Fiber Coupling: Steer a Laser into a Single-Mode Fiber
Sooner or later, almost every optics lab has to get a laser beam into a single-mode optical fiber. The fiber carries the light cleanly to another table, another room or another instrument, and it cleans up the beam shape on the way. The catch is the target: the light-carrying core of a single-mode fiber for visible and near-infrared light is only about 5 micrometres across, a tenth of the width of a human hair. To get the light in, you steer the beam with two mirrors and focus it with a small lens onto that core.
The simulator below lets you try it. The mirrors start misaligned and only a few percent of the light gets in. Turn the four adjuster knobs and bring the power up as close to 100% as you can.
Two things have to be right at once
A lens turns angles into positions and positions into angles. If the beam reaches the lens at a small angle θ, the focused spot lands a distance f·θ from the center of the fiber, where f is the focal length. If the beam hits the lens off-center by a distance x, the focused light arrives at the fiber at an angle x/f. The fiber only accepts light that lands on its core and arrives from within a narrow cone, so both the angle and the position of the beam have to be right.
The share of the power that gets in is the overlap between the focused beam and the fiber’s own light pattern, its mode. Both are close to Gaussian, and for a lens chosen to match them the overlap is
η = exp(−(f·θ)² / w_f²) · exp(−(x/f)² / θ_f²), θ_f = λ / (π w_f)
Here w_f is the radius of the fiber mode (2.7 µm in the simulator) and θ_f is the half-angle of the cone it accepts (about 0.09 rad). The first factor is the cost of the spot missing the core, the second the cost of the light arriving at a slant. With the 780 nm laser, 0.5 mm beam and 5.5 mm lens used here, a beam angle error of 50 µrad or a position error of 50 µm at the lens each cost about 1% of the power.
How to play
- Watch the two round views. The left one shows the focused spot on the end of the fiber; the dashed yellow circle is the fiber mode. The right one shows the direction the light arrives from; the yellow circle is the cone the fiber accepts. Get the red spot and the white dot both inside their circles and the power goes up to 100%.
- Turn the knobs. Each mirror has a horizontal and a vertical knob. Drag the sliders for big moves and use − and + for small steps. The power meter shows how much light comes out of the fiber, and the orange mark on its bar is your best so far.
- Pick the difficulty. “Easy” makes both tolerances three times larger than a real fiber, so the light is easier to find. “Realistic” uses the true numbers for a single-mode fiber at 780 nm.
- Stuck? “Show the solution” turns the knobs to the perfect position, and “New misalignment” starts a new round.
What to look for
1. Both mirrors move the spot. Tilting either mirror changes the beam angle at the lens by the same amount, so either one can bring the red spot onto the core. That is usually the quick first step, and it often gets you to 50% or more.
2. Then you need to walk the beam. The two mirrors are at different distances from the lens (0.9 m and 0.6 m here), so the same tilt shifts the beam by different amounts there. Once the spot sits on the core, the only way to fix the remaining position error is to use both mirrors together: tilt M1 a little, which costs some power, then win the power back with M2. If the new maximum is higher than before, keep going in that direction; if it is lower, go the other way. This is called beam walking, and it is how people align fibers, cavities and interferometers in real labs.
3. Each mirror tilt counts twice. Tilting a mirror by θ turns the reflected beam by 2θ. For the vertical knobs the effect is smaller, √2·θ instead of 2θ, because the mirrors sit at 45° to the beam. You can see this in the numbers: in realistic mode a horizontal tilt of 20 µrad on M1 alone costs about 1.2% of the power, the same vertical tilt only about 0.6%.
4. The power falls off fast. The overlap is Gaussian, so small errors cost very little and large ones cost a lot. In realistic mode a tilt of 20 µrad on one mirror costs about 1%, 50 µrad about 5 to 7%, and 100 µrad about 20 to 25%. The last few percent are where alignment gets slow.
The numbers
| Quantity | Formula | What it tells you |
|---|---|---|
| Fiber mode radius | w_f = λf / (πw) | The focused spot size. The lens is chosen so it matches the fiber mode: 2.7 µm here. |
| Acceptance angle | θ_f = λ / (π w_f) | How far off-axis the light may arrive. About 0.09 rad (5°) here. |
| Spot offset | f · θ | A beam angle error θ at the lens moves the focused spot sideways. |
| Arrival angle | x / f | A position error x at the lens tilts the light arriving at the fiber. |
| Mirror tilt to beam angle | 2θ (horizontal), √2·θ (vertical) | Reflection doubles a tilt in the plane of the beam; at 45° incidence an out-of-plane tilt counts √2 times. |
| Tolerances at the lens | w and λ / (πw) | The beam radius and the beam’s divergence set the scale: a position or angle error of one tenth of these costs 1%. |
How the simulation works
The beam is traced as a ray in three dimensions. At each mirror the mirror’s surface normal is rotated by its two knob angles, plus a hidden error that makes up the misalignment, and the ray is reflected exactly. The simulator then finds where the ray crosses the lens and at what angle, converts those into the spot offset and arrival angle at the fiber, and applies the overlap formula above. The ray trace agrees with the simple 2θ-times-distance rule to better than 0.01%, and the overlap formula matches a direct numerical overlap of the two Gaussian beams.
Each new misalignment is random, but always leaves between about 0.2% and 6% of the light in the fiber, the faint signal you would have after a rough alignment by eye.
What the model leaves out
- Focus. The fiber sits exactly at the focus of the lens, and the beam size matches the fiber mode. In practice you also adjust the distance between lens and fiber, and a mismatched beam size limits the best coupling to less than 100%.
- Losses at surfaces and lens errors. Uncoated glass reflects about 4% at each surface, and a real lens adds aberrations. With good coatings and an aspheric lens, labs typically reach 70% to 90% into a single-mode fiber.
- Real knobs. Real adjuster screws have backlash, the mount can shift a little when you let go of the knob, and turning one axis can nudge the other. Here every knob does exactly what it says.
- Polarization. Polarization-maintaining fibers also need the light’s polarization lined up with the fiber’s axes. The model ignores polarization.
Where stable optics comes in
Getting to 90% is half the job; staying there is the other half. Once a fiber is aligned, every microradian a mirror mount drifts costs power, and the loss grows with the square of the drift. Ordinary kinematic mounts can tilt by several microradians for each degree of temperature change, and they settle a little after every adjustment. Over a day, that adds up to tens of microradians, and as the simulator shows, 50 µrad on one mirror already costs several percent. The fiber output sags, and someone has to walk the beam again.
That is what Physiverse mounts are built for: monolithic flexure mounts with less than 0.1 µrad of tilt per degree, so your coupling stays where you left it. See the product line.