Optical delay line

An optical delay line makes light arrive later by a known, and often adjustable, amount of time. Almost all delay lines work by adding path length: the delay is the group delay of the extra path, $\tau = n_g L/c$, where $n_g$ is the group index of the medium and $L$ the added length. In air a retroreflector moved by $d$ on a translation stage lengthens the round trip by $2d$, so 1 mm of travel adds 6.67 ps, and a 1 µm step adds 6.67 fs. A meter of standard single-mode fiber adds about 4.90 ns. These two forms cover most laboratory needs, from femtosecond scanning to microsecond storage; on-chip waveguide spirals and switched networks of fixed delays serve integrated systems.

Free-space delay lines

A free-space line folds the beam onto a corner-cube or hollow roof retroreflector mounted on a linear stage. The retroreflector returns the beam parallel to itself, so small tilts of the stage do not steer the output. Delay per unit travel is

$$\frac{\Delta\tau}{\Delta d} = \frac{2}{c} = 6.67\ \text{ps/mm},$$

or 0.150 mm of travel per picosecond. Double-passing the stage doubles it. A 300 mm stage spans 2.00 ns. The resolution follows from the stage step and the stability from its straightness: a stage that tilts or wanders as it travels moves the output beam laterally, which changes the overlap with a second beam or the coupling into a fiber across the scan. Beam divergence over long travel changes the spot size in the same way. Rapid-scanning variants use rotating mirrors, voice coils or galvanometers to sweep picoseconds of delay at tens to hundreds of hertz.

Fiber delay lines

In fiber the delay per unit length is $n_g/c$. With the group index of standard single-mode fiber, 1.4682 at 1550 nm, this is

$$\tau/L = 4.897\ \text{ns/m} = 4.90\ \mu\text{s/km},$$

the figure behind the speed of light in fiber. One picosecond corresponds to 0.204 mm of fiber, so fiber is cut or stretched for fine trims and combined with a short free-space section or a fiber stretcher for continuous adjustment. Spools give long fixed delays: the delayed self-heterodyne linewidth measurement uses tens of kilometers, and 25 km is 122 µs. Recirculating loops, closed by a coupler or switch and often amplified, reuse one spool many times to emulate transmission over thousands of kilometers, and fiber loops have long been studied as optical buffers.

On-chip and switched delays

Integrated delay lines use long waveguide spirals. A silicon strip waveguide has a group index near 4.2 and a delay of about 139 ps per centimeter, so 1 ns needs about 7.2 cm of waveguide, which at a propagation loss of 2 dB/cm costs about 14 dB. Lower-loss silicon nitride waveguides are therefore preferred for long on-chip delays. Switched delay lines route light through binary-weighted sections (τ, 2τ, 4τ, ...) with optical switches, giving digitally selected delays.

Delay and phase shift

A phase shifter changes the optical phase by a fixed angle, which corresponds to a delay only at one wavelength. A true-time delay shifts the whole signal envelope in time and therefore acts equally on all frequencies. The distinction matters in beam steering. An optical phased array steered with phase alone has $\sin\theta = \lambda\,\Delta\phi/(2\pi d)$ for element spacing $d$, so its angle depends on wavelength: a beam set to 10° at 1550 nm points to 10.07° at 1560 nm. With true-time delays, each element is delayed by $d\sin\theta/c$, and the angle is the same at every wavelength; across a 1 mm aperture steered to 10°, the delay difference end to end is 0.58 ps.

Uses

• Pump-probe measurements and autocorrelation, which scan the delay between two copies of a pulse with femtosecond steps.
• Optical coherence tomography, in which the reference arm sets the depth being probed; time-domain systems scan it.
• Path matching in an interferometer, balanced receivers and coherent combining, where the arms must agree within the coherence length or within a small fraction of a symbol period.
• Timing calibration for time-of-flight ranging and for clocks and sampling systems.

Limits and pitfalls

Long fiber delays add loss, about 2 dB for 10 km of standard fiber at 0.2 dB/km, and chromatic dispersion: at 17 ps/(nm·km), a signal with 1 nm of bandwidth spreads by 17 ps per kilometer, which broadens short pulses and blurs timing. Fiber delays drift with temperature, by roughly 30 to 40 ps per kilometer per kelvin from the thermo-optic effect and thermal expansion, so a 1 km spool that warms by 1 K changes its delay by more than the period of a 40 GHz signal. Polarization also evolves along a long fiber. In free space, air currents and the temperature of the stage limit stability to fractions of a wavelength, so interferometric scans need active stabilization.

Common questions

How much delay does 1 mm of stage travel give?

Moving a retroreflector by 1 mm lengthens the round trip by 2 mm, which in air is 6.67 ps. A single-pass geometry, where the beam crosses the moving element once, gives half that.

How long a fiber is needed for 1 ns of delay?

At a group index of 1.4682, about 20.4 cm of standard single-mode fiber.

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010); A. M. Weiner, Ultrafast Optics (Wiley, 2009); R. A. Minasian, "Photonic signal processing of microwave signals," IEEE Transactions on Microwave Theory and Techniques 54, 832 (2006).