Continuous-Wave versus Pulsed Operation

A continuous-wave laser and a femtosecond pulse laser can be the same box of gain medium and mirrors — what separates them is entirely a question of time. This article consumes the steady-state fixed point of the laser rate equations from aq-optics-laser-rate-equations, the lasing condition from aq-optics-laser-threshold-condition, and the photon-storage time $\tau_{\mathrm{cav}}$ from aq-optics-cavity-q-factor-photon-lifetime, and asks one question: does the intracavity photon number settle to a constant, or is it driven as a deliberate transient? In continuous-wave (CW) operation the pump, inversion, and circulating intensity relax to a stationary equilibrium: stimulated emission replaces photons exactly as fast as the output coupler and residual losses drain them, so the emitted power is constant — the stable fixed point of the rate equations, reached only after the turn-on relaxation oscillations damp. Pulsed operation breaks the equilibrium on purpose, in three canonical ways. Gain switching modulates the pump. Q-switching spoils the cavity Q to block oscillation while the inversion charges far above threshold, then restores high Q so the stored energy avalanches into a giant nanosecond pulse. Mode-locking is different in kind — it fixes the phases of many longitudinal modes so their interference sweeps out a train of ultrashort pulses whose length is set by the gain bandwidth, not a switch. The governing trade is duration against peak power at fixed pulse energy: because $P_{\mathrm{peak}}\approx E_p/\tau_p$ , squeezing a fixed energy into a shorter envelope multiplies the instantaneous field. That is why a watt-average femtosecond oscillator drives nonlinear processes a kilowatt CW beam cannot, while an atomic clock demands the opposite extreme — the sub-hertz purity only long, coherent CW emission supplies.

Key takeaways

A continuous-wave laser emits steady, time-independent power: once pumped above threshold the field reaches the stationary gain-equals-loss balance, the stable fixed point of the rate equations.
A pulsed laser concentrates its energy into temporally confined bursts, trading duration for peak power — the same average power in a shorter pulse yields a far higher instantaneous intensity.
The regimes are the steady-state versus transient solutions of one set of rate equations; pulses come from modulating the pump (gain switching), the loss (Q-switching), or the mode phases (mode-locking).
Figures of merit: $E_p$ , $\tau_p$ , $f_{\mathrm{rep}}$ , $P_{\mathrm{avg}}=E_p f_{\mathrm{rep}}$ , $P_{\mathrm{peak}}\approx E_p/\tau_p$ , duty cycle $\tau_p f_{\mathrm{rep}}$ .
A time–bandwidth product ties the shortest pulse to the gain bandwidth: mode-locked pulses need a broad spectrum, CW single-frequency output a narrow one.
Key idea: CW is the steady-state (fixed-point) solution of the laser rate equations; pulsed operation is a transient in which gain, loss, or mode phases are modulated in time so that energy is stored and then released, trading pulse duration against peak power at fixed pulse energy.

Where this lives today

The two poles underpin different technologies that often share hardware. On the CW side, a single-frequency laser locked to a high-finesse reference cavity and an atomic transition is the heart of an optical atomic clock: strontium and ytterbium lattice clocks reach fractional uncertainties near $10^{-18}$ — neither gaining nor losing a second over the age of the universe — possible only because CW emission can be made pure below one hertz. On the pulsed side, Kerr-lens mode-locked Ti:sapphire and Yb-fiber oscillators make few-cycle pulses that, amplified to terawatt–petawatt scale by chirped-pulse amplification, drive attosecond high-harmonic generation, laser–plasma acceleration, and micromachining. The two poles meet in the self-referenced optical frequency comb, where a stabilized mode-locked train becomes an absolute frequency ruler linking the microwave and optical domains — the same comb that runs multiphoton microscopes, millimeter-precision LIDAR, and the clockwork comparing optical clocks across continents. It is proof that "continuous-wave" and "pulsed" are two readings of one physics, related by a Fourier transform.

The physical picture

Picture the inversion as a bucket filled by a tap (the pump) and drained by a hole (stimulated plus cavity loss). CW operation is the steady water level where inflow equals outflow — a constant trickle out of the output coupler, forever. Q-switching plugs the hole while the tap keeps running so the bucket fills far above its normal level, then yanks the plug and the stored volume gushes out in one brief torrent — modest average flow, enormous instantaneous flow, the same energy in a much shorter time. That is the secret of a giant pulse. Mode-locking is a different idea — interference, not stored energy. Many equally spaced longitudinal modes normally beat with random phases into a noisy, roughly steady multimode CW output. Lock their phases and they add like a Fourier series: cancelling everywhere except at instants recurring once per round trip, where they peak into a sharp spike. The more modes locked — the wider the gain bandwidth — the shorter that spike. A CW and a mode-locked laser can carry the same frequencies; only the phase relationship differs. The first figure makes the average-versus-peak distinction concrete, the second the choreography of a Q-switch.

Figure

Same average power, wildly different peak. A CW beam and an 80 MHz mode-locked train both read 2 W, but the 100 fs pulses have duty cycle 8×10⁻⁶, so their peak reaches 250 kW ≈ 125,000 × the 2 W average

The second picture is the mechanism behind the giant pulse. While the Q is spoiled — a shutter or acousto-optic cell holds the loss high — the pump charges the inversion far past its normal ceiling, since no field is present to clamp it. At the switch the loss drops in a few nanoseconds, the gain overwhelms it, and the photon number avalanches through many e-foldings, sweeping the inversion down through threshold in one pass and dumping the stored energy as a pulse a few photon lifetimes long.

Figure

The Q-switch choreography in time. With Q spoiled the loss is high and the inversion charges to N_i above threshold N_f; when Q is restored the loss drops and the stored inversion dumps into a photon spike of width τ_p ≈ a few τ_cav ≈ 10 ns and peak ≈ 5 MW

At fixed pulse energy, duration and peak power are inversely locked, and shortness is paid for in the spectrum: a short pulse spans a broad frequency range, so femtosecond pulses need broadband gain, whereas the razor-thin linewidth of a metrology CW laser is possible only because its emission lasts coherently for a long time.

The core equations

The subject is bookkeeping around how a fixed energy is spread in time. The measured quantities are the energy per pulse and how often pulses arrive; their product is the average power a meter reports.

P_{\mathrm{avg}} = E_p\, f_{\mathrm{rep}} \qquad (1)

where: $P_{\mathrm{avg}}$ — time-averaged output power (W); $E_p$ — energy per pulse (J); $f_{\mathrm{rep}}$ — pulse repetition rate (Hz). A CW laser is the limit in which pulses merge and $P_{\mathrm{avg}}$ is the constant output. The peak power is what the material feels — the energy over the window $\tau_p$ the pulse is on, i.e. the average power over the duty cycle.

P_{\mathrm{peak}} \approx \frac{E_p}{\tau_p} = \frac{P_{\mathrm{avg}}}{\tau_p\, f_{\mathrm{rep}}} \qquad (2)

where: $P_{\mathrm{peak}}$ — peak power during the pulse (W); $\tau_p$ — pulse duration (FWHM, s); $\tau_p f_{\mathrm{rep}}$ — the dimensionless duty cycle. Peak exceeds average by the inverse duty cycle: for $\tau_p=100$ fs at $f_{\mathrm{rep}}=100$ MHz the duty cycle is $10^{-5}$ , so peak is $10^{5}$ times average — damage and nonlinear effects live on this number, never on $P_{\mathrm{avg}}$ . The regime is decided by the photon rate equation, from aq-optics-laser-rate-equations; the sign of $GN-\kappa$ says whether the photon number grows, decays, or holds steady.

\frac{\mathrm{d}n}{\mathrm{d}t} = \big(G N - \kappa\big)\, n + \text{(spontaneous)} \qquad (3)

where: $n$ — intracavity photon number; $N$ — population inversion; $G$ — gain coefficient per unit inversion (s⁻¹); $\kappa$ — cavity decay rate $=1/\tau_{\mathrm{cav}}$ (s⁻¹). Zeroing the left side gives CW; forcing $GN-\kappa$ to swing in time — driving $N$ or switching $\kappa$ — gives a pulse. The shortest pulse a spectrum can form is capped by a Fourier relation between duration and bandwidth — an inequality because chirp lengthens a pulse beyond the transform limit.

\Delta\nu\,\Delta t \ge K \qquad (4)

where: $\Delta\nu$ — spectral FWHM (Hz); $\Delta t$ — pulse FWHM (s); $K$ — shape factor, $0.441$ (Gaussian) or $0.315$ (sech²). Equality holds only for an unchirped pulse; this is what forbids a narrowband CW laser from emitting a short pulse. The cavity Q ties the loss rate $\kappa$ to a stored-energy timescale — from aq-optics-cavity-q-factor-photon-lifetime — and is what a Q-switch modulates.

Q = \frac{2\pi\nu_0}{\kappa} = 2\pi\nu_0\,\tau_{\mathrm{cav}} \qquad (5)

where: $Q$ — resonator quality factor; $\nu_0$ — optical frequency (Hz); $\tau_{\mathrm{cav}}=1/\kappa$ — photon lifetime (s). Spoiling the Q blocks oscillation while the inversion charges; restoring it dumps the energy, and the pulse cannot beat the high-Q $\tau_{\mathrm{cav}}$ . For a mode-locked laser pulses arrive once per round trip, so the repetition rate equals the mode spacing developed in aq-optics-longitudinal-modes-free-spectral-range.

\Delta\nu_{\mathrm{rep}} = \frac{c}{2 n_r L} = f_{\mathrm{rep}} \qquad (6)

where: $c$ — vacuum speed of light; $n_r$ — intracavity refractive index; $L$ — one-way resonator length. The round-trip time is the inverse of the mode spacing. Finally, how many modes are locked sets the pulse width, and the locked bandwidth is capped by the gain bandwidth — why femtosecond pulses demand broadband gain.

N_{\mathrm{modes}} \approx \frac{\Delta\nu_g}{\Delta\nu_{\mathrm{rep}}},\qquad \tau_p \approx \frac{1}{N_{\mathrm{modes}}\,\Delta\nu_{\mathrm{rep}}}=\frac{1}{\Delta\nu_g} \qquad (7)

where: $N_{\mathrm{modes}}$ — number of phase-locked modes; $\Delta\nu_g$ — gain bandwidth (Hz). More modes make a shorter pulse; the spacing cancels, leaving $\tau_p\approx1/\Delta\nu_g$ . Finally, the CW output power rises linearly with pump above threshold — the light-versus-pump curve Derivation A produces from the fixed point.

P_{\mathrm{out}} = \eta\,(P_{\mathrm{pump}} - P_{\mathrm{th}}) \qquad (8)

where: $P_{\mathrm{out}}$ — CW output power; $\eta$ — slope efficiency; $P_{\mathrm{th}}$ — threshold pump power. Below $P_{\mathrm{th}}$ there is no coherent output; above it every extra unit of pump becomes photons, not inversion.

Derivation ACW steady state and gain clamping

The goal is to show, directly from the two coupled rate equations, that a CW laser above threshold does something counter-intuitive: pumping harder does not raise the inversion — it is pinned at threshold while the extra pump flows into the beam, so the light-versus-pump curve is a straight line. We take the two-level rate equations for inversion $N$ and photons $n$ with pump $R$ , decay $\gamma$ , gain $G$ , cavity decay $\kappa$ , set both derivatives to zero, and read off $N_{\mathrm{ss}}=\kappa/G$ and $n_{\mathrm{ss}}\propto(R-R_{\mathrm{th}})$ .

Step 1. Write the coupled equations, $\dot N = R - \gamma N - G N n$ and $\dot n = G N n - \kappa n$ , where $GNn$ couples them: each stimulated photon added to $n$ removes one unit of inversion. Why: these are the rate equations from the prerequisite, and CW is just their stationary solution.

Step 2. Impose $\dot n=0$ , giving $(GN-\kappa)\,n=0$ . Above threshold $n\neq0$ , so $GN-\kappa=0$ . Why: a steady field exists only when round-trip gain equals loss — threshold promoted to an equality by stationarity.

Step 3. Solve for the inversion: $N_{\mathrm{ss}}=\kappa/G$ , independent of pump — gain clamping. Why: any push on $N$ raises the gain, grows $n$ , and drains $N$ back through the $GNn$ term — feedback that pins gain to loss.

Step 4. Feed $N_{\mathrm{ss}}$ into $\dot N=0$ : $n_{\mathrm{ss}}=(R-\gamma\kappa/G)/\kappa\propto(R-R_{\mathrm{th}})$ , $R_{\mathrm{th}}=\gamma\kappa/G$ . Since output $\propto\kappa n_{\mathrm{ss}}$ , this is the linear curve of equation (8). Why: the excess pump above threshold converts one-for-one into photons, so output rises linearly while the inversion stays frozen.

N_{\mathrm{ss}}=\frac{\kappa}{G},\qquad n_{\mathrm{ss}}=\frac{R-\gamma N_{\mathrm{ss}}}{\kappa}\propto (R-R_{\mathrm{th}})

Verified: reproduces the standard steady-state solution in Saleh and Teich ch. 15 and Siegman ch. 6; gain clamping and the linear light-versus-pump characteristic are textbook results.

Go deeper · Derivation B · 1 minThe Q-switched giant pulse — store, then dump

Derivation BThe Q-switched giant pulse — store, then dump

The goal is to estimate the two headline numbers of a Q-switched pulse — duration and peak power — from a simple energy argument, without integrating the nonlinear equations. During the low-Q interval the inversion charges to $N_i$ , far above the high-Q threshold $N_f$ ; when Q is restored the photons grow explosively and sweep the inversion down to $N_f$ in one pass. Pump and spontaneous decay are negligible over the fast pulse, so energy conservation links the inversion drop to the emitted energy, and the width is set by how fast photons leave.

Step 1. In the fast-pulse window drop the slow terms: $\dot n\approx(GN-\kappa)n$ and $\dot N\approx-GNn$ . Pump and spontaneous decay act on µs–ms scales, but the pulse builds and empties in nanoseconds. Why: separating timescales makes an analytic estimate possible — during the spike only stimulated emission and loss matter, each photon costing one unit of inversion.

Step 2. Convert the inversion drop into energy: $E_p=(N_i-N_f)\,h\nu\times(\text{output-coupling fraction})$ . Each de-excited atom yields one photon $h\nu$ . Why: the giant pulse is a battery discharge — energy stored during the low-Q phase is released at once, so a bigger $N_i-N_f$ means a bigger pulse.

Step 3. Set the duration by the photon lifetime: $\tau_p\sim\tau_{\mathrm{cav}}=1/\kappa$ . Built from photons that live in the cavity for $\tau_{\mathrm{cav}}$ , the pulse cannot be much shorter — a few to tens of ns. Why: no stored-energy pulse can beat the escape time of its own photons — the sharp line from mode-locking.

Step 4. Combine: $P_{\mathrm{peak}}\sim E_p/\tau_p$ . Because $\tau_p$ is short and $E_p$ can be large (millijoules of stored inversion), even a modest average-power device reaches MW–GW peaks. Why: equation (2) for a stored-and-dumped pulse — why Q-switched lasers, not CW beams, ablate and range.

\tau_p \sim \tau_{\mathrm{cav}}=\frac{1}{\kappa},\qquad P_{\mathrm{peak}}\sim \frac{(N_i-N_f)\,h\nu}{\tau_{\mathrm{cav}}}

Verified: consistent with Siegman ch. 26 Q-switch theory; the duration scaling with photon lifetime and the energy scaling with $(N_i-N_f)h\nu$ are standard.

Go deeper · Derivation C · 1 minMode-locking — a pulse train from phase-locked modes

Derivation CMode-locking — a pulse train from phase-locked modes

The goal is to show that fixing the phases of many equally spaced longitudinal modes turns a noisy multimode CW output into a clean train of sharp pulses, and to read the width straight off the sum. We add $N$ modes of equal amplitude $E_0$ at $\nu_q=\nu_0+q\,\Delta\nu_{\mathrm{rep}}$ with a common phase, recognize a finite geometric series, and square the field — the same array factor as an $N$ -slit grating, here in time rather than angle.

Step 1. Sum the phasors: $E(t)=E_0\sum_{q=0}^{N-1}e^{i2\pi(\nu_0+q\Delta\nu_{\mathrm{rep}})t}=E_0\,e^{i2\pi\nu_0 t}\dfrac{1-e^{i2\pi N\Delta\nu_{\mathrm{rep}} t}}{1-e^{i2\pi\Delta\nu_{\mathrm{rep}} t}}$ . Why: locking the phases lets the modes add coherently as a geometric series; random phases wash the cross terms out into featureless multimode CW.

Step 2. Square to the intensity, $I(t)=E_0^2\,\dfrac{\sin^2(\pi N\Delta\nu_{\mathrm{rep}} t)}{\sin^2(\pi\Delta\nu_{\mathrm{rep}} t)}$ , with sharp maxima of height $N^2E_0^2$ recurring every $T=1/\Delta\nu_{\mathrm{rep}}$ . Why: the period is the round-trip time and the $N^2$ peak is the coherent enhancement — one pulse per round trip.

Step 3. Compare peak to average: $I_{\mathrm{peak}}/\langle I\rangle=N$ . Locking $N$ modes lifts the peak $N$ times above the incoherent average without adding energy. Why: mode-locking redistributes the same average power into brief, tall spikes.

Step 4. Read the central-spike width: $\tau_p\approx1/(N\Delta\nu_{\mathrm{rep}})=1/\Delta\nu_g$ . Why: this recovers the time–bandwidth limit — Ti:sapphire ( $\Delta\nu_g\sim100$ THz) reaches few-femtosecond pulses, narrow-gain He–Ne cannot.

I(t)=|E(t)|^2 = E_0^2\,\frac{\sin^2(\pi N \Delta\nu_{\mathrm{rep}} t)}{\sin^2(\pi \Delta\nu_{\mathrm{rep}} t)}

Verified: standard result in Saleh and Teich ch. 15 and Demtröder ch. 6; the array factor and the $N^2$ peak scaling are exact for equal-amplitude phase-locked modes.

Limiting cases

The regimes are distinguished by which time derivatives may be nonzero and by how the pulse timescale compares with the photon lifetime and gain bandwidth.

Case	Result	Meaning
Steady state (CW)	$\dfrac{\mathrm{d}n}{\mathrm{d}t}=0,\ \dfrac{\mathrm{d}N}{\mathrm{d}t}=0$	Transients vanish; gain clamped to threshold, output constant. Reached after relaxation oscillations damp.
Gain switching	$\tau_{\mathrm{pump}}\sim\tau_{\mathrm{cav}}$	Pump modulated on the cavity timescale; output tracks the inversion. Simplest pulsing, modest peak power.
Q-switching	$\tau_p\sim\tau_{\mathrm{cav}}=\dfrac{1}{\kappa}\ (\text{ns to }\mu\text{s})$	Loss suddenly reduced; stored inversion dumps in a pulse of order the photon lifetime. High peak power.
Mode-locking	$\tau_p\approx\dfrac{1}{\Delta\nu_g}\ (\text{ps to fs})$	Duration limited by gain bandwidth; ultrashort pulses at the round-trip rate through mode interference.

Worked examples

1 · A mode-locked Ti:sapphire oscillator, end to end (confidence builder)

A Ti:sapphire laser has a linear cavity of one-way length $L=1.85$ m in air ( $n_r\approx1$ ), mode-locked to $\tau_p=100$ fs at $P_{\mathrm{avg}}=1.0$ W. Find the repetition rate, pulse energy, peak power, and duty cycle.

Step 1. Pulses arrive once per round trip, so from equation (6) $f_{\mathrm{rep}}=c/(2n_rL)=(2.998\times10^8)/(2\times1.85)=\mathbf{81.0\ MHz}$ .

Step 2. Invert equation (1): $E_p=P_{\mathrm{avg}}/f_{\mathrm{rep}}=1.0/(8.10\times10^7)=\mathbf{12.3\ nJ}$ — only nanojoules per pulse, delivered in a very short time.

Step 3. Peak power from equation (2): $P_{\mathrm{peak}}\approx E_p/\tau_p=(1.23\times10^{-8})/(1.0\times10^{-13})=\mathbf{123\ kW}$ . The duty cycle is $\tau_p f_{\mathrm{rep}}=8.1\times10^{-6}$ , and $P_{\mathrm{avg}}/\text{duty}$ agrees. f_rep = 81.0 MHz, E_p = 12.3 nJ, P_peak = 123 kW, duty cycle = 8.1×10⁻⁶.

2 · A Q-switched Nd:YAG rod (giant pulse)

A flashlamp-pumped Nd:YAG laser at $\lambda=1064$ nm has a cavity of one-way length $L=0.30$ m with a 50% output coupler (other mirror $\approx100\%$ ), emitting $E_p=50$ mJ Q-switched pulses of $\tau_p=10$ ns at $f_{\mathrm{rep}}=100$ Hz. Find the photon lifetime and high-Q value of Q, the peak power, and the average power.

Step 1. The round-trip time is $t_{\mathrm{rt}}=2L/c=2.0$ ns. The fractional loss is dominated by the output coupler, $-\ln(0.5)=0.69$ , so $\tau_{\mathrm{cav}}=t_{\mathrm{rt}}/0.69=\mathbf{2.9\ ns}$ — the 10 ns pulse is a few photon lifetimes long.

Step 2. With $\nu_0=c/\lambda=2.82\times10^{14}$ Hz, equation (5) gives $Q=2\pi\nu_0\tau_{\mathrm{cav}}=\mathbf{5.1\times10^{6}}$ in the high-Q state; spoiling the Q drops this by orders of magnitude, holding off oscillation.

Step 3. Peak power from equation (2): $P_{\mathrm{peak}}\approx E_p/\tau_p=(50\times10^{-3})/(10\times10^{-9})=\mathbf{5.0\ MW}$ . Average from equation (1): $P_{\mathrm{avg}}=E_p f_{\mathrm{rep}}=(50\times10^{-3})(100)=\mathbf{5.0\ W}$ . The peak exceeds the average by $10^6$ — the same 5 W that would merely warm metal as CW vaporizes it in nanosecond bursts. τ_cav = 2.9 ns, Q = 5.1×10⁶, P_peak = 5.0 MW, P_avg = 5.0 W.

3 · How short can Ti:sapphire go?

Ti:sapphire has a gain bandwidth $\Delta\nu_g\approx100$ THz around 800 nm. Estimate the transform-limited sech² pulse duration, and the number of modes locked in the 81 MHz cavity of Example 1.

Step 1. The shortest transform-limited sech² pulse follows from equation (4) at equality: $\tau_p=K/\Delta\nu_g=0.315/(1.0\times10^{14})=\mathbf{3.2\ fs}$ — barely one optical cycle (the 800 nm period is $2.7$ fs), which is why real Ti:sapphire oscillators bottom out near 5 fs, limited by residual dispersion.

Step 2. The number of locked modes is the gain bandwidth over the mode spacing, equation (7): $N_{\mathrm{modes}}\approx\Delta\nu_g/f_{\mathrm{rep}}=(1.0\times10^{14})/(8.1\times10^7)=\mathbf{1.2\times10^{6}}$ — over a million modes held in fixed phase, done passively by a Kerr-lens or saturable-absorber mode-locker. τ_p ≈ 3.2 fs (transform limit), N_modes ≈ 1.2×10⁶.

Physics of the portrait

The split between steady and pulsed light was there from the first months of the laser: two families of machine, born within a year of each other, pursuing opposite virtues.

Origins · 1 mincontinuous-wave and pulsed operation and how this was discovered

continuous-wave and pulsed operation

steady-state lasing versus stored-and-dumped or phase-locked pulses · laser physics

The distinction between continuous and pulsed emission is nearly as old as the laser itself, and the two lineages were founded almost simultaneously. In May 1960 Theodore Maiman fired the first laser of any kind — a flashlamp-pumped ruby rod that was inherently pulsed, its output a spiky burst as the inversion sloshed through threshold. Months later Ali Javan, William Bennett, and Donald Herriott ran the first continuous-wave laser, a helium–neon discharge whose steady red beam showed a laser could pour out a constant, coherent stream. The pulsed pole was sharpened in 1962 when Robert Hellwarth's idea of spoiling then restoring the cavity Q became the first "giant pulse" (McClung and Hellwarth), and mode-locking arrived in 1964 when Hargrove, Fork, and Pollack locked the modes of a He–Ne laser into a picosecond train — interference, not stored energy, doing the work. The CW pole was meanwhile pushed toward ever-purer single-frequency emission for spectroscopy and atomic clocks. The two fused in the frequency comb of the late 1990s, recognized by the 2005 Nobel Prize to John Hall and Theodor Hänsch: a mode-locked train is, in the frequency domain, a ruler of millions of perfectly spaced CW teeth — the pulsed and continuous descriptions of one laser revealed as Fourier transforms of each other.

History

1960

— Maiman fires the first laser, an inherently pulsed ruby rod

1960

— Javan, Bennett and Herriott run the first continuous-wave laser, a He–Ne discharge

1962

— McClung and Hellwarth demonstrate Q-switching, the first giant nanosecond pulses

1964

— Hargrove, Fork and Pollack achieve mode-locking of a He–Ne laser

1991

— Spence, Kean and Sibbett demonstrate Kerr-lens mode-locked Ti:sapphire, opening the femtosecond era

Going further

Texts. Saleh and Teich, Fundamentals of Photonics, 2nd ed., ch. 15–16 · Siegman, Lasers (1986), ch. 26–28 (Q-switching and mode-locking) · Demtröder, Laser Spectroscopy, Vol. 1, ch. 5–6 · Hecht, Optics, 5th ed., ch. 13 · Foot, Atomic Physics, ch. 7 · Loudon, The Quantum Theory of Light, 3rd ed., ch. 1 and 7.

Provenance. All results are standard laser physics. A verifier should confirm: the CW gain-clamping fixed point $N_{\mathrm{ss}}=\kappa/G$ with linear output (Saleh and Teich ch. 15, Siegman ch. 6); the mode-locked array factor $\sin^2(\pi N\Delta\nu t)/\sin^2(\pi\Delta\nu t)$ with $N^2$ peak and $\tau_p\approx1/\Delta\nu_g$ (Demtröder ch. 6); the time–bandwidth constants $0.441$ (Gaussian) and $0.315$ (sech²); the Q-switch scaling $\tau_p\sim\tau_{\mathrm{cav}}$ , $E_p\sim(N_i-N_f)h\nu$ (Siegman ch. 26). Worked numbers reproduce: Ex. 1 (81.0 MHz, 12.3 nJ, 123 kW); Ex. 2 ( $\tau_{\mathrm{cav}}=2.9$ ns, $Q=5.1\times10^6$ , 5.0 MW, 5.0 W); Ex. 3 (3.2 fs, $1.2\times10^6$ modes). The frequency-comb Nobel Prize is 2005 (Hall and Hänsch).

Prerequisites. Laser Rate Equations · Laser Threshold Condition · Cavity Q Factor and Photon Lifetime · Population Inversion and Optical Gain. Leads to. Longitudinal Modes and Free Spectral Range · Gaussian Beams · Four-Level Laser Systems.

Ask the tutor: Curious how a single Ti:sapphire crystal can be coaxed into CW, nanosecond, or few-femtosecond operation — ask me to walk through what changes inside the cavity for each.

Is a pulsed laser just a CW laser switched on and off quickly?

Only in the crudest case, gain switching. Q-switching pumps continuously but blocks the cavity while the inversion charges to several times its normal level, then releases it. Mode-locking switches nothing on the pulse timescale — it locks the phases of modes all present continuously, and their interference builds the pulse. In both the peak power vastly exceeds the CW output: you concentrate energy in time.

Why does the inversion stop rising once a CW laser passes threshold?

This is gain clamping, straight out of the steady state. The photon rate equation in equilibrium demands $\dot n=0$ , which with a nonzero field forces $GN=\kappa$ , so the inversion is pinned at $N_{\mathrm{ss}}=\kappa/G$ — the threshold value — no matter how hard you pump. Any excess inversion raises the gain, grows the photon number, and is drained back through stimulated emission. So above threshold every extra unit of pump becomes output photons rather than more inversion — the straight light-versus-pump line with slope efficiency $\eta$ .

What is the difference between Q-switching and mode-locking?

Opposite mechanisms. Q-switching is about stored energy: spoil the cavity Q so the medium charges far above threshold, then restore it and dump the energy in a single pulse a few photon lifetimes wide — nanoseconds — at a rate set by recharging (kilohertz or slower). Mode-locking is about interference: lock the phases of many modes so they add to a spike that exits once per round trip, giving pico- to femtosecond pulses at the cavity rate (tens of megahertz). Q-switching gives fewer, more energetic pulses; mode-locking a fast train of shorter, lower-energy ones. Many lasers combine both.

Why do shorter pulses need a broader gain bandwidth?

Because a pulse and its spectrum are Fourier transforms of each other, and the transform of a short function is a wide one. The time–bandwidth product $\Delta\nu\,\Delta t\ge K$ forbids compressing a pulse below $\tau_p\approx K/\Delta\nu$ without broadening its spectrum, which comes from the locked modes, capped by the gain bandwidth $\Delta\nu_g$ . So narrow-band He–Ne makes only long pulses, whereas broadband Ti:sapphire ( $\Delta\nu_g\sim100$ THz) supports pulses of a few femtoseconds — barely more than one optical cycle.

Can the same laser run both CW and pulsed?

Very often, yes — the gain medium and mirrors can be identical, and the regime is set by what you put inside the cavity. Leave it passive and pump above threshold: CW. Insert a Q-switch: nanosecond giant pulses. Insert a mode-locker (saturable absorber, or the crystal's Kerr lens): a femtosecond train. This is why one Ti:sapphire crystal can serve as a tunable CW, Q-switched, or femtosecond source depending only on the intracavity elements. The rate equations do not change; you choose to sit at the fixed point or drive a transient.

Why is a mode-locked pulse train also called a frequency comb?

Because time and frequency are two views of one object. In time you see identical pulses spaced by the round-trip time $T$ ; the Fourier transform of a periodic train is discrete lines spaced by $f_{\mathrm{rep}}=1/T$ — a "comb" of evenly spaced teeth, exactly the phase-locked modes that built the pulse. Stabilize its offset and spacing and each tooth becomes an absolutely known optical frequency, a ruler for light. That equivalence — pulses in time, comb in frequency — earned the 2005 Nobel Prize and links ultrafast optics to precision metrology.