Glossary entry

Optical soliton

A pulse that propagates without changing shape because nonlinear self-phase modulation exactly balances chromatic dispersion. The natural pulse shape for ultra-long-haul transmission and microresonator frequency combs.

In the anomalous dispersion regime ( $D > 0$ for typical fiber telecom convention), chromatic dispersion and self-phase modulation produce opposing effects:

Dispersion broadens a pulse by sending different frequency components at different group velocities
SPM chirps a pulse: the leading edge is red-shifted (lower frequency) and the trailing edge is blue-shifted (higher frequency)

In anomalous dispersion, red frequencies travel slower than blue. The SPM-induced chirp therefore acts to compress the pulse: the red-shifted leading edge slows down while the blue-shifted trailing edge speeds up. At a specific peak intensity, SPM compression exactly balances dispersive broadening — the pulse propagates indefinitely without changing shape.

Fundamental soliton solution of the nonlinear Schrödinger equation:

A(t, z) \;=\; A_0 \, \text{sech}\!\left(\frac{t}{T_0}\right) \exp(i \, \beta_2 z / (2 T_0^2)).

The soliton energy and pulse width are related:

P_\text{peak} \cdot T_0^2 \;=\; \frac{|\beta_2|}{\gamma},

where $\beta_2 = -\lambda^2 D / (2\pi c)$ is the GVD parameter and $\gamma = 2\pi n_2 / (\lambda A_\text{eff})$ is the fiber nonlinear coefficient.

For SMF-28 at 1550 nm ( $\beta_2 \approx -21$ ps²/km, $\gamma \approx 1.3$ /(W·km)): a 10 ps fundamental soliton requires $\sim$ 1.6 W peak power.

Higher-order solitons ( $N = 2, 3, \ldots$ ) require power $N^2 P_\text{peak}$ and undergo periodic shape oscillations (soliton breathers) with period $z_0 = \pi T_0^2 / (2 |\beta_2|)$ .

Applications.

Application	Use
Telecom soliton transmission (1990s)	Long-haul transmission with pulse-shape preservation; superseded by dispersion-managed coherent transmission
Dissipative solitons in mode-locked fiber lasers	Soliton plus gain/loss balance — produces sech²-shape femtosecond pulses
Microresonator soliton combs	Single solitons circulating in high-Q microresonators produce ultra-clean optical frequency combs
Soliton supercontinuum generation	Soliton instabilities produce dramatic spectral broadening
Optical clocks via stable comb anchoring	Frequency comb sources for absolute frequency metrology

Dissipative vs conservative solitons. Pure (conservative) solitons solve the lossless nonlinear Schrödinger equation. Real solitons in fiber lasers also balance gain and loss — they are called dissipative solitons and exist only in laser cavities or amplified spans, not in passive fiber.

Microresonator solitons revolutionized optical frequency comb technology in the 2010s. Pumping a high-Q microresonator with a narrow-linewidth CW laser at the right detuning produces a single soliton circulating in the ring; its output spectrum is an octave-spanning comb with line spacing equal to the FSR. Used in compact optical clocks, ranging, and dual-comb spectroscopy.