Glossary entry

Mode locking

A laser operating regime in which many longitudinal cavity modes oscillate with locked relative phases, producing a periodic train of ultrashort pulses. The technique that produces femtosecond and picosecond pulses.

A laser cavity supports many longitudinal modes equally spaced by the free spectral range $\text{FSR} = c / (2 n_g L)$ for a linear cavity of length $L$ . In a normal laser, these modes oscillate with random relative phases — their interference produces a broadband, noisy continuous output.

In mode locking, all oscillating modes are forced into a fixed phase relationship. The constructive interference of $N$ in-phase modes produces a pulse:

Pulse repetition period = $1/\text{FSR}$ = round-trip cavity time
Pulse duration $\Delta t \sim 1 / (N \cdot \text{FSR})$ — narrower for more locked modes
Time-bandwidth product $\Delta t \cdot \Delta\nu \sim 0.44$ (Gaussian) or 0.32 (sech²) — Fourier-transform-limited

For a Ti:sapphire mode-locked laser with $\Delta\nu =$ 30 THz and FSR = 100 MHz, the pulse duration is $\sim$ 15 fs, and $\sim 3 \times 10^5$ modes are simultaneously locked.

Standard mode-locking mechanisms:

Method	Implementation
Passive — saturable absorber	An intracavity element absorbs CW light but bleaches under high intensity, favoring pulsed operation
Passive — Kerr lens	Nonlinear self-focusing tightens the spatial mode under high intensity, increasing gain for pulses
Active — amplitude modulator	An intracavity AOM or EOM modulated at the FSR keeps the pulses synchronized
Active — frequency modulator	A phase modulator at FSR achieves similar locking via FM resonance
Synchronous pumping	Pumping the gain medium with another mode-locked laser at the same repetition rate

Typical mode-locked laser specifications:

System	Pulse duration	Rep rate	Peak power
Ti:sapphire (Kerr-lens)	10 – 100 fs	70 – 100 MHz	$\sim$ 100 kW
Er-doped fiber (SAM or NPR)	100 fs – 10 ps	10 – 100 MHz	$\sim$ 1 kW
Yb-doped fiber, high-power	100 fs – few ps	10 – 100 MHz	$\sim$ 10 kW
Mode-locked semiconductor diode	0.5 – 10 ps	10 – 100 GHz	mW – W
Microresonator soliton comb	sub-ps	10 – 1000 GHz	mW

Applications.

Ultrafast spectroscopy — pump-probe with femtosecond resolution
Optical frequency combs — equally-spaced lines for metrology and atomic clocks
Optical sampling — high-bandwidth optical sampling for electronics characterization
Multiphoton microscopy — high peak power excites two- or three-photon fluorescence
Material processing — clean ablation with minimal heat-affected zone

Stability requirements. A mode-locked laser is inherently unstable in the sense that locked operation must be maintained against perturbations. Saturable absorbers provide automatic restoration to mode-locked operation. Active modulators require electronic phase locking to a stable reference.

The repetition rate is set by the cavity length and is therefore a stable, narrow-linewidth RF signal (typically 10 MHz to 100 GHz), making mode-locked lasers also useful as ultra-low-jitter clock sources.