OpticStudio Proves Theory

Leading-edge laser system designers use OpticStudio to confirm a mathematical theory that allows cost-saving,relaxed laser standards for ultra-precise micromachining. Jan Kleinert is no stranger to advances in laser design and machining. In fact, as head of the central research group at Electro Scientific Industries (ESI)—a creator of laser-based manufacturing solutions primarily for the semiconductor and consumer electronics industry—he was responsible for the first deployment worldwide of high-powerultra-fast lasers on an industrial scale.

In a more recent innovative turn, Jan and his colleagues discovered a way to employ a laser beam’s astigmatism and asymmetry values to balance each other—and turn what might have been an unusable laser into a serviceable one, even for precision applications.

With the right calculation, one of these aberrations ca nnegate the other sufficiently to create a better-quality, rounder beam using more forgiving specs (and therefore at a lower cost).

In the process, they also found that the kind of beam-shape control afforded by this technique has a unique purpose in one of their newest leading-edgepursuits: the use of elliptical beamsfor particular beam-steering applications.

As they focus on dynamic beam steering and shaping, Kleinert and his team have begun employing elliptical laser beams in an unusual way—and using this new “theory of conversation” to ensure that the beam becomes round again when it reaches the work surface.

Jan and his colleagues were able to use OpticStudio to prove the absolute applicability of this useful new calculation, where exceedingly complex mathematics alone could not.

Now pursuing industry journal publication, Jan and colleagues are eager to share this significant finding with the laser design community.

Recently, we sat down with Jan to discuss the fascinating process of proving this theory, its implications for laser design in practical terms, and how this actually led them to explore more complex and leading-edge uses for a beam’s ellipticity. We also learned how OpticStudio was instrumental in the testing and validation of the theory, and what features were most helpful.

ZEMAX:Tell us about the basic idea of this theory.

Our company, ESI, makes large laser systems used for micromachining—very sophisticated high-precision beam delivery systems. We start with a high-powered laser and send it through optics and down to a work surface. These lasers are used to melt or ablate or blow holes or scribe a surface.

Our team basically used two negative aspects of lasers in a way that these “faults” balance each other out—to make better quality possible with less cost.

For those who don’t work with lasers, here’s laser 101:when it comes to beam quality, the quality propagation factor is an M squared parameter. If this value equals 1, the beam is perfect. A perfect beam is easy to work with. It scribes nicely.

It’s hard to get laser beams that have an M squared of 1.The closer to 1 the M squared value is, more expensive it is and harder to manufacture. Nevertheless, those whose tasks require precision lasers want to buy lasers that have a high M squared value.

What causes deviation from this ideal value is if you have poor astigmatism and asymmetry. What Jan and his colleagues workedout was a way to use astigmatism and asymmetry—to offset one another and create a better beam.

The quality of a beam is determined by how well it comes to a focus at the smallest point. That's where you can describe asymmetry and astigmatism as different values in the x and y axis (like height and width).

One is talking about size of the beam: at a certain point in space the beam can be bigger along the x axis than the y axis. It becomes more elliptical and that means it’s asymmetric. If it’s not asymmetric, it’s a is perfect circle, which is usually what we want.

Astigmatism is relative to where the smallest point is. The beam comes down to focus and then expands again, and it can do that at different locations in different axes.

I and David Lo and other colleagues came up with this idea and set out to prove it. If it worked, we hypothesized, it would be a different way of thinking about how to use a laser beam with a “bad” M-squared factor. By controlling these two parameters, a lower-cost laser could conceivably produce a higher-quality result.

In the past, we specified the maximum amount of astigmatism and maximum asymmetry the beam is allowed to have. What this discovery allows us to do is that if a laser has more astigmatism than we wanted, but at the same time if the asymmetry is better, that’s permissible. That laser will still perform adequately and we can be confident that those lasers will work for our systems. For us this applies to lasers we create or lasers we acquire from other vendors.

And of course, this reduces costs. You can always specify that the beam meets necessary roundness everywhere in the focal plane and focal region, and push that problem onto your laser supplier. You might out of caution reject other pieces. You can do that, but you make life harder for the supplier and they will charge you for it.

We have shared this insight with variety of laser vendors. We have begun to specify our lasers differently in order to give vendors more headroom in their design and specs without compromising on performance side for our applications. And now this is a model that other companies can use in designing laser systems.

ZEMAX: How did this idea about “offsetting” astigmatism and asymmetrycome to you?

We stumbled across this idea a few years ago. In precision micromachining, you want a very round spot at the work surface,and sometimes in more demanding applications you want that not just atthe work surface but throughout the focal region.

It’s one thing to have a perfectly round beam in one thin plane. It’s another matter to have a round beam across an entire focal region.

If you dig deeper into your material, or if you can’t perfectly control the vertical positions of the work piece or any other combo of things, it becomes very difficult.

Typically what you see in OpticStudio is geometric optics where all the rays are straight, and you can of course also go into principle optics in Zemax or in real life, and you have Gaussian optics, where all those rays converge into a finite size. The layout plots in OpticStudio show rays that converge to an infinitely small point, but in reality lines can't all intersect at a perfect point—as points of light try to occupy the same spot, fundamental properties force them to spread out and they “push each other apart” (the point spread function). So there is a finite limit as to how small of a spot you can get.

OpticStudio can also simulate this finite spot size, using diffraction calculations.
That region where things are not perfectly linear is called Rayleigh range. Rayleigh range is a quantity that relates the distance over which a spot stays small. The way in a magnifying glass rays come through a small point and then expand again. It depends on wave size—how tightly you'refocusing the beam—as well as wavelength.

When wave size approaches wavelength, that Rayleigh range becomes very short. When you have very small Rayleigh range,because you’re focusing very steeply down, your beam changes very quickly over very small distance.Rays come to focus really fast. You get a smaller spot size, but the steeper focus angle means as you move up and down your beams will change significantly, which could be a problem if you have to have a specific size beam. it would mean you could only work in one specific region.

If you want a certain size for your beam at the work surface to do yourtask, you have to be very careful how you control your beam.

That essentially was the origin of looking very carefully at the astigmatism and asymmetry of our beam.Because if our waves in the horizontal and verticalpositions—the X and Y axis—are not perfectly matched, then we never have a small spot.That's basically astigmatism and if you want to have a small or round spot and the beam is astigmatic, you’re out of luck.

And similarly if your wave size is one axis is larger than in the other, then again even if the wave location is perfectly matched,you'll just have an elliptical beam in location, which again prevents very small wave location.

What we used to do to guarantee very small spot sizes compared to their wavelengths was have very stringent specs on lasers, both in astigmatism and asymmetry. Because we treated them as independent variables.

When we looked at a bunch of scenarios with OpticStudio as to how those two values conspired, we found that in the right plot, you can normalize your axis.So you get a certain, which means you have a constant.

In other words, you can trade astigmatism for asymmetry.

We found that instead of having these very strict specifications for each quantity individually, we could say “okay, this laser can have more astigmatism because has less asymmetry” and vice versa.

So first we tested this to first order, for small astigmatism and asymmetry values.

When we dug in writing our paper on this, we found that it was not only true to first order but actually exactly true. It’s true to all orders. Meaning it’s more than an approximation. It doesn't matter how big the astigmatism or asymmetry is, it is a fundamental property of the Gaussian beam.

ZEMAX: Where did using OpticStudio come into the picture? How did the software help with the process of proving your theory?

This a mathematical concept, but it needed validation. The math of this theory is really complicated, and it’s much easier to let OpticStudio do it for you.

To our surprise in our literature search, even though this discovery seems to be a fundamental quantity, we weren't able to find any publication speaking to this. Yet in the review process, we were told that this theory and of itself was not interesting enough and that we should expand our analysis to what’s called a general astigmatic beam.

For background, you can have a simple stigmatic beam—a beam without astigmatism. Here the wave location in x and y always match. A simple astigmatic beam has a non-zero astigmatism where the two wave locations can be different.

With asimple astigmatic beam, a standard Gaussian beam, if you have no asymmetry (meaning the two wave sizes are the same) but have some astigmatism) you have an ellipse. The orientation of that ellipse will always be along the x or y axis of the beam.

Basically on one side of focus you have an ellipse that's flattened let’s say around the y axis, and then on the far side of the other focus you have long side along the x axis.So you have an ellipse that starts to shrink, becomes round, then becomes an ellipse along other axis.

The principle axes of that ellipse stay same. In one case it’s “squished” in one way,in another case the otherway, but if you draw an ellipse there are two principle axes and those two stay constant.

In a general astigmatic beam, what happens is that the ellipse starts to rotate as you go through the focus. You can add some rotation to your beam,or it becomes a rotating beam, there are avariety of ways to introduce that, or how you end up with that. But you need to have non-rotationally symmetrical optics—something to break the symmetry of the original beam.

This general astigmatic beam is mathematically a bit more interesting and complicated. And so for the simple astigmatic beam we were able to give closed analytical forms of the solutionto show that extreme ellipticity is conserved when you go through a simple lens.

When you go from the simple case to a general astigmatic case, however, the math gets so complicated that we were no longer able to provide closed forms. And so we were not able to prove, in that way, that extreme ellipticity is a conserved quantity.

So OpticStudio was our validation tool of choice to make sure this theory would work in real systems. We were able to set up different systems with these values and prove that you can get a good result with this approach. We ran a bunch of numerical cases with different input parameters. And we found out numerically that extreme ellipticity is still conserved with a general astigmatic beam.

That basically shows you that the power of having a tool like that—where we could no longer solve this analytically, but could use the software to show that the behaviors we anticipate do stay the same in all cases.

So we were able to use software to prove what math could not. When we did define this law and wanted to extend it to general astigmatic beams and a simple piece of paper or mathematical way to do this analytically failed us, we could go back to OpticStudio and instead simulate these scenarios in general astigmatic cases which are too complicated to calculate analytically. We could numerically find out if our suspicion was correct about what we thoughts was true.

Now, proving something numerically is very hard. It’s not true “proof” doing this numerically, a mathematician would say. But for all intents and purposes, it is true and we haven't been able to find a case where it is not true.

OpticStudio has always allowed us to map out what's allowable in our beam for our purposes, and where to things start to fall off a cliff. This process got even easier now that we have this conservation law, even when we use elliptical beams.

ZEMAX: So, this isn’t just theory for you any more—you’reable to use this law functionally, other than simply for publishing it?

Yes, exactly. One might reasonably ask “Who cares about general astigmatic beams?” Well, we do—and not only because the editor of the magazine made us do it. We actually are starting to use elliptical beams in our systems. As we get into more complicated modern systems, we have just recently started to actively control elliptical beams, instead of just using beautiful round beams.

When we started, we weren’t necessarily using these beams, But I’m in research, so I'm looking out a bit further. We are just now getting to point where comfortable using elliptical beams.

To create these beams, wehave to use prisms or cylindrical lenses that are not rotationally symmetric. So now we run the risk that even though the laser still puts out a simple beam, our optical train might actually transform that simple astigmatic beam into a general astigmatic beam. When you start out with elliptical beams it’s easy to get to a general astigmatic beam if you’re not careful. Your optics have to be very well aligned so you don't introduce any rotation to a beam.

So in that sense it was also interesting for me in hindsight to learn that this is a bounded problem. Given that now in some systems we deal with elliptical beams, we know that if you go from a simple astigmatic beam to a general astigmatic beam, the ellipticity will not get beyond our control.

Therefore, working on this paper in hindsight turned out to be very helpful. What started as an interesting academic exercise is becoming a very useful thing in designing laser machining systems.

Working with these beams is tricky. On a high level, if you start with a nice round beam and also want a round beam at the work surface, you tend to not want to mess with it because chances are you won’t get it back. If you mangle your beam along the way, you have to do a whole to more work to ensure that no matter what happens you get that round beam back at the end.

ZEMAX: So why would you go through that work? What is the advantage of“going elliptical” in the middle?

Where elliptical beams have a purpose for us is in a specialty of ours called Acousto-Optic Deflectors (AODs). ESI is now famous for what we call“third dynamic”—that’s a marketing term for using AODs in a very specific way.

To squeeze maximum performance out of AODs,sometimes it’s preferable to use elliptical beams with them rather than round ones, even though at the work surface we still want to have a round beam. We start out with round beam, we make an elliptical beam, send it to the AOD, and then reshape it back into a round beam.

That’s whenwe run the risk of introducing general astigmatism, and our law and the paper helped us to understand where things can and cannot go awry.

ZEMAX: Can you tell us a little more about what an acousto-optic deflector does?

An acousto-optic deflector is a non-mechanical way of steering your beam—very, very fast. No moving parts;it works using sound.

In a classic laser machining systemyou have a beam and use mirrors on rotationa lmotors and stages that move your beam or workpiece with respect to the beam. You have two motorized mirrors perpendicular to each other and a focusing lens. These two mirrors can steery our beam and can do it pretty fast, but because this is mechanical, you’re limited by math of your mirror.

If you think about it terms of bandwidth, or how long takes to turn around a mirror or steer to a certain position, typically it’s single digits of khz, like 2-3 khz, so roughly like 2-3000 points per second within your scan field.

In past that’s been sufficient, but we find that for a lot of applications, for us that speed is no longer sufficient. As lasers get more powerful, they have higher repetition rates so that pulses need to be faster.

So we introduced another layer of beam steering: the acoustal optical deflector. This can move beam several hundred times faster than the mirrors. These have bandwidth of 1 mhz, meaning they can reposition the beam a million times instead of a thousand per second.

With the acousto-optic deflector, between the laser and work surface you might want to switch to an elliptical beam,then make it round again before hits work surface. Why? Because the way an AOD works is it sends a sound wave through a crystal or other transparent material and creates a grating off of which the laser beam can diffract.

When you change the frequency of the sound wave through the AOD, you change the periodicity of grating, and with that you change the angle of the laser beam. Your sound wave has a finite velocity and your beam needs to see that grating with a certain periodicity.

So you can appreciate why these devices are so much faster than mechanical beam steering, because the rate at which you can change your beam position is the time takes a sound wave to propagate through crystal over the size of your input laser beam.

When we process materials, we often use pulse lasers.Pulses can be milliseconds, microseconds, nanoseconds, or in our case picoseconds or femto seconds? A pico is onetrillionth of a second;afemto is 1/1000 of a trillionth?

To make a long story short, short pulse lasers havehigh repetition rates. So if you want to performm achining where you have control over every single pulse that hits the work surface, you want to draw dots, not lines—and move fast so the dots can be separated.

For this you need a very fast beam steering mechanism. And,if your acoustal optical deflector is twice as fast as your laser, you can slow down the AOD and get a larger deflection range out of it, so you can steer beam farther.

And do that, you need these elliptical beams.You make the beam along the acoustaloptic axis longer,without changing the perpendicular axis to that.

So it remains true that at the work surface you still want a small round beam, even when you’re working with acoustal optical deflectors.It’s just that with very advanced systems at the edge of what we do, there comes a point where in order to manipulate that spot at work surface as efficiently as you can, you might want to go to elliptical upstream and convert back to round before it hits the work surface.

ZEMAX: What is an example of a product you use this newer process on, where this provides an advantage?

Yes, a great example is what’s called memory link repair. Memory links are tiny metal bars embedded in silicon. For any of our devices today that have memory like DRAM, those memory modules have individual bits that are either storing zeroes or ones—millions and trillions of these with little cells holding what is now usually gigabytes of memory.

The thing is, usually not all of these little bits, these cells, are working. In the process that generates these memory cells, there is a test procedure that can map out which ones are working and which are not.You usually put memory cells together in a cluster, so if something bad is happening in the cluster, you can address it through a fuse. If you remove that fuse, the computer cannot access that bad memory cell.

There are two ways these fuses can be “blown” if a bad memory cell is detected, thus disabling that bad cell. One is electrically. The otheris with a laser pulse.

The goal is that,with a single pulse, you remove all of this little metal bar embedded in the silicon, so the electrical connection is destroyed—but without harming the surrounding silicon.

Because we live in 21st century, these things get very small. We might have 1 micron size link bars we’re trying to hit. So we have to create these very small optical spots that match in size to these little metal bars. And moving at very high speed, we fly over the links and if we need to “blow” one, we can send a single laser pulse shaped exactly to hit the center of the metal bar, remove all of the metal cleanly, and then move on.

This pulse must be strong enough to remove all of the metal, but precise enough not damage the silicon. And they are very densely stacked. So this is an exceedingly well controlled process. To do this reliably, we have accuracy of 150 nanometers. And if vapor starts to warm up, the thermal expansion will mess things up fast.

This memory link repair system is an example of something ESI creates. We’re the last company standing that can make these laser-based memory repair systems; we are unique in that capability. And this gives you a feel for the scale of what micromachining actually is.

This is the process that got all of this started with the conservation of ellipticity theory. It makes doing something so precise more manageable. It’s the first process where, after we went through this exercise, we could actually relax the specs for the laser we are using for this product, in spite of the precision needed.

ZEMAX: Last question—were you actually the first to discover this? identify this theory/relationship?

It’s hard to believe, to be honest, but it seems so. We don’t intend for there to be a patent on this—we want it to be open access. The whole point is to inform our laser suppliers, when we negotiate specs, to explain why we’re using such oddball specs instead of going with what we’ve done in the past. We want to specify not separate astigmatism and separate maximum asymmetry, but rather this combined quantity that is meaningful because relates to actual ellipticity we’ll see at work surface.

if anyone else picks up on it, the more the merrier. If this becomes industry standard we’ll be happy, because it could save others aggravation and money if they’re sticklers for beam roundness at the work surface.

BIO

Jan Kleinert heads the central research group at Electro Scientific Industries (ESI), a creator of laser based manufacturing solutions primarily for the semiconductor and consumer electronics industry. After studying Physics at the Ruprecht-Karls-Universität Heidelberg, the University of Oklahoma, the Max Planck Institute for Nuclear Physics, and the University of Rochester, he received his PhD in 2008 for creating, characterizing and electrostatically trapping ultracold dipolar NaCs molecules.

At ESI Jan first joined the Laser and Optics development group, focusing on industrial ultra-fast lasers, which led to the first deployment worldwide of high-power (>5 W) ultra-fast lasers on an industrial scale in early 2010. Dynamic beam steering and shaping, as well as the simulation of laser-material interactions, have been his primary areas of interest since joining (2012) and then leading (2014) the central research group at ESI.

ESI's integrated solutions allow industrial designers and process engineers to control the power of laser light to transform materials in ways that differentiate their consumer electronics, wearable devices, semiconductor circuits and high-precision components for market advantage. ESI's laser-based manufacturing solutions feature the micro-machining industry's highest precision and speed, and target the lowest total cost of ownership. ESI is headquartered in Portland, Oregon, with global operations from the Pacific Northwest to the Pacific Rim.

CAPTIONS

This is an older picture (modern memory has a smaller link pitch) but I still think it is impressive to see the scale at which we can manipulate matter. The spot size at the work surface can be changed from 1.4 to 2.7 um with a wavelength of 1.064 um. So the spot size is close to the wavelength, which is pretty hard to do properly and can be changed at the push of a button. The laser can provide pulses between 10 and 100 ns pulse width, where the amplitude of the pulse can be arbitrarily shaped with 1 ns resolution. (I.e. it doesn’t have to be a Gaussian or rectangular temporal pulse shape, but is pretty freely programmable.)

The accuracy of the system is 0.15 um (|M|+3 sigma) – necessary to be able to hit those fuses reliably, which takes a lot of tricks to achieve.

We move the laser beam at up to 400 mm/s while hitting those accuracy requirements.