Fast and slow axis

"Fast axis" and "slow axis" name two orthogonal directions in two unrelated settings. In laser-diode optics they describe the beam's divergence: the fast axis of an edge-emitting laser is perpendicular to the epitaxial layers, where the beam spreads quickly, typically 25–40° full width at half maximum, and the slow axis lies in the plane of the junction, typically 6–12°. In polarization optics they describe propagation speed: the fast axis of a birefringent element is the polarization direction with the lower refractive index, along which light travels faster, and the slow axis the direction with the higher index.

Laser diodes: divergence

The emitting aperture of an edge emitter is set by the waveguide: about a micrometer high, fixed by the thickness of the epitaxial guiding layers, and a few micrometers wide for a ridge laser or tens to hundreds for a broad-area laser diode. Diffraction spreads light faster from the narrower dimension. For a Gaussian near field of waist radius $w_0$, the far-field $1/e^2$ half-angle is

$$\theta_0 = \frac{\lambda}{\pi w_0},$$

and the FWHM full angle is $1.177\,\theta_0$. At 980 nm, a near field 1 µm high at the $1/e^2$ points ($w_0 = 0.5$ µm) gives $\theta_0 = 0.62$ rad, or 42° FWHM; a 4 µm wide ridge mode ($w_0 = 2$ µm) gives 10.5°, a ratio of 4. The paraxial formula overstates such large angles, and real vertical modes extend into the cladding, so measured values fall in the 25–40° range quoted under far-field divergence. The fast axis is close to diffraction-limited because the vertical waveguide supports a single mode; in broad-area devices the slow axis is highly multimode.

Fast-axis and slow-axis collimators

Diode-laser optics usually treat the two axes separately with cylindrical lenses. A fast-axis collimator (FAC) is a short-focal-length, high-NA cylindrical or acylindrical microlens mounted a few hundred micrometers or less from the facet; the $1/e^2$ half-angle of 0.62 rad in the example above corresponds to an NA of 0.58, so the lens must accept a wide cone without truncating it. Its short focal length makes residual divergence and pointing sensitive to micrometer-scale placement errors. A slow-axis collimator (SAC) follows, and for a diode bar it is an array of cylindrical lenslets at the emitter pitch. The general procedure is in How to collimate a laser beam.

Birefringent elements: phase velocity

In a birefringent material, light polarized along the fast axis sees index $n_f$ and light along the slow axis sees $n_s > n_f$. After a thickness $L$ the slow component lags by the retardance

$$\Gamma = \frac{2\pi (n_s - n_f) L}{\lambda} .$$

In a uniaxial crystal which axis is slow depends on the sign of the birefringence: quartz is positive, so its optic axis (the extraordinary direction in a plate cut parallel to it) is the slow axis; calcite is negative, and there the optic axis is the fast one. A zero-order quartz half-wave plate for 633 nm is about 35 µm thick, corresponding to $\Delta n \approx 0.009$. Waveplate mounts usually carry a mark for one axis, but conventions differ between makers, so the documentation or a check against a plate of known orientation decides which axis is marked.

In polarization-maintaining fiber the two axes are set by stress. In PANDA and bow-tie fibers the line through the two stress-applying regions is the slow axis, with a birefringence of about $5 \times 10^{-4}$, which gives a beat length $L_B = \lambda/B$ of 3.1 mm at 1550 nm. Light is usually launched on the slow axis, and most PM connectors put the slow axis on the connector key.

Pitfalls

The near field of an edge emitter is elongated along the junction, while its far field is elongated perpendicular to it, so the ellipse appears to rotate by 90° between the facet and a distant screen; identifying the axes from the spot shape requires knowing which plane is being viewed. On a quarter-wave plate, swapping the fast and slow axes reverses the handedness of the circular output. In PM fiber, launching at a few degrees off the slow axis puts part of the power on the fast axis, which limits the polarization extinction ratio at the output.

Common questions

Which direction is the fast axis of a laser diode?

Perpendicular to the junction plane, the growth direction of the epitaxial layers. The far-field spot is therefore elongated perpendicular to the junction plane.

Why is it called the fast axis?

For laser diodes, because the beam diverges fastest in that direction. For waveplates and fiber, because light polarized along it has the lower index and the higher phase velocity.

Does it matter which waveplate axis is aligned to the light?

For a half-wave plate rotating linear polarization, no: the output is rotated by twice the angle to either axis. For a quarter-wave plate making circular polarization, yes: input at +45° to the fast axis gives one handedness and +45° to the slow axis the other.

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012); E. Hecht, Optics, 5th ed. (Pearson, 2017); M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).