Coupling a Free-Space Beam into Single-Mode Fiber: Lens Choice and Alignment

Scope

This article gives the procedure for coupling a collimated, near-Gaussian free-space laser beam into a single-mode fiber with a single lens: how to choose the lens, how tightly each degree of freedom must be aligned, the alignment sequence, and how to verify the result. The same principles apply to coupling light out of a fiber and back in, as in a free-space section between two fibers. Coupling from a fiber to a photonic chip is covered in Active Fiber Alignment to Edge Couplers and First-Light Grating Coupler Alignment; characterizing a beam that is not near-Gaussian is covered in M² Beam Quality Measurement. The Fiber Coupling Efficiency Calculator computes the losses discussed here for other parameters.

Choosing the lens

The fiber accepts light efficiently only in the shape of its own mode, which is close to a Gaussian beam whose waist diameter is the mode field diameter (MFD). A lens of focal length $f$ focuses a collimated Gaussian beam of $1/e^2$ radius $w_\text{in}$ to a waist of radius

$$w_f \;=\; \frac{\lambda f}{\pi\, w_\text{in}},$$

so the focal length that matches the fiber's mode radius $w_0$ is

$$f \;=\; \frac{\pi\, w_\text{in}\, w_0}{\lambda}.$$

For a 1550 nm beam 2 mm in $1/e^2$ diameter ($w_\text{in}$ = 1 mm) and a fiber with a 10.4 μm MFD ($w_0$ = 5.2 μm), $f$ = 10.5 mm. Stock aspheric lenses come in discrete focal lengths, and a small mismatch costs little: the coupling efficiency of two Gaussian modes with waist radii in the ratio $r$ is $\left(2r/(1+r^2)\right)^2$, which gives

A focal length within about 10% of the ideal is therefore adequate. An aspheric singlet or a fiber collimation package designed for the wavelength keeps spherical aberration low; a spherical singlet at this focal length and beam size adds aberration loss that the Gaussian formulas do not include. The lens should have an anti-reflection coating for the wavelength, and its clear aperture should be at least about 1.5 times the beam's $1/e^2$ diameter, since clipping the beam's wings changes the focused spot and costs power (see mode mismatch loss).

Alignment tolerances

For the matched case above, each misalignment reduces the coupling by the overlap of the displaced or tilted Gaussians. The tolerances for 1 dB of loss at the fiber face are:

These tolerances map back through the lens onto the collimated beam. A change in the angle of the incoming beam by $\alpha$ moves the focused spot sideways by $f\alpha$, and a sideways shift of the beam by $s$ at the lens tilts the focused beam by $s/f$. With $f$ = 10.5 mm:

The beam's pointing is therefore the critical adjustment: a quarter of a milliradian is a small fraction of a turn of a typical mirror-mount screw. The fiber's lateral position has the same 2.5 μm tolerance directly, and the focus tolerance is loose by comparison.

Equipment

Procedure

1. Set the beam height and direction

Level the beam at a constant height over the table using the two mirrors and two irises along the intended beam line. The lens and fiber mount are then placed on that line, which leaves the fiber stage's travel for the final adjustment rather than for correcting a skewed beam.

2. Place the lens and the fiber

Mount the lens with the beam centered on it, and place the fiber end near the lens's focal plane. For a connectorized fiber in a lens-matched adapter the spacing is set mechanically; for a bare fiber, set it by eye to the specified back focal length.

3. Find first light

The most reliable way to find first light is to send light backward: connect a visible or infrared laser to the far end of the fiber, so the fiber emits a beam that the lens collimates. Adjust the fiber stage until the emitted beam overlaps the incoming beam on the irises, in both position and direction. By reciprocity, when the two beams are overlapped the forward coupling is already near its peak. Without a back-propagating source, scan the fiber in X and Y around the estimated focus while watching the power meter on its most sensitive range; the tolerance of a few microns makes a blind scan slow, so a coarse visual alignment of the focus onto the fiber face first is worthwhile.

4. Peak the lateral position and focus

With signal on the meter, maximize with the fiber stage's X and Y adjustments, then adjust focus (Z) and re-maximize X and Y. Repeat until the reading no longer improves.

5. Walk the beam

The fiber stage cannot correct the angle at which the focused beam arrives, which is set by the beam's position on the lens. Walk the beam with the two mirrors: adjust the first mirror by a small amount in one axis, which lowers the reading, then recover the reading with the second mirror in the same axis. If the recovered reading is higher than before, continue in that direction; if lower, reverse. Repeat in the other axis. Each step trades beam position against beam angle while keeping the spot on the fiber core, and converges on the combination that the lens maps to the fiber's position and angle.

6. Iterate

Alternate steps 4 and 5 until neither improves the coupling by more than the meter's noise. Record the final reading and the incident power.

Fiber end faces

A flat, uncoated fiber end in air reflects about 3.4% of the light (0.15 dB), which is part of the expected loss, and returns that light toward the laser, where it can disturb a laser without an isolator (see optical feedback regimes). An angle-polished (APC) fiber end sends the reflection away from the beam path, but it also refracts the beam: with an 8° polish and a core index of 1.468, the light inside the fiber meets the end face at 8° and leaves it at 11.8°, so the beam outside is tilted by 3.8° from the fiber axis. Coupling into an APC fiber therefore requires the fiber to be tilted by that angle relative to the lens axis, or the beam to be offset on the lens so the focused beam arrives at the correct angle; collimators built for APC connectors include this offset. The connector types are compared in PC, UPC and APC connectors, and the end face should be inspected before alignment as in Fiber Connector Inspection and Cleaning.

Verification

The coupling efficiency is the power at the fiber's output divided by the power incident on the lens. The expected value is the product of the computed mode match, the lens transmission, the reflection loss at the fiber face, and any loss in the fiber and connectors between the coupling point and the meter. A result close to that product means the alignment is complete; a result well below it points to one of the failure modes below rather than to further alignment.

Common failure modes

Cladding light counted as coupled. With only a short length of fiber before the meter, light in the cladding reaches the detector and the efficiency reads high, and the apparent peak is broad. Use a metre or more of fiber with a loop, or a mode stripper.

Beam not Gaussian. A multimode or astigmatic laser, such as an uncorrected diode, cannot be matched by a single spherical lens; the achievable efficiency is limited by the beam's overlap with a Gaussian, and its M² is the first thing to check.

Wrong focal length. A waist far from the MFD, from a mistaken beam diameter or focal length, limits efficiency however well the alignment is done. Measure the beam diameter at the lens rather than taking it from a datasheet.

Aberration. A spherical singlet at short focal length, or a lens used backward, spreads the focused spot beyond the Gaussian waist.

Stage drift. Flexure stages and fiber holders relax after adjustment, and the coupling falls over minutes. Tighten locks lightly and re-peak after a settling time.

Polarization. For polarization-maintaining fiber, the beam's polarization must also be aligned to the fiber's axis; see Measuring PER and PDL.

References: A. E. Siegman, Lasers (University Science Books, 1986), chapters on Gaussian beams; H. Kogelnik and T. Li, "Laser beams and resonators," Applied Optics 5, 1550 (1966); D. Marcuse, "Loss analysis of single-mode fiber splices," Bell System Technical Journal 56, 703 (1977), for the offset, tilt and mismatch overlap formulas.