Moiré Magic: Unlocking On-Axis Structured Light Beams

Hey there, fellow light enthusiasts! Ever heard of structured beams? Imagine light that doesn’t just shine straight ahead but has cool, complex patterns – like tiny light tornadoes or beams with multiple twists. These aren’t just pretty; they’re super useful for things like grabbing onto microscopic particles, boosting communication speed, or seeing things with incredible detail.

For a while now, folks have been making these special beams using different gadgets. There are things like *spiral phase plates*, which are a bit tricky to make because they aren’t flat. Then there are *fork gratings*, which are easier to fabricate because they’re flat, but the special beam they create doesn’t come out straight ahead; it gets diffracted off to the side. And finally, *metasurfaces*, which are tiny, intricate patterns that can do amazing things with light, but designing them can be a real headache, and they’re not always easy to change once they’re made.

We really wanted a way to get these structured beams right on the main axis – the “zeroth order” – where the original light is going. This is particularly handy for applications like microscopy, where you want everything lined up neatly without bulky extra optics.

The Moiré Magic

So, we put our heads together and thought, “What if we used a classic trick?” You know how sometimes when you overlap two patterns, you get a third, larger, cooler pattern? That’s the magic of *moiré*. We figured we could apply this to light gratings.

We took two *binary forked gratings* – think of them as simple patterns of lines with a little “fork” in them, each designed to give light a specific “twist” or *topological charge*. Instead of physically stacking them, we used a logical “OR” operation to combine their patterns into one single pattern, which we call a Logically Flattened Grating (LFG). This process creates a moiré pattern within the LFG itself, with a larger effective period than the original gratings.

And guess what? When we shone light through this moiré-patterned LFG, it generated a structured beam! But here’s the really neat part: this structured beam appeared right at the *zeroth order* – exactly where we wanted it, on the main axis of the incoming light.

Why Zeroth Order Matters

Getting the structured beam on-axis at the zeroth order is a big deal. Traditional fork gratings push the structured beam into the first diffraction orders, meaning you need extra optics to steer and use it. This makes experimental setups more complicated and bulkier. For applications like integrated microscopy or tiny optical devices, having the structured beam come out straight is crucial. Our moiré method achieves this using a single, planar grating, which is much simpler and more compatible with standard fabrication techniques.

Putting it to the Test

We didn’t just stop at the idea. We tested this concept using both simulations and real-world experiments. First, we ran simulations based on Huygens’ principle, which basically treats every point on the grating as a tiny light source and calculates how their waves combine. The simulations confirmed our idea – the moiré pattern indeed generated an on-axis structured beam.

Then, we moved to the lab using a *Spatial Light Modulator* (SLM). Think of an SLM as a programmable screen for light; we can load our LFG patterns onto it and change them on the fly. This allowed us to quickly test different LFG designs created by combining binary forked gratings with various *topological charges* ((ell_1) and (ell_2)).

The experiments with the SLM beautifully matched the simulations. We saw the on-axis structured beams appear, and their shape – specifically, the number of “petals” or vortices around the central spot – was directly related to the difference between the topological charges of the two original forked gratings ($2|ell_1 – ell_2|$). It was super satisfying to see the theory play out in practice!

Tackling the Glare (DC Component)

Okay, so we had our on-axis structured beam, but there was a slight issue. Along with the cool patterned light, there was also some plain, unmodulated light coming through at the zeroth order – a “DC component.” This is like having a bright, uniform background that can wash out the structured pattern you want to see.

To fix this, we incorporated a clever technique called *crossed polarization microscopy*. By shining polarized light onto the grating and then using a second polarizer (an analyzer) oriented perpendicular to the first, we could filter out the unwanted DC component. The trick is that the structured light we wanted to keep *interacts* with the grating in a way that changes its polarization, while the plain DC light doesn’t. So, the analyzer blocks the plain light but lets the polarization-rotated structured light through.

However, for this polarization filtering trick to work really well, the grating needs to be *resonant* – meaning it interacts strongly with light at specific wavelengths.

Going Standalone and Color-Selective

This led us to the next step: creating standalone, physical gratings that were also resonant. We fabricated *metallo-dielectric* LFGs – basically, patterns etched into a thin layer of metal (gold) on a glass substrate, covered with a dielectric material (PMMA). We used electron beam lithography to make these tiny, precise patterns.

These fabricated gratings were designed to exhibit *Mie resonance*. Mie resonance happens when light interacts with particles or structures of a size comparable to the wavelength of light, causing strong scattering or absorption at specific colors. By carefully designing the period of our metallo-dielectric moiré gratings, we could tune this resonance.

When we tested these standalone gratings under broadband light (like white light), we observed something fantastic: *color-selective* on-axis structured beam generation! The structured beam at the zeroth order appeared predominantly in specific colors, and these colors shifted as we changed the grating period. This color selectivity is a direct result of the incorporated Mie resonance. It means we can design a grating that generates a structured beam only for, say, green light, while letting other colors pass through or diffract into different orders.

The Science Behind the Colors (Mie Resonance)

Digging a bit deeper into the simulations, we saw how the light waves interacted with the tiny metal and dielectric structures in our fabricated gratings. At certain wavelengths, the electric and magnetic fields of the light would get strongly concentrated and circulate within the grating’s features. This is the signature of Mie resonance.

Unlike other types of resonances, Mie resonance in our structure seemed to involve energy flow patterns within the tiny air gaps and PMMA grooves of the grating. This strong, localized interaction at specific wavelengths is what causes the polarization rotation needed for our DC filtering trick and, consequently, leads to the observed color selectivity. The simulations helped us understand *why* the color shifted with the grating period – it’s all tied to how the size and shape of the resonant structures match the wavelength of light.

Wrapping It Up

So, what have we got here? We’ve demonstrated a pretty cool and versatile way to generate on-axis structured beams at the zeroth order of a grating. By leveraging the simple concept of moiré patterns created by overlapping binary forked gratings, we bypass some of the complexities of traditional methods.

We showed it works with reconfigurable tools like SLMs, allowing for dynamic beam shaping, and also with standalone, nanofabricated metallo-dielectric gratings. The ability to make these gratings using standard planar fabrication techniques makes this approach scalable. Plus, by adding Mie resonance, we unlocked color-selective structured beam generation, adding another layer of control.

This method opens up exciting possibilities. Imagine using these compact, on-axis structured beams for more precise optical trapping of tiny particles, enhancing microscopy techniques, or developing new types of sensors. It feels like we’ve just scratched the surface of what moiré patterns can do for structured light!

Source: Springer