}

Two crossings are required for either pulse quantity. The entire cycle includes subsequent output under the continuing pump.

Common difficulties

A giant pulse is not mode locking

Typical misconceptionEvery short laser pulse requires many phase-locked modes.

Better mental modelThis pulse is single-mode energy storage and extraction over many optical round trips; mode locking is a different mechanism.

A high-Q cavity is the release stage

Typical misconceptionHigh loss creates the giant pulse directly.

Better mental modelHigh loss enables storage; lower loss enables stimulated release.

Cycle energy is not pulse energy

Typical misconceptionPeak power times the cycle length is pulse energy.

Better mental modelIntegrate a defined burst window; keep subsequent emission in a separate cycle total.

Run the experiment

01
Store without oscillating
Prepare to active opening and compare inversion with the closed threshold.
What to observe: Gain can accumulate while high loss keeps the cavity dim.
02
Resolve the giant pulse
Complete the cycle and inspect the pulse detail plot, peak, width and energy window.
What to observe: Inversion falls through threshold as output peaks; later emission adds cycle energy.
03
Manufacture failures
Compare early opening, slow opening and premature lasing.
What to observe: Insufficient storage, release during the loss ramp, or leakage reduces useful pulse quality.
04
Let the absorber choose timing
Choose passive absorber and record several cycles; change saturation energy or recovery.
What to observe: Pulse timing follows self bleaching and recovery; it need not equal the display window period.