Photonic crystal fibers (PCFs) steer light with patterns of microscopic air channels, but they are normally drawn from a heated preform, which distorts the hole pattern, rules out some geometries and makes µm-precise short segments very hard to make. The authors ask whether high-resolution 3D printing (two-photon lithography) can build PCF-design waveguide segments directly, in one step, on the end of a standard optical fiber. They print five very different PCF classes (highly nonlinear, helically twisted coreless, photonic-bandgap hollow-core, anti-resonant hollow-core, fractal ring-core) and

Some of the most powerful optical fibers are full of microscopic air holes, and their pattern decides what light does. Many promising patterns have never been made. Andrea Bertoncini and Carlo Liberale 3D-printed such patterns straight onto the tip of an ordinary fiber, then stacked three of them into a 210 µm tower that sorts light by the direction it vibrates.

Follow the light from a single missing hole to that tower and its measured performance — and try the steps yourself.

1 Holes guide light

2 Draw vs print

3 Five printed fibers

4 Light that hops

5 The print farm

6 The measured split

7 What next

Holes that guide light

An ordinary optical fiber traps light in a glass core that slows light slightly more than the glass around it. A photonic crystal fiber does the same job with air: a lattice of microscopic channels runs the full length of the fiber, and the pattern of holes decides where light can live, how big its spot is and how it behaves.

Tap holes to remove or restore them

illustrative model Scalar wave model solved live at 1550 nm (polymer n = 1.532, pitch 2.3 µm). The authors used full vector simulations; hollow-core guidance is not captured here.

What you just saw. Air has a lower refractive index than the polymer — light moves faster through it. A spot with a missing hole is, on average, “slower” than its holey surroundings, so light gathers there. It is the same total internal reflection that ordinary fibers use, built from geometry instead of chemistry (the paper calls it modified total internal reflection). Bigger holes squeeze the spot; two missing holes make two cores that share light.

So the magic is in the pattern. Making the pattern is the hard part.

The guided light obeys a wave equation across the cross-section: ∇²ψ + k₀² n(x,y)² ψ = β² ψ, where n is the refractive index map and β tells how fast the pattern travels along the fiber (neff = β/k₀). The fundamental mode is the pattern with the largest β. Starting from a rough guess, the page repeatedly nudges ψ toward that solution — the “settling” glow is this relaxation converging. For twin cores it also finds the odd (opposite-sign) pattern; the difference between the two neff values gives the beat length you will meet in section 4. This simplified scalar model ignores polarisation, which is exactly what the real splitter exploits.

Why print instead of draw?

Photonic crystal fibers are normally drawn. A glass rod a few centimetres across, carrying a scaled-up copy of the hole pattern, is heated until soft and pulled into a fiber far thinner than a hair. On the way, viscosity, gravity and surface tension tug at every hole: small holes can close, shapes round off, and some designs cannot be made at all. Cutting precise micrometre-long pieces, or tapering them, is harder still.

The same design, two ways

cartoon The drawn version exaggerates the distortions the paper names (viscosity, gravity, surface tension); it is not a fluid simulation. The printed version on the right copies the design.

Laser focus (violet) hardens resin only where it is brightest. Drag to rotate. Printed on a fiber end (grey), stylised scale.

Five fibers, printed

To show the method can copy almost any design, the authors printed examples from five families of photonic crystal fiber that guide light in completely different ways, and sent light through each. Every one carried the expected mode — the stable spot or ring of light the design is meant to hold. Hollow-core designs are very sensitive to shape, so their working at all is evidence that the printing is accurate.

measured Mode sizes are the measured mode-field diameters (Fig. 1). Cross-sections are redrawn after the paper's figure; the glowing light shapes are schematic.

The price of plastic

Printed polymer absorbs much more light than fiber glass. For a solid-core printed segment the authors measured 0.44 dB/mm at 1070 nm and 0.79 dB/mm at 1550 nm — essentially the resin's own absorption — against about 8 dB per kilometre for a silica fiber of the same design. No good for cables; for a device a fraction of a millimetre long, it costs only a few percent.

Printing also allows something drawing never could: stacking different segments, each tens of micrometres long, with tapers and precise offsets, into a single device. The authors used that freedom to build something new.

Light that hops between twin cores

Put two cores close together and they share light. Launch light into core A and it leaks into core B, then back again, like two coupled pendulums trading their swing. The distance for one full transfer is the coupling length, CL.

Light also has a polarisation: the direction its wave vibrates. Here red is light vibrating side to side (↔ horizontal) and green vibrates up and down (↕ vertical); added together they look yellow, like ordinary mixed light. The splitter's cores are oval and its central hole elliptical, so the two polarisations hop at different rates.

Final printed design: CL↔ 71 µm, CL↕ 140 µm — measured CLR; lengths inferred from the 140 µm coupler.

Find the cut where red has come home to core A while green has crossed to core B.

Switch to the first print. Can you still separate them cleanly? Where is the best compromise?

Compare “on paper”. The paper estimated about 13.5 dB at 140 µm for this simulated design.

Why the magic number is 2. A splitter needs a length that is an even number of coupling lengths for one polarisation (so it returns home) and an odd number for the other (so it ends up across). The shortest such device has CL↕ = 2 × CL↔: the coupling-length ratio, CLR , must be 2. The closer the ratio is to 2, the cleaner the best possible split: in this ideal model it falls from essentially perfect at 2 to about 17 dB at 2.27 and about 12 dB at 1.6 — and at 1.6 only at an awkward compromise length. The paper lists “CLR not exactly 2” among the reasons a real splitter's working band narrows.

ideal model Fraction in core B = sin²(πL / 2CL), the curve the authors fitted to their measurements. simulated “On paper” values from Fig. S5.2a. measured First print from Fig. S5.2b; final lengths inferred from the 140 µm coupler and its measured CLR of 1.97.

Two neighbouring cores support two shared patterns: an even one (same sign in both cores) and an odd one (opposite signs). They travel with slightly different effective indices, so they drift in and out of step; light starting in one core is their sum, and it appears in the other core when they are half a cycle apart. Hence the paper's Eq. 1: CL = λ / 2(neven − nodd). Try the Twin cores preset in section 1 to see a beat length computed this way.

The authors' simulations also show how sensitive these lengths are. Shrinking the whole cross-section by a few percent — as printed resin can shrink during development — shortens both coupling lengths a lot:

The print farm: print, measure, adjust

On paper, the starting design had a CLR of 2.27. Printed, it measured 1.6. Tiny real-world deviations — the printer's discrete steps, the resin shrinking slightly as it is developed — shift the coupling lengths in ways simulations could not pin down. So the authors used the speed of printing instead.

Each round they printed 16 towers on a glass slide: four versions of one geometric tweak, each at four coupler lengths (about 6 hours). An infrared camera measured how the light split; fitting the hop curves gave both coupling lengths and the CLR. They kept the best version and tweaked something else, guided by simulated trends. Your turn: choose a knob, print an array, keep the best row. Reach CLR 2.00 ± 0.04.

CLR after each kept round

game model Interpolated from the reported measurements and simulated trends (Figs. 3, 4, S6, S7); it reproduces the authors' path 1.60 → 1.68 → 1.72 → 2.07 → 1.97 but is not a simulation of the device. Knob names follow Fig. S5.1: L2 (row spacing), n1x (centre-hole width), r2 (hole radius).

The authors' real sequence: move six holes closer (L2 1.77 → 1.67 µm), widen the centre hole (n1x 0.90 → 0.95 µm), enlarge ten holes (r2 0.48 → 0.60 µm, overshooting to 2.07), then narrow the centre hole back (0.90 µm) to land at 1.97 . The result: a 140 µm coupler in a 210 µm device, reached through an optimisation loop they describe as significantly faster than anything possible with drawn fibers, where every new geometry means a new preform.

On the fiber: the measured split

The optimised splitter — down-taper, 140 µm coupler and fan-out, 210 µm in all — was printed in one go, in about 25 minutes, on the end of a standard single-mode fiber. The authors then sent light of different wavelengths through it and measured how cleanly each core held its own polarisation: the extinction ratio. 10 dB means the wrong polarisation is 10 times weaker; 20 dB, 100 times.

measured Curves traced approximately from Fig. 5c. Spot brightness ratios within each core follow these extinction ratios; absolute brightness is not to scale.

Around 1550 nm — the band that carries most long-distance internet traffic — the split is clean: both cores stay above 10 dB over a 100 nm range, above 12.6 dB across the whole telecom C-band (1530–1565 nm), and at least 14.37 dB at 1550 nm itself. At 1330 nm the two polarisations still mix. The band is narrower than the 150 nm predicted for the original design, which the authors attribute to higher-order modes neglected in that prediction, a CLR not exactly 2, and some scattering in the polymer.

This is the first polarising beam splitter built from photonic-crystal-fiber designs. Earlier splitters printed on fibers work by diffraction and send their light into open space; this one keeps both outputs inside waveguides, ready to connect onward.

What could be printed next?

Back to the opening question. The authors anticipate that their method will “unleash the creativity” of fiber designers: geometries once considered impossible to fabricate become printable, and new ideas can be tested without long waits for a custom fiber. These are the directions they point to.

Colour sorters and switches

A similar dual-core structure could be optimised to separate wavelengths or to switch light with light.

Twist on demand

Very high twist rates, varied finely along or across the fiber, could lead to new optical effects.

Sensors at the tip

Printed hollow-core designs on a fiber end could probe liquids and biological samples.

Glass instead of plastic

High-resolution printing of glass-ceramics could cut losses and improve mechanical and thermal robustness.

Longer and lighter

Faster multiphoton printers could make segments longer than today's few millimetres; unused cladding could be a light wireframe.

Hybrid fiber tips

Combined with printed lenses, mirrors, metamaterials, metals or liquids — for optical tweezers, light with orbital angular momentum, quantum technologies and biomedical probes.

Andrea Bertoncini and Carlo Liberale , “3D printed waveguides based on Photonic Crystal Fiber designs for complex fiber-end photonic devices,” arXiv:2009.04209 [physics.optics] (2020), King Abdullah University of Science and Technology. arxiv.org/abs/2009.04209

All numbers come from the paper and its supplement. Diagrams on this page are redrawn from the paper's figures; values marked “traced” were read approximately from plots. Interactive models are simplified teaching models and are labelled as such: the lattice solver is a scalar approximation, the coupler uses the ideal two-mode curve, and the print-farm game is interpolated from reported measurements. The graphical abstract is an AI-generated conceptual illustration based on the paper's Fig. 2.

3D graphics with three.js (MIT License). Fonts: Bricolage Grotesque, IBM Plex Sans and IBM Plex Mono (SIL Open Font License).