L16 · Store energy, then release

Q-Switched Giant Pulse

How can stored inversion become a giant pulse? High cavity loss holds back oscillation while the pump stores energy in excited particles. Lower the loss quickly and light rapidly drains that store. The pulse decays when inversion falls below threshold; some excitation remains. A saturable absorber can provide the switch by becoming less lossy as the field grows.

Keep the cavity lossy so the laser cannot start while the inversion builds, then open the loss gate and resolve the burst that follows. Compare an actively timed switch with a saturable absorber that bleaches on its own, and run the laser repeatedly.

Recorded duration $\text{—}$

Mechanism / final gate state $\text{—}$

Effective active hold time $\text{—}$

Final threshold-normalized inversion $\text{—}$

Final inversion threshold $\text{—}$

Upper-population energy $\text{—}$

Cavity optical energy $\text{—}$

Final 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}

Build up the stored inversion first, then complete a cycle. Compare the energy in the pulse window with the energy over the whole cycle. In passive mode the storage and opening controls do not drive the absorber.

The model is spatially uniform, four-level and single-mode, and it runs in continuous time. It couples the inversion, in units of its threshold value, to the energy stored in the cavity. The upper-level lifetime is two hundred microseconds, and the inversion at threshold stores an illustrative half millijoule. You set the open-cavity photon lifetime in nanoseconds; seventy percent of its base escape rate is useful output and the rest is internal loss. The extra loss of the switch is given in units of that base escape rate, not as a mirror power percentage. A constant pump feeds the upper level at a rate in units of threshold, during both storage and emission. The active gate closes at the start of each cycle and opens after the effective hold time; its loss then falls linearly over the chosen opening time. The effective hold is at most ninety percent of the period. In passive mode the absorber recovers on its own and bleaches in proportion to the energy it actually absorbs; the hold and opening controls do nothing, and the period only sets the length of the recording window. A tiny, steady average share of the spontaneous emission seeds the cavity, and the rest of the population decay is dissipated; this is not a random noise run. The pump, escape, stimulated exchange and absorber bleaching are each solved exactly as positive sub-steps and combined with adaptive step doubling. The energy tally accumulated over the run conserves energy across injected energy, inversion, cavity energy, useful output and dissipation. The strongest burst in the latest cycle is measured from the simulated trace. Its full width at half maximum needs a crossing on each side, and its pulse energy integrates the useful output between the points where the power crosses one percent of the peak. If either side is missing, the window is marked unresolved. Because the pump stays on, the cycle energy also includes the emission after the pulse; it is not the pulse energy. The repetition frequency shown refers to the active trigger; passive pulses set their own timing. The drawing along the axis is schematic. The active gate is a lumped loss, not a calibrated Pockels cell or acousto-optic device, and the passive absorber is uniform. Diffraction, polarization, spatial hole burning, beating between modes, distributed gain, heating and quantum fluctuations are left out. The marker fractions and logarithmic brightness are not detector data. The output monitor shows computed laser power with an ideal response; detector bandwidth and saturation are not modeled.

Start with the essentials

Focus question: How do the stored energy, the cavity loss and the switch timing shape the burst?
One-sentence intuition: The pulse grows while gain exceeds loss and decays when the inversion falls below threshold. A stronger field bleaches a passive absorber further, lowering its loss and accelerating the burst.

Core mathematical model

Rate equations for inversion 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}

Inversion and cavity energy are both measured in units of the same threshold energy. The spontaneous term sends a fraction of the population decay into the cavity.

Storing with the gate closed, releasing with it open

\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 formula assumes stimulated emission removes almost nothing yet. If the closed-gate loss is too small, the laser starts too early.

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}

The power the absorber takes from the cavity drives its bleaching. In passive mode the coupled equations set the pulse timing, not the active trigger.

Useful output and the 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}

Energy leaves through the output, the base internal loss, absorption in the switch and population decay outside the laser mode. The pump here is an ideal input of excitation energy, not electrical power from the wall.

The fast-pulse limit

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

Assume the gate is fully open, pump and decay are negligible during the burst, and the seed is negligible too. Then integration removes time from the equations. The peak comes when the inversion crosses the open-cavity threshold.

Measuring width and energy in a defined 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}

Both the width and the pulse energy need a crossing on each side of the peak. The whole-cycle energy also counts the output that follows while the pump stays on.

Common difficulties

A giant pulse is not mode locking

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

Better mental modelHere a single mode stores energy and releases it over many optical round trips. Mode locking is a different mechanism.

Lowering the loss releases the pulse

Typical misconceptionThe high loss is what creates the giant pulse.

Better mental modelHigh loss lets the energy be stored. Lowering the loss lets stimulated emission release it.

Cycle energy is not pulse energy

Typical misconceptionPeak power times the cycle length is the pulse energy.

Better mental modelIntegrate the power over a defined window around the burst. Count the emission that follows separately, in the cycle total.

Run the experiment

01
Store energy without lasing
Start with the default recorded cycle. Follow the rising inversion and the high threshold before the gate opens.
What to observe: The gain keeps building while the high loss keeps the cavity dark.
02
Resolve the giant pulse
Compare the nanosecond-scale pulse with the storage trace. Expand Pulse window and cycle energy to inspect the whole-cycle output.
What to observe: After rapid opening, the pulse peaks near the open-cavity threshold. Emission after the pulse adds to the cycle energy.
03
Make it fail on purpose
Compare Slow opening and Premature lasing. The early-opening example is in Advanced controls.
What to observe: Too little stored energy, light released while the loss is still ramping down, or early leakage each make the pulse less useful.
04
Let the absorber set the timing
Choose Passive absorber. Change Absorber saturation energy or Absorber recovery time; each edit records a new window.
What to observe: The pulses come when the absorber bleaches and recovers, so their timing need not match the length of the recording window.

Q-Switched Giant Pulse

Delay oscillation to store energy

Core mathematical model

Rate equations for inversion and cavity energy

Storing with the gate closed, releasing with it open

Absorber recovery and bleaching

Useful output and the full energy balance

The fast-pulse limit

Measuring width and energy in a defined window

Common difficulties

A giant pulse is not mode locking

Lowering the loss releases the pulse

Cycle energy is not pulse energy

Run the experiment

Store energy without lasing

Resolve the giant pulse

Make it fail on purpose

Let the absorber set the timing

Related experiments and articles

Controlled light and precision measurement