>>Hello, everybody, everyone in this room and
hopefully lots of you out there in the virtual world. I’d like to introduce Alan Zhan who’s in
the Department of Physics, PhD student who is
soon to be graduating. His work is in
the very exciting field of Dielectric Metasurface optics. So that’s what he’s going
to talk about today. The UW group that he’s
in is ARCA [inaudible]. Fantastic work and everyone should check it out
on the web. Thanks.>>Thanks for
the introduction, Joule. I’m Alan and I’m
a physics graduate student. I’d like to present some
of the work that I’ve done under Design and Optimization of Dielectric Metasurface Optics
in addition to presenting some of the context
that my work fits into. Before I want to talk of
metasurfaces, I’d like talk about optics in general. The first thing that
comes to my mind when I think about optics are pictures. Many metasurface
researchers including myself are very much
in the business of making pictures whether they’re
for human eyes like these, which help me because I have
bad vision to make images, or if we’re interested in imaging large things that are far away
like these using this telescope, or if we’re interested in imaging
small things that are relatively close using this
microscope objective. So these are all some pretty nice optics and they
work really well, but they’ve been known
since the late 1800s. As optical researchers,
we always want to push further to get
better functionalities, and so we’re currently pushing our optical hardware
in many different ways, and in my research, I want to push it in terms of
miniaturization and functionality. So first talking of miniaturization, there a lot of
applications for meeting compact optical systems
including Internet of things, smartphones, lidar for
autonomous vehicles. One thing that is actually
really interesting is in fundamental biological studies where this is actually the mini scope. It’s a microscope that’s about
the size of your fist or smaller, and it’s small enough and light
enough such that you can put it on top of a mouse’s head. It can actually monitor neurons
firing in vivo in real time. That makes me a little
squeamish but it’s also really cool for super research. So another thing that
we’re really interested in is increasing functionality. I think a lot of people here
will recognize the Kinect, which is one of the first commercial
products that really pushed 3D imaging and depth sensing. Something that is also
really interesting for us is this idea of
passive optical computing. So here is a wavelet
transform of a scene, and one of the things
that we want to do is, can we think of optical elements as performing some passive
optical computation? This can be as simple as
something like a lens that produces a Fourier transform
at its focal point, or maybe something more
interesting like a classifier. So something like an image
recognition task. Can we make these passive
optical opponents do these tasks without using
any electronic power? Of course, I’m here to tell you that metasurfaces are the solution or at least part of
the solution to all of these problems that we’re facing. So when we talk about metasurfaces, metasurfaces are actually
form of diffractive optics. When we talk about
diffractive optics, what we’re really concerned about
is the wave nature of light. So we’re no longer thinking
of light as a ray, but we’re actually
thinking of it as a wave. Given that it’s a wave,
we have two things we can control; amplitude and phase. So amplitude diffractive optics
such as the zone plates. This zone plate is
designed to focus light at some finite distance away from it. It functions by blocking light that doesn’t interfere
at the focal point, or in allowing light that will interfere constructively at
the focal point to pass. It works quite well for a lot of different applications
like X-ray lenses, but ultimately if you want
an efficient optimal device, you really don’t want to
block half of your light. So metasurfaces are generally implemented as phase
optical elements. So in this case, this is
a diffractive phase element. It has multi-levels,
and then you can see that each of these levels
has a different thickness, and this thickness correspond to different discrete phase shifts that the light experiences
as it pass it.>>Is that an actual picture?>>That is not a metasurface.>>Okay.>>It is an actual picture.>>It is an actual picture.>>Okay.>>Fabricated diffractive
optical element. So if we want to understand
diffractive optics, we want to go from refractive optics
to diffractive optics. One easy way to do that
is to consider a lens. So if we consider a lens and
some wave optics picture, this lens has some refractive
index n and it has some spatially varying
thickness along this vertical axis,
which I’ll call x, and we can describe
the phase of light with some wavelength Lambda
passing through this lens as some 2Pi times refractive index
divided by Lambda multiplied by some spatially
varying thickness of the lens. As you can see from Wikipedia, we have a plane wave incident
from the top of the lens. The waves that are incident towards the center of the lens experience a larger phase delay
and they are delayed, whereas the light that’s incident on the edges of the lens experience a smaller phase delay so
they’re allowed to advance, and this actually causes
a focusing effect in the far-field. So now that we understand
light as a wave, we also know that from
a signal’s perspective, only phases between zero
and 2Pi mean anything. So we don’t have to actually think about this entire lens as
this entire optical element, we can cut away a bunch of the bulk. We’ll get something that looks
something like a Fresnel lens. This Fresnel lens performs basically the same functionality
as this conventional lens does, but it’s not very compatible with our conventional two-dimensional
lithography practice. So if we want to do
top down lithography, we can’t really make
these smooth curved surfaces. So what we can do is we can discretize our element
into multi-levels. So in this case, again, we have some spatially
varying thickness but now is of a discrete nature. So each of these discrete levels,
there’s four of them, can implement
any discrete phase shift. So we’ve gone from a continuous curvature lens to a multi-step diffractive
optical lens. These work quite well, but it turns out that using our conventional top down
lithography practices, the first one is almost impossible
to make and the second one is still very hard if we want
to do four face steps. We need to do four different steps of lithography and
four steps of etching, and this gets complicated
pretty quickly because in general you want
more than four phase steps. If you want eight you
have to do eight. So one way to make these diffractive optics
compatible with these top down lithography
practices that Intel uses, is you can think about
a binary grading. So in this case, we’re no
longer achieving phase by modulating the thickness
of our element, we’re now achieving phase by spatially modulating
the refractive index of our element. So in this case, you can see there’s this n_effective that replaces the n, and now this n_effective
as a function of space. You can crudely construe this to be areas where
there’s more material, n_effective is larger so it
experiences a larger phase delay. Areas where n_effective is smaller, you experience less phase delay. Areas with this less material, n_effective is smaller and you
experience less phase delay. Yeah.>>Potentially a stupid question. Why the gaps between them? The original continuous
design on the left, it does have notches where
the thickness is nearly zero, but on the rightmost side, you have lots of air gaps in between.>>Yeah. So you’re talking
about these air gaps?>>Yes.>>This is actually not
a very good picture, I guess, but in this case,
these air gaps, if you have some
spatially varying grading that has some specific phase
response that you’ll get from it, you essentially just
modifying the duty cycle. The bigger the air gaps are,
the less material you have, and the smaller your effective
refractive index is going to be.>>He’s basically [inaudible]
around it [inaudible] right. So wherever you have a
cross or the thickness, it goes rounds to zero.>>Oh, I see. So that makes sense. Yeah.>>So then when we talk
about diffractive optics, we also have to talk
about diffraction orders. In general, if we have
some diffraction grating with some periodicity capital lambda, and some incident light
with wavelength lambda is incident on this grating. As it’s transmitted, it not only it goes straight
through but it also gets diffracted into all these
extra orders, and this is true. In general, if
your grading periodicity is greater than
your operating wavelengths, and if I’m making
something like a lens, I really want my light to go straight
through into the focal point and all this extra light
that’s getting wasted is just costing me efficiency. So this is something that
we can actually solve by reducing our grating periodicity to below the operating wave length. In this way, we can actually show that all of these higher orders
of diffraction are completely suppressed and
this qualification is actually what brings us from diffractive optic specifically into metasurface optics. So these are called sub wavelength gratings or zeroth order gratings, and if we wanted to modulate
the phase using these gradings, if we want some uniform phase shift, we can send some plain wave at a uniform grating
and then we will get some uniform phase shift and
uniform plane wave exiting. If we want to have
some spatially varying phase shift, we need to spatially
modulate our grating. So in this case, the thick
or the duty cycle of my grating has a linear ramp and that corresponds roughly in most cases to a linear phase shift, and you can think of
a linear phase shift as something like a beam deflector. So in the top, we have a higher effective index or we have denser material so we have a higher reflective index and that means that delay is delayed more. So dielectric metasurface optics is a body of research that goes
back to like the mid 90s. This is one of the first works
that is demonstrated a high efficiency optic and it was made and titanium oxide
all the way back in 1998. More recently, there has been
work with silicon gratings. This one’s from HP labs. There’s also been work using silicon cylindrical posts
from Caltech, some rotated titanium oxide
nano fins from Harvard. These Gallium nitride
pillars that are rotated, and also they change the duty cycle. This is a collaboration between the University of Nanjing and Taiwan, and also some more recent work with these really strange looking
silicon pillars from Columbia. So all of these look a
little different that all lenses except for
the first one on the top-left, but there’s something
that is very consistent here and it’s that we
have some pure lattice. We have some regular lattice. In this case, the one on
the top middle is hexagonal lattice, and below it is
a rectangular lattice. So there’s some lattice and
on these lattice points, we put some dielectric structure, and this dielectric structure
has some degrees of freedom. We can be changing
the radius of the pillar, we can be changing the rotation of a nanofan or we can be changing
the geometry of these pillars. By changing the geometry
of these pillars, we can achieve different phase shifts and in general, also
amplitude shifts. This constitutes a large complex
system that has a large number of degrees of freedom that we are able to play with
and not only is it complex, but in general, these could also
be couple degrees of freedom. So it’s difficult design
problem, and really, what we’re interested in is
if we have this metasurface, how do I best implement a given
optical function on a metasurface? That question boils down
to how do I best take advantage of the large numbers of degrees of freedom
available to me? Just as a ranging number, a relatively small metasurface is about a hundred micron
by a hundred micron, and if you have
a grating periodicity of around 500 nanometers that has at least 4 times
104 degrees of freedom. So that’s like if you just changing a single parameter in each unit cell. So if we want to solve
the design problem, I think there’s two general ways where we can think about
solving the design problem. One is Forward design which is intuition-based which I would
argue is more intuition-based. So from here in forward design, essentially, we need to calculate all the properties
of the scatterers that we’ll use. So
we’ll calculate it. We’ll just have some lattice,
we’ll put some scatterers on it, we’ll calculate all of
these individual scatterers and their properties, so their amplitude and their
phase transmission coefficients, and then we have some functionality
that we want to implement. Maybe it’s a lens and we know how
to implement that functionality. We know that a lens
is some hyperbolic or some quadratic
face profile that we can implement using these scatterers, and so that’s something that
has been very successful. There’s another way of doing it, a complimentary way, it’s called inverse design which I’d argue
is more computationally based. In this case, we may have
some functionality that we want to achieve but we don’t really have a specific phase
profile distribution. We don’t really know
how to get there, but we can define
this functionality and we can encapsulate it in terms
of some figure of merit, and after we accept encapsulated
into configure of merit, we can use some optimization
Inspired Approach to actually arrive at the distribution of scatterers that shifts
our functionality. So as far as I’m going to cover, first I’ll cover some work on single element metasurface optics that I’ve done and
also some other work. Then I’ll go over
some metal surface optical system. So this is like
two metasurfaces or more, and then I’ll go over
some inverse design and optimization of metasurfaces, and lastly, I’ll go over some of the future work in Outlook
that I’m interested in. So my group uses silicon nitride for our metasurfaces
primarily and that is motivated by four major reasons. One is its high refractive
index, a brand two. By high we mean higher than glass. Two is it’s relatively wide band gap. It has a band gap of
around 4-5 electron volts which puts it in the UVA band. On the left is a picture of silicon nitride piece or
a thin-film silicon nitride. So you can see that it’s
actually transparent. Yeah.>>Why is wide band gap
important or useful?>>So materials like silicon
are opaque to visible light, and if you’re interested in making a metasurface that’s
transparent to visible light, you need to have something
that has a wide band gap. Does that answer your question?>>Yeah.>>Okay. Third, it’s
potentially CMOS-compatible. So that means that you could
potentially use NTLC CMOS foundries to produce these metasurfaces or
other CMOS-compatible foundries. In general, silicon
nitride is used as a hard mask but it’s also
possible to etch it, and it’s capable of making these photonic nanostructures that require strict
fabrication tolerances. So these two are pictures of
a nano beam photonic resonator and also photonic ring
resonator that were produced in our lab using
our silicon nitride. Forth and maybe most importantly, it was readily available in our local clean room
and there were already etching recipes developed for it so I didn’t have to do any of that work. So now that we have our material, we need to perform
a parameter search, and one way of doing this is using rigorous couple
of wave analysis. This is a frequency domain method. So you send one wavelength
in at this set, and it assumes that you have
some unit cell that it’s infinitely periodic in all space and it’s
a four-year domain method as well. So what happens is you
split this structure into different layers along the direction
of the light propagation, you split this structure
into different layers. So for us, that is along the line
of the thickness of the pillar, and in the in-plane, you actually expand
the refractive index in a periodic set of
four-year series, and then you can solve
this and then you set your solution in terms of
some set of four-year modes. So to begin, we start by
defining some unit cell. Here, I’ve defined a square
with some periodicity p, and I’ve placed
cylindrical scatterer with some thickness t and some
diameter d in this unit cell. What we do is we run our simulations and while we’re running
our simulations, we keep T fixed because that’s how we keep our compatibility with
traditional top-down lithography. But we can vary d as much as we want. So for a given
periodicity, we vary d, and then after we run
all of our simulations, we can arrive at something like this, where now we can see that this pillar has
some real amplitude response and some real phase response. So in general, if you want a
high efficiency metasurface, you want a high near
unity transmission amplitude, and that’s what these
parameters show in blue, and in general if you
want a metasurface that can implement
any arbitrary spatial face pattern, you need to be able to cover zero
to Pi and that’s what red is. So now that we have a parameters, this set of parameters on the right is actually a set
of parameters that we used in all of the following silicon nitride
surface demonstrations. We want to implement
some phase profile. So in forward design, we generally know
what kind of face profile we want to implement beforehand. So we have some face profile as a function of
some spatial coordinates. In this case, I chose to use circular coordinates
with r and theta. We have some wave vector
two Pi over lambda. So this is focusing
vortex steam generator. The first term is just that of a
lens with some focal length f, and then the second term is
some angular momentum term that determines
how many singularities there are in the phase profile. So if l equals one, there’s one for singularity. If l equals two, there’s two, and these corresponds to different quantized orbital
angular momentum states that you can generate. So if I just calculate
this face profile, I guess something that looks
like this for l equals one, and you can see that there
is a discontinuity that starts from the middle and
it goes towards the left, and this is a continuous
phase profile but in general, we know that only phase values between zero and two Pi are physical. So we can do a mod
operation and we get this nice little vortex picture. Again, the finest we can sample our phase profile is at
the periodicity of our lattice. So now, we discretize our phase profile into the periodicity of the lattice
that we calculate. So now we have some discrete blocks and that are the size
of our periodicity.>>Which size can you get down to?>>So for these specific
parameters our PDC is 400 nanometers, 440 nanometers.>>What optical function
will you try to enable this pretty
good phase profile? This is a vortex beam generator. It creates a little.Net profile that has applications in
[inaudible] microscopy.>>Nice. Cool.>>Okay. So we have our face profile
and now we can just essentially do a
one-to-one mapping from our phase to a diameter value. On the right is where we actually
get when we do this mapping. We can simulate this and FDTD. So we can simulate
scaled-down structures in FDTD which is finite
difference time domain simulation. On the top left, you can see the little door knob profile
that this vortex beam generates. On the bottom left, you can
see a cross-section along the optical axis showing that
the door knob profile forms around 25 micron and on the far
right is an example of a structure that we simulate, where the yellow is a refractive index of around two and the blue is
a refractive index of one. So this shows the meshing that FDTD does when it
stimulates your structure. So it doesn’t actually simulate
perfect circles but it stimulates these rectangular blocks
that make up circles.>>Just to verify. So that’s the geometry
at the end of the day?>>Yes, that’s what we’re
going to fabricate.>>Those yellow dots
are the actual radii, the T values you were
talking about. I see.>>So in general, we simulate very scaled down versions of
these limits and receive.>>Each yellow block, it has many many smaller
features in it, right?>>Each yellow block
is just a cylinder.>>Just one cylinder?>>Yes. I can show you the picture right here. It’s
actually not very good. But each yellow blob is a single
cylinder and it has some diameter and essentially what we did here
is that it’s consistent to that.>>So actually if you
look at the scale, the scale is quite small in
the previous diagrams, correct? So you’re actual lens
is very small here.>>In this case, this lens is
about 30 microns in diameter. Yeah.>>I just have a quick question. So when you design the stuff, you said you keep the P fixed.>>Yeah.>>So you’re changing
the [inaudible]?>>Yes.>>Okay, and that’s
the only thing you changed.>>That is the only thing we
change for this demonstration. There has been other groups
that have done more with different unit cells
and that’s something we’re also working on in my group.>>So a larger yellow blob just
means a larger [inaudible]?>>Yes.>>Okay.>>Do you recall what the cell size was for the [inaudible] simulation?>>Lambda over 10n which makes
it around 25 nanometers.>>So it was determined
by Lambda, right?>>Yes.>>Okay. But that was still much
smaller than the value of d you get about because
the shape is going to get quantized and steelcased when
you’re doing the simulations.>>The smallest radius
pillar that we fabricate was probably around 150
nanometers in diameter.>>Okay.>>So roughly seven unit
cells for instance.>>Okay.>>Yeah. So we were actually able to fabricate
these structures. Here’s a lens. We can see that this lens
is designed for 250 micron. You can see that there is some
finite focal shift with this lens, and that’s actually because
we designed this lens for 602 nanometers and
we tested it with, or I tested it with an LED that
has a very large bandwidth. So we actually ended up getting
something that looks like this. There’s a focal spot of the lens. It looks nice and mostly
circular, vary on aberrated. We also made the
vortex beam generator, which looks like this. Then here’s an example of an intensity profile before
the vortex beam focuses, and then this is an example
of the vortex beam itself, where you can see that donut beam
profile actually being formed.>>That’s still with LED?>>This still with LED.>>How come you didn’t use
a [inaudible] you could get it.>>So one thing we are
interested in that we didn’t really understand
at that point when were doing this research is if whether or not we need
the coherent light to make these structures work. So naively we would think that if
we’re playing with phase maybe we need to be playing
with coherent light in order for this to work, and that was something that
people hadn’t really tested. So we were like, we should test
with an LED and see what happens.>>I just realized. So when you’re doing this optimization of FDTD, are you doing it for
a single frequency like most monochromatic
for all of this?>>Yes.>>I see.>>So these elements work quite well. We have lenses that work. They’re ultra-thin, they have
small focal lengths. They work well. The problem is what you guys
are heading at is that we have very large chromatic aberrations and these are characteristic
of any defective optic. So what ends up happening is
that we design our wavelength. We design a lens for
a wavelength of 692 nanometers. It focuses pretty close to
there for red color. But we observe as much
as of the 50 percent focal length shift over
our entire visible spectrum. So for blue, yeah.>>How long does FDTD simulation
and optimization process take for something of this size?>>So FDTD isn’t optimizing anything. It’s just simulating some
structure that I give it to. I would say that it takes
around 20-30 minutes.>>For each evaluation or for
the entire optimization multiples?>>There is no optimization
that’s happening. In this process we have a phase value and we pick a diameter that corresponds
to that face value. Then we can simulate the
structure using FDTD, just as a check that it would work. We don’t actually optimize an FDTD, and it’s impractical
to optimize an FDTD. But that’s something I’ll go over. So yes, large chromatic
aberrations characteristic of defective optics, not
good for imaging. So if you’re not familiar
with chromatic aberrations, the picture on the top is a sharp picture that has
very little chromatic aberration. The picture on the bottom is
chromatically aberrated and this is chromatic aberration
associated with the refractive lens. So if a chromatic aberration
associated with a diffractive lens would actually be worse than it will
picture on the bottom. So that’s a serious problem
that we want to correct. So that brings me to the next topic, which is Correcting
Chromatic Aberrations. So there’s been a lot of work
in correcting operations. This is a problem that
the [inaudible] community has been very interested in over
the past few years. So these works all came out in 2018. They do different things but what they’re really doing is they’re doing something called
dispersion engineering. So the problem of Chromatic
Aberrations is a subtle problem. It doesn’t result from
the way that [inaudible] refractive optics exhibits chromatic
aberration which is some kind of anomalous dispersion
in your refractive index. This is actually a product of
the way that we wrap our phase. So when we do this mod
operation of mod two Pi for the wavelength of interest
that we wrap, it wraps correctly. But for other wavelengths, we actually might wrap too early or we might
actually wrap too late. This actually causes the chromatic
aberration and there are some associated phase error with this wrapping operation
that we perform. You can actually attempt to
correct for this phase error, and this is what these
groups have done, and you can see on the
top-left that they get some nice focal lengths or nice focal spots that are all
in the same area for this lens. But you can also see that
it’s a very extended focus and these are very low
numerical aperture lenses. On the bottom, you can see that
these are some of the devices or the structures that
they’ve engineered to perform this
dispersion engineering. So there are limits to this technique of dispersion
engineering. Yeah.>>What’s the intuition for why some of these structures might
help to reduce [inaudible]?>>So you can think of
these as wave guides.>>Okay.>>For different wave guides, we
have different effective indices that determine how these
different wavelengths propagate. So there’s a certain setup
of a different allowed modes that are allowed by these wave guides and they all have
different refractive indices, and they will delay different
wavelengths by different amounts. So if you build a very large library
of these wave guides and then you have a very large
number of different delays, you can think about just optimizing or using
your look-up-table to pick out. If red light needs some specific delay to match
up with the green light, can I find a pillar that
gives me that delay?>>Got it, and then these sorts of rectangular structures
then orientation. I mean, they probably have
an increased grammars space in terms of orientation. Or is it as you say
like a library, I mean, there’s just these fives
that they’re modified?>>So in this paper in the below, they have three generations. The one on the bottom they have
five primitive unit cells, and they can modulate
the size of the whole of this unit cell or
the thickness of like this.>>Okay.>>So they can make the pillar on
the far-left bigger or smaller, they can make the hole appear in the middle left bigger or smaller
and not on the pillar itself. I think you can see that from
what they’ve done there.>>Right. Got it.>>Yeah.>>So each one of these delays a different wavelength,
a different amount, has a different phase shift, and then how does that work? When you put them together, isn’t there still
some light that’s going through the wrong of these things, that’s getting the wrong delay? How does just that pillar provide the phase shift
for say, red light? None of the other pillars that
are tuned for green light, the red light doesn’t go
through those or is it some weird coupling
between these things?>>So first, nobody in
for design actually accounts for any kind of
coupling between the pillars, which is one of the problems
with this body of research. But in terms of how they know, what they’ve done is they basically calculate all of
the modes for all of these pillars, for all the interest wavelengths
they are interested in. So let’s say, pillar one gives
you phase shifts for red, phase shift for blue and
phase shift for green. You know that in order to
implement a perfect lens, your red phase shift needs
to be some certain function, your blue phase shift needs to
be some certain function and your green phase needs to
be some certain function. If you have a large enough
Library of pillars, you can choose the correct
pillars that will always produce those phases.
Does that make sense?>>Yeah. You choose a combination that gives you
the phase shift you want.>>Right.>>So this is basically a matter of how many degrees of freedom do I have to basically get
these different modes to get these different phase shifts. There’s a limitation
to it and it actually is limited by the height
of your pillars. So these different modes have different effective
refractive indices. But just having a different effective refractive index isn’t enough. If you want to have
a finite fish shift, you also need to have a thickness. What ends up happening is that this limitation is
defined by this equation. But essentially, what it
is if you want to have a numerical aperture or
some certain radius, you’re limited by the total
delta phase shift between these that you can achieve. So delta is the compensation that if you’re designing for green you can compensate delta for red or blue. What this basically says
is that if you want a high number cooperator lens,
in order to do so, you have to make
very very tall pillars or else you have to make
a very very small radius lens. So for this group right here, what they’ve done is they have these 800 nanometer pillars in
these 1400 nanometer pillars. You can see it, the
effective phase shifts that they get don’t actually correspond to much larger performance or
like much better performance. So this is something that my lab was interested in
solving at a different way, and we came at it from a
computational imaging approach. So in this case, we wanted
to find some face profile. In this case, we have face profile of just an
ordinary hyperbolic lens, and we add to that a cubic function. This cubic function
serves the function of creating an airy beam which
is a diffraction invariant beam. So as stated before, if alpha is equal to zero, we just get a lens and at
the focal point of the lens, if we design our lens for green, we have a nice tight focal spot, but there’s a significant blur
in blue and red. But by making
alpha some finite value, we create a roughly propagation
in variant beam. So we can see that at
our focal point now, instead of having
a nice point for red, we have an L-shaped point spread function for all
of these different colors and they look really ugly, and if you know the imaging is the convolution of your object
with the appointment function. But even though they
look really ugly, they all look fairly similar. So then that means that we can use
a single filter essentially to the department
de-convolution operation and maybe you can retrieve
the actual image back. So this is some very
basic wave for. Yeah.>>Because of this filter
function that filters is acceptable or [inaudible]
unacceptable so its [inaudible].>>Yes. But we don’t actually
use that property of it, we just use the Wiener filter
because I’m not a computational imaging guy
and this is our first work. But this is work that was
from the early ’90s from Edward Dowski and H. Watch and they basically laid the foundation
for this work and what we’ve done was so essentially we’ve combined the two elements into one, and we have demonstrated
that they can actually work with diffractive optical
elements as well. So for some experimental results, if we can make a singlet this is
just a singlet metasurface lens, you can see that’s symmetric axially. This is what an EDOF lens looks like. It looks similar, but you can see
that on the top and on the left. You get this L-shaped that appears, and that’s due to the cubic
functions that we’re adding to it. So these are some of
the imaging performance and color. So in this case, we have some
ground truth image on the far left. RGB, some rainbows and
relatively natural scene. When image with the
metasurface singlet we get, so the singlets designed
for green wavelength we get a very nice sharp green. But every other
wavelength is blurred. On the middle right we
have the raw EDOF image. There we can see that
all of the images are relatively blurred using by this L-shaped point
spread function and on the very far right is the filtered image. So what we’ve done is we’ve
just used a Wiener filter, and we can see that at least for
the RGB the R and G and B are better defined compared
to the singlet for RGB the yellow is noticeably better, but there’s still these
like L artifacts and these we attribute to essentially
the accomplishing of our system. and also that we just
use a Wiener Filter. So that also comes with
some noise amplification as well.>>I’ll also just Docker, does that represent something like the efficiency of the system
or something like that?>>Yes, the efficiency of this particular system was a little bit lower than that of
the singlet lengths, but it has a more uniform efficiency
over the bandwidth because the singlet is more
efficient for Green. Yes.>>Is there a contrast problem here? Some not being focused by the lens, so there is a reason high
contrast on the right?>>So some of the lights
not being focused by on.>>I’m just wondering
because if the lens is less efficient you could just
take a longer exposure, Right?>>Yes.>>It has smaller exposure.
So why is there so little contrast on the very rightmost image as compared to the original images. So because you have
light leakage that’s, it’s not being focused in background.>>So these meta-surfaces
are around on 40 percent efficient and they focus around 40 percent of
the light that is transmitted into this area beam spot, and that’s a rough estimate of
how efficient are lenses are.>>So that the other 60 percent just get spread across
the whole [inaudible].>>Yeah. It gets spread across. Some of it definitely gets rejected
into the side bands and that’s the most notable source of
loss that we’ve noticed is that what we see is that we see, I think this is due to
a sampling issue that we have. Is that we don’t sample fine enough, we actually create different face
profiles called just based on aliasing and these aliasing effects inject light into
the side bands sometimes. I’m also not the best
experimentalist. This is some work that I
collaborated with Shane and Shane is the first other
and a very interesting stuff. So these are all single
metasurface works and I’ve covered some of
like color chromatic imaging, there’s a lot of other stuff
that’s being done. So there’s holography,
polarization optics, nonlinear optics and
some review articles. Yeah. There’s some cool
stuff that’s being done in a lot of
different fields and. So next I will cover something towards medicine
offers optical system. So this is two metasurfaces
together in tandem. So one thing that we demonstrated
was an Alvarez lines. So for those of you who
are familiar with it it’s two face plates that are obeyed
this these cubic functions. When they are aligned,
they have no function, they provide no optical power
but for some finite displacement in along the x dimension
that we call d, we get a tunable focal length. So the power is related to
one over the focal length, so the power goes up linearly
with the displacement. We can simulate how these work using some and
we’ve optics simulation. So for small displacements, we get a long focal length, and for a large displacements
we get a short focal length. Of course we experimentally
tested these. We fabricated these in
our cleanroom well. So our fabrication has gotten
better in the time pen and we’d get around three millimeters of total tunable focal length across a 100 micron of
physical displacement. Where 50 micron is displacement in one direction and each of
the plates is displaced 50 microns, so it’s a 100 microns to
physical displacement. In this case, this focal
length change corresponds to a optical power change
around 1,600 diopters. There’s other tunable
systems that are more monolithic that have been
demonstrated more recently. In this case, there’s have Palmer lens that they
use MEMS to stretch, and also pretty interesting
like doublet that is formed and they can change the distance between these two doublets or these two lenses to create
a tunable focal length lens. Yeah. So in this case, they have a monolithic system and they use these MEMS
devices to actuate. But what actually
ends up happening is that they require very high voltages on the order of 60 to a 100 volts to operate these and
also their relative to tunable focal lengths and
their relative optical powers are a little bit lower
than that Alvarez lines.>>How big are these lenses?>>The red scale bar is
about a 100 micron and the white scale bar
is about 20 micron. So this one is probably around
like 400 micron in diameter, the bottom one and the top one
is relatively large. So in addition to
tunable optical systems, there’s also systems
for angular incidence. The group at Caltech has been very prolific in making these systems. What they’ve shown is they’ve shown matters of infrastructural
reflectors, which have applications in
optic communications and such, and also really interesting
angular aberration correction. Because as these
metasurface lenses are generally designed for
straight on illumination, they have a small field of view. So what they showed is that by
fabricating another metasurface, they can correct angle aberrations
up to around 20 degrees, having a nice focal spot. Something that our lab has also
demonstrated is large area design. So we always claimed that
these metasurfaces are compatible with conventional
photo-lithography, and this is something that
we actually implemented. In this case, what we’ve shown are these large area Alvarez lenses. In this case they’re about
a centimeter by a centimeter. We can perform
some very focal imaging. Here in the bottom
is a great work done by the group at Harvard that
also has done something similar, and they also have a centimeter
by centimeter lenses. So these active elements are compatible with
traditional lithography, and you can actually
make them quite big and quite easily using
photo-lithography. So now I’d like to go over some
of the work that I’ve done in the inverse design of
these optical elements. So again, we have
this design problem. We can use forward design
which is more intuition-based, or we can use inverse design which
is more computationally based, and more of an optimization
inspired method. That’s what I’ll be talking about. So it’s formulated as
an optimization problem. Mathematically, if we’re given
some figure of merit f of x, where x is a function of
some set of parameters, p, we want to minimize f of x, while constraining x to solve some linear system of
equations, ax equals y. So for a physical representation, f might be some
intensity distribution that we want to achieve
in the far field, x might be the electric field that the figure of merit is
expressed as a function of, and p might be the radius of our cylinders or it might be the dielectric permittivity
of our system. So while we can’t change x directly, we can change p, and by changing p, we can get x. That’s what ax equals y, it’s like the physics of the system. In general, we use a gradient-based
solution to do this. So here’s a layout of
the optimization procedure. We start with some initial condition, we solve our forward problem, we calculate a figure of merit, we solve our inverse problem, and then we calculate our gradient, and we update continuously until our figure of merit
reaches some exit condition. So this is a field that has been growing in popularity in
the nanophotonics community. One of the first demonstrations
that caught a lot of attention was this
wavelength demultiplexer. So what happens is you have two wavelengths incident
from the top-left, and those wavelengths are split
into these other two waveguides. So one wavelength goes
into the top waveguide, and one wavelength goes
to the bottom waveguide. In addition, we also have some demonstrations of
two-dimensional metasurface lenses. So what this is actually done in
the radio and microwave band, and they’ve shown
a highly micro aperture lens and also a more normal lens. These are two-dimensional lenses, so they focus light into a line or also known
as cylindrical lenses. Here’s a group work
showing two devices; one is a high angle beam deflector, and one is a wavelength
demultiplexer in frees pace. So what they’ve done is they have
these unit cells that they tile, and they design a space of
around two micron by two micron. So what you notice
about these inverse design demonstrations
is that they all tend to be either limited to small volumes, or
two-dimensional designs. So the first one is a two micron by two micron by a few hundred nanometers area that
they’re designing, the bottom left is
some two-dimensional design, and on the right they’re designing some periodic unit cell that
they tile on a larger area. So while these methods all result into
different kinds of structures, they all rely on
the same underlying method, and it’s a finite difference method. So we can solve these finite
difference methods in the time domain in which we
saw at some initial field, and we propagate it through
using Maxwell’s equations or using Faraday’s law
or Ampere’s law, or we can solve it in
the frequency domain, where now we’re solving
the vector wave equation, and we can form our equation that’s like ax equals b using
this wave equation. But the issue is that because we’re measuring all of our design space
into a finite volumes, the memory scales with
the volume of the system. So for large systems, the scales poorly, and it becomes
very untenable very quickly. So how do we get to
large-scale optimization? There’s two main challenges
that we have to overcome. One is we need a fast and memory
efficient simulation method. We can’t use a finite
difference method for a large volume without doing some tricks because it just takes up too much memory
and it becomes too slow, and we need to run a light iterations
so it also needs to be fast. Two, we also need to faithfully
numerically simulate the system. So in this case, we want to be able to capture
all of the electromagnetic of the system to be able to have the most robust optimization
method possible, and take advantage of
all the physics that we can. So the idea is that we had was to achieve both with an analytical scattering theory, and this is actually called the generalized
multi-sphere Mie method. So what we gain from this is we
gained an analytical theory. So in this case, we have
a scattering theory that is exact. We can calculate
the inter particle couplings exactly.. All of
these scattering functions are easily computed
mathematical functions, so we can actually
calculate them very quickly instead of storing
finite difference matrices, so our memory usage is also lower. What we lose is we lose our flexibility in designing
arbitrary scatters. So well, the groups before were able to make
these arbitrary scatterers, now we’re restricted
to spherical scatters. So what we’re doing is we’re
optimizing arrays of spheres, and we’re changing their radii to
achieve some optical function. We’ll show that we can actually do some quite cool things with this. This method is also easily extended into scatters of larger dimensions.>>So spheres are three-dimensional?>>Yes. So this is
a three-dimensional method.>>Okay.>>We’re optimizing, yeah.>>I guess you will probably
talk about how you reduce that to two-dimensional fabrication.>>We use the nanos right.>>Okay.>>Yeah. So the forward method
is also already implemented by a group
from KIT called Celes, and it solves this matrix
system of equations, so linear system of equations. I was able to contribute
a little bit to this by allowing this code to solve
spheres of different radii. So before it was just spheres
of the same radii, and it’s been proven to be
able to solve systems with spheres numbering up
to around 100,000. So it is relatively large-scale, we can simulate large three
dimensional distributions of spheres with this code, and that was a good place to start. So one, we now need
to find application, one thing that was really
interesting to me was depth sensing. So I was really
inspired by this paper, where they have some point
spread function that varies as a function of defocus. So these two lobes rotate in
space as you defocus a system, and if you are able to accurately characterize
the rotation of the space, different images at
different values of defocus will be convolved with
different point spread functions, and then if you can deconvolve them, you can get some depth map. Then they can do it actually
with very high resolution. So we want to do something similar, but instead of doing
a continuous two rotating lobes, I chose to have
one focal spot that rotates around four different
values of defocus, and it rotates in a discrete helical pattern
with eight focal planes. So our first focal plane, I want to focus light
at the yellow point, and I want to minimize the light intensity that
goes to the blue point, that’s because that blue point is the location of
the next focal plane. So at the next focal point
which is at 120 micron, the focal point moves
counterclockwise, and now I want to maximize
again intensity at the yellow point and minimize
intensity at these two blue points. At the next focal-plane, I do the same thing and at the end I get something that
looks something like this. This function can be
roughly described by this figure of merit where I set some non-zero intensity at yellow, so I want to maximize
my intensity there, and I set our blue equal to zero, so I want to minimize
my intensity there. So I put this into that method and outcomes and array of spheres. This array is about
a 150 micron by a 150 micron, and it looks pretty useless
to me on first look, but it looks like a more or
less random array of spheres, but so we tested and simulation, and we actually see that
at these focal planes, we get this nice little
spot that rotates around as we defocus the system. So now when you actually need
to make these structures it turns out that you can
actually make spheres. If you use Nanoscribe GT printer. So the Nanoscribe is a 3D printer that works using
two-photon lithography. So essentially, how it works
is you have some polymer. This polymer can be denatured by
light of a certain intensity. So what you do is you focus
your pulse laser beam, and at the areas where the pulse
laser beam is intense enough, you get polymerization and you
get something that sticks. Everywhere else, you can just wash off after you’ve done
exposing your city. So they can get these really cool relatively high-resolution
three-dimensional structures.>>[inaudible] material,
and this is the polymer.>>This is like a UV epoxy.>>Okay.>>It’s hard to define bandgap
for something like a polymer, but it is transparent
to visible light.>>Could you Modeled
the scene that we had before with
two or fewer forced years, on top of each other
or next to each other?>>Cylinders, it turns out that
that’s not a very good way because the spheres have near-field interactions that are not
present in cylinders.>>Okay.>>You can extend. So I will talk about how you can
extend this method into accepting different geometries, and it will with some modifications that can accept ellipsoids
are like cylinders. So we actually ended
up fabricating it. It looks similar on the top-down
view to what we actually wanted. But on the right, you can see that their spheres
aren’t quite spherical, but they look like layers of pancakes at different radii
stacked on top of each other, but we might as well tested, and so for reference here are
the simulation results again, and then here are
the experimental results. So we observe a higher noise floor and this device was designed
for 1550 nanometers. Part of the noise part
comes from dark counts from our camera which is not very good. In addition, there’s
very noticeable fabrication defects that we saw in the previous slide. But ignoring all of that, we do see that we have this very high-intensity focal spot that’s rotating around
in the same direction, and in the roughly the same locations and we can characterize this. So in simulation, we compare
the simulation spot location with the experiments up spot
location and we see besides the first envelope
last focal spot, they actually might quite
match up quite well, and most of them have an
error of under one micron, though the first spot has an error that’s a little bit above one micron. That’s couldn’t be accounted for by some finite amount of translational
error or some fitting error, we’re not fitting error because
I didn’t fit the peaks. So now, I want to go into some of the future work and
outlook, where I think that yeah.>>Can I ask a question? So the structure you had also have these connective lines
between the cedars right? If you go back a bit, the example you have that printed
in the bottom right.>>If you wanted a big array of spheres or if you want to three-dimensional
distribution of spheres, then they will need some support.>>Right.>>But in my case, I
didn’t need to do that.>>You didn’t.>>No, so in this case the spheres
are independent of each other. They’re just on a glass substrate.>>Are they spheres or phosphate?>>They are phosphate. So
this the top-right picture is an angled view and
it doesn’t really show how the photosphere physical
part but you can see it a little bit maybe. But yeah.>>When maybe it’s hard to get but
when looking from not top-down, I mean were you able to observe a greater turned out of irregularities and
the spheres because I mean, when you’re looking
top-down right you can.>>Yeah.>>This might be I’m
assuming that the printer is printing along with parallel to the substrate and layers
parallel to the substrate right?>>Yeah.>>When you’re looking
from the other perspective that’s maybe a cross section of this the spheres will look more like half
submerged cylinders may be.>>I guess that might be true, but what the printer does is it doesn’t actually
print any material. It selectively polymerizes right, so you have a focal spot that’s like a pixel that you scan
over your resist.>>Yeah.>>So I don’t see any reason why they would be less focal on the top and they
wouldn’t be on the bottom, because it’s just is
a focal spot that’s scanning. There might be some mechanical
issue with the resist.>>Suddenly, imagine it as
focusing layer by layer right?>>Yeah.>>Otherwise, you won’t
even get visibility into southern slots
and things like that. So it is a preferred direction
here in which it’s going. So I guess what you’re
saying is stopped down. You can see nice disks still, but sideways and you look at it, you might see
some other sheep issues.>>All right, that’s aspect
mechanical issues actually.>>So there might be
mechanical issues, but they have been groups that have been
actually able to make these kinds of structures. So like while there might be mechanical issues with larger
three-dimensional and raises fears, I wouldn’t actually expect
it with what I’m doing, just because they have
some really nice results, and this is a epoxy has basically SU-8 which
has relatively well-studied mechanical properties and
it is capable of producing very high aspect ratio like pictures.>>So you can bet your navel
spheres that are balanced on without having rural rounder?>>With some trial and error, yes. So there is, so when I
make these spirits are is like a little bit of a little bit of like a flat surface because
I sad to say a little bit.>>Skewed in the bottom here.>>Yeah.>>I have had these samples
like fly off when I like try to rinse them off with something and they’ll
just like float up.>>That’s okay. It’s
like 20 minutes of work. So it’s like not that bad. That’s another benefit.>>[inaudible].>>Yeah.>>Oh maybe was, yeah so these are actually
pretty big spheres right? These are visible light.>>This is. Okay say I forgot to mention this
is for infrared light.>>Infrared light.>>So the resolution
of the Nanoscribe is roughly 200 by 700 nanometers. That’s like your smallest
dimension or you could do. So the smallest spheres that you
could reliably make spherical, they quoted as around a 100 micron
or one micron in diameter. So we decided to use
infrared light because we couldn’t actually resolve
the small enough. The caveat this actually
isn’t a metasurface per se, because the periodicity is actually
greater than the wave length.>>This is like a period of wrath.>>Yeah.>>But the simulation method
doesn’t really change. It’s more just like the
fabrication that we forced us to make
these bigger structures.>>[inaudible] Term
disappeared refractive.>>Maxwell doesn’t
care whether you know.>>What labels deeply.>>Yeah.>>So outlook. So we can extend this method to arbitrary shapes using something called
the T-matrix method. This is the method that’s
actually developed mostly for use by astronomers
or astrophysicists, who want to study space dust
and aerosol particles. So this extension is something
that I’ve been working on, and we’ve actually been able
to implement it in the code. We don’t have any preliminary
results quite yet. We don’t have publishable
results quite yet. But we have shown that we
can increase the efficiency of lens with the
numerical aperture of around 0.83 from 20 percent to 26 percent using
these ellipsoidal scatterers. So in this case, it wasn’t
an inverse design method, we have some existing
lens design that we made, and then we optimized
it using this method. We were able to see a pretty significant efficiency
increase in my opinion.>>Now, in these types of designs, where is that 80 percent
of the light go? Is it just scattered uniformly
across the image field?>>So I don’t know anything about
ellipsoids there’s actually a lot of backscattering. So a lot of ellipsoids will
actually reflect light back at you, and that’s something that
I learned very recently, when I was trying to figure
out these intensities. So in this case, some of
the light is being backscattered, and some of this light isn’t being
focused it’s at a focal point, but it’s a pretty commonly
accepted I think problem for high numerical aperture
lenses to focus light with high efficiency just based
on like Cornell’s equations, as you light this incident
on larger angles, it starts being less efficient
based on the Theta term.>>I think what Brian
is implying is that, if you are scattering a light
into where your image is, random, or pseudorandom way, you’re lowering your contrast, therefore, your image quality.>>Yeah.>>So whereas, if it goes backwards, maybe that’s a different problem
but the efficiency, but maybe it doesn’t
affect you image quality.>>In this case, I think there would definitely be light that would be scattered into a random background. But I think that would be true of any refractive high NA lens as well.>>[inaudible] Since
they’re good at reflecting, gradual reflecting or reflecting, if you look at using these more as little mirrors and little lenses.>>That’s something that
[inaudible] that’s taking over this project
you guys interested in. That was not something
that I have thought of.>>Okay.>>So maybe if more than the feature like the idea of designer optics
because right now, the model for an optical
element is you go to a website like Sorlabs
or Edmond Optics, and you buy an optical
element off the shelf. If you want some A sphere that
can maybe make it for you, or if you want some special coding on your lens, they
can do that for you. But if you wanted
some really weird optical element, they probably wouldn’t
build to make it for you. I think that’s largely due
to manufacturing reasons. So metasurfaces are already compatible with these top
down lithography practices. So maybe there’s a new model
where you can actually have some design that you
give to some company, and then they can fabricate
this optical element for you. Now, you can have these custom
optical elements that are designed to work with your sensor instead of using
off-the-shelf components. Another really interesting
application is towards volume optics. So metasurfaces are
these 2D arrays of scatters, and we think about optics, we always think about
some 2D input plane as incident on some 2D surface, and that focuses on
some 2D output plane like a lens. But there’s no reason
that has to be the case, if we have some extended
optical element, we can think about
light entering from different ways like some cube. That’s something that has been
done with very low contrast glass. So what they do is they
focus a laser beam on glass, and then at high intensities, this glass can get
small refractive index changes on the order of 0.001 or so. But even with this really small
refractive index contrast, and this really weak scattering, they can show that they can actually multiplex
different functions, or different holograms in addition
to with respect to angle, and also with respect
to a wavelength. That’s something I’m
really interested in working with because I think inverse design really shines in this situation where we have to design some three-dimensional volume. In that case, I don’t think that it’s really practical to make
some forward design.>>Do you think that this type
of design would work well with the liquid crystal, the helical types of geometric phase
that dimension optics does?>>So the very phase optics?>>Yeah.>>In what context?>>So I mean, they have
this nice technology where they basically they have this helical LCs that come with geometric phase optics similar to metamaterial we currently use
but they’re actually higher, more efficient, meaning
slightly more mature technology. Can you apply your types of design
techniques to their materials?>>So these are helical scatters?>>These are helical liquid crystal, I can show you later if
you’re not familiar. You should definitely check it out.>>Those are corkscrew?>>Yeah. They are like
corkscrew liquid crystal. So they work with left and
right-handed circular polarization.>>Right.>>So that you get
the geometric phase a different way than you do with these thing room.>>So in this case, it’d be
polarization sensitive, right?>>Yes, very.>>Okay. I think it would be
possible to arrange them. You would have to find
some parameterization of this corkscrew structure, and that’s how, and then be able to, so if this corkscrew
structure has some height, it has some winding number, and it has some radius, and then if you weren’t able to express the surface in
terms of these parameters, you could probably
plug it into my code, and then optimize those parameters. I think it’s hard to
parameterize a helical surface.>>That’s not something that I
have very much experience with.>>It could be basically
selectively blast away.>>So they’re actually changing
rotation angle, right?>>I think they lost the way.>>How did they get
their different phases by changing the orientation
of their helix, the rotation of the helix.>>I think that the helix is, if you have these devices like that, the helix goes like this. So the axis of the helix is
parallel to your substrate.>>Because perpendiculars.>>Perpendicular.>>When we’re dealing with that like these right hand circular
polarized light, you can think of these helices, as essentially being like
polarization converters, and essentially it’s like
the very phase is like your phase changes tied to
the rotation of your polarization.>>Yeah.>>Of your light. So it makes sense for the axis is perpendicular
to your substrate.>>I think even if their axis
goes horizontal with the plane, if you look on the
vertical, you’ll still see another helix because if you think.>>It maybe.>>Yeah.>>I think they design these things with their further perpendicular. I think other people might
have done that for Morgan fret Street Prep design
what you’re talking about.>>I’ve another question. When you design, for example, like in the future you want to
design these 3D volume optics, you have to worry about
the fact that light as being multiply scattered within the optics [inaudible] model
that somehow, right?>>Yes. So that’s
really a good point. If you have these scatterers they
have to be coupled together, and that’s something
that meet there actually does for us very well is that it computes all these particle
particles coupling is analytically.>>[inaudible] helix spherical.>>Assuming spherical, but
the formalism is the same, if you have different scatters
at different geometries. The only thing you
can run into is that, with Mie theory, if you have
very closely packed particles. So if you have very
closely packed particles, there’s another extension
that you need to add because if your particle has some
circumscribing sphere, and that circumscribing sphere can intersect with the boundary
of another particle. And that is due to some singularities in the Bessel functions that
you use to expand your Bessel. You can fix that in different ways, but that is something you
have to be careful about. The last thing is some idea is that one of my advisor had is like the optics and computational
algorithm customization. So if we have some scene or you have some feature that we
were interested in, maybe we want to create an image of the scene or maybe you want
to make some decision. So we can think of having the computational design
of a metasurface or of a stack of metasurfaces together that perform some optical function. In this case, it can be
trying to image it in which case the metasurface
apply some blur, or it can be performing
some mathematical operations, some linear operation on this scene and having some
post-processing software afterwards. So this is like an imaging pipeline. But in practice, what
has been done is that these two elements of
this are DC components, the post-processing software and the computational design are
optimized independently. So one thing that we’re interested is essentially like
this co-optimization of these metasurfaces with
some optimization algorithm, and that’s something
that metasurfaces really make possible because now you really have a lot of control over the face profiles over
your scattering properties. Just an overview, I went over
some single element metasurfaces. I went over some metasurface
optical systems, some work on the inverse design of metasurfaces, and
some acknowledgments. I’m from the noise lab, the nano optoelectronic integrated
systems engineering lab, archives on the top left and then I want to thank some
of the collaborators. From left to right is
Taylor, Shane, Chris, James, and Max, and also some collaborators at
the Air Force Research Lab who helped us with
the inverse design project. Developers’ facilities and
some of the funding sources from our lab. Yeah.>>These kinds of metasurface lenses
seem to have problems with dispersion, efficiency,
angular dependence. What do you see as the future
prospect of addressing those issues. Do you think in the next 10 or 20 years we’ll see
a flat metasurface lens that can rival conventional
refractive lens or are these devices going to
be more specialized, like where you meet some exotic
control over the wave front, and these other issues
are not important like you’ve always know that light
is coming from a certain angle, you know the wavelength and so forth.>>Yeah, so that’s a good point is that it seems like there’s
a lot of problems right now. But one thing is that all of these problems have been solved
relatively independently. So we have achromatic operation that works for these small
numerical apertures. We have these angular
corrected lenses. I don’t see them in the near future replacing the lenses in
your smartphone, for example. But definitely in anything where you have interested
in a single wavelength, I think that these metasurfaces
are very interesting. So if you have some optical sensors for that
rely on a single wavelength. So that’s like autonomous cars
like Internet of things. That is a very good application for these so definitely
customized sensors. But if you were able to integrate
these metasurface into volumes, I think that is
one straightforward pathway to actually solving all of these problems that including
like angle aberrations, chromatic aberrations and efficiency. But maybe not efficiency problems. But efficiency problems are
lessened when you’re not forced to solve all these problems
in a single surface. I think it’s important to note that conventional optics doesn’t solve these problems that a
single element either, and it’s like if we want a really
high-performance optical system, we have to have a lot of
different optical elements in it, and it’s not a fundamentally
different problem that the metasurfaces have.>>It seems different in the sense that it would be hard
to stack these things.>>Yeah.>>Like the efficiency would go down as you stack
more and more of these. It goes down a little bit as
you stack more and more lenses, but it doesn’t go down a lot, right?>>It doesn’t go down that much. So one problem with efficiency is when we’re creating high
numerical aperture lenses, we have these very high
phase gradients and that causes some problems with efficiency, but like conventional lens, if you wanted to have
a small focal length, we could have one focal length lens of F1 and stack another
F2 on top of it, and that’s how we get our next
focal length without actually having to implement all of
these extra phase gradients, and that’s another way
that we can also use these dispersion
engineering techniques. Now if we have one corrected lens at F1 and other corrected lens at F2, we can make our next focal length, and that’s something that
would be interesting for them.>>So the LC PC line device like they’re over 99 percent efficient
for one handed polarization. What efficiency do
you think is possible with these types of not just yours but
everybody’s infrastructures?>>In a single layer, efficiencies of around 70-80 percent have been
shown for metasurface lenses.>>At one wavelength?>>At one wavelength. But it’s important to note that even these helical properties
are also diffracted lenses. If you have a 100 percent
efficiency at one polarization and
these applications where you have unpolarized light, you have that immediately. In addition, these elements
likely also display chromatic aberrations because
this geometric phase is also.>>Yes.>>So these are not like this
helical think solves everything, but it is interesting
that they could do this.>>I guess what I’m hoping is that, is there a path to
making these devices 99 percent efficient because then we can stack them and incorporate them.>>Yes, I really do think so.>>Okay. So what does
it take to get there?>>I think these conventional
metasurface elements have all been fabricated using clean rooms
that are university clean rooms. So I mean if you look at
the devices that we generally make.>>Just lack of
precision and features.>>I think that’s a big part of it. We experience a lot of
overetching and underetching. So I won’t bring up my nano scribe, but particularly in
the case of, where is it? Like this lens right here, you can see there’s obviously defects where dust
particles have come in.>>[inaudible] clean room. Okay.>>Yeah. I’m not very
good at fabrication. This is actually, it
wasn’t work that I was experimentally involved
with or fabricate these. But it’s like a big issue
with fabrication as our clean rooms are
not very reliable, and that’s like the catch-all
response that we always give, is that we overetch our pillars, our structures aren’t actually
what we want them to be. Another option is that we actually when we design these
using the forward design method, we don’t actually account for
the coupling between these pillars. So what we’ve done is we’ve
simulated these pillars in an infinitely periodic array
and then we take one out and we plug it in somewhere and it’s surrounded by maybe things that look similar or maybe
drastically not similar, like in this case.>>[inaudible] designing
it to say that the surrounding pillars should
coordinate in a certain way, so that light doesn’t scatter
around and wave directions.>>That’s something that inverse
design has actually shown that it’s capable of helping it because now if we can actually account for all these
couplings that happen, one of the things that these
authors in particular, the bottom, they complain about is that they are not
able to accurately characterize all of the couplings
between these pillars, and you can see that
they’re really dense, and it doesn’t really make sense
to consider them independent. So I think there’s also
a very big design factor that is important when you’re considering
how efficient these things are.>>So you’d have to do
a more rigorous inverse design, and you have to get
fabrication [inaudible] , then maybe you could get. So in stimulation, have you’ve
gotten close to 100 percent?>>In simulation, we’ve gotten
up to 80 or 90 percent?>>But that was simulations, not this stuff, right, [inaudible]
scattering simulation.>>That was in the
full-wave FTTD simulation.>>Of what kind of structure?>>Some lens.>>Okay.>>It’s not a very
highly recapture lens.>>But I’m asking was it exotic
shapes like these pillars here.>>No it’s just dumb
circular cylinders.>>Okay, that’s what I was asking.>>I could take his question
in different direction. I mean, he’s asking more about generalized imaging optics for multiple wavelengths
and stuff, but I mean, metasurfaces have
a few unique properties, right, where they’re definitely might be well-suited to
very specific applications. I mean, things that mean
something that’s very thin. There’s a man’s very light
or something where you could define an arbitrary optical wave
front, these sorts of things. So what applications you see there where there might be
more low hanging fruit for metasurfaces where
a traditional or optical system might not fit well for
what they have now.>>So one thing that
maybe is not a frame. So biological imaging is one thing that we’ve always
been very interested in. Is if we have these very thin
optical elements and we can implement we could put it
on some optical fiber.>>Okay.>>We can now actually
if we attach this, we can at least increase the
collection efficiency of our fiber, and maybe increases
numerical aperture. That thing is really
interesting for us. That’s pretty low lying fruit
and these kinds of sensors, there are already
a certain sensors that use these kinds of diffractive
optical elements. In that sense, maybe it’s not as plug and play or it’s
not as useful currently, but that’s something
that could be of use. There’s been a lot of interest in roll-to-roll printing of
metasurfaces recently, and then you could maybe see
some polymer-based metasurfaces, where if you could actually get the resolution required for these
roll to rolled methods to work, you could print out
these rolls of metasurfaces, and maybe on a solar panel to get
uniformity on your solar cell. Or in the case of these
gallium-arsenide solar cells, maybe a really high and
a metasurface that’s fairly efficient can focus light onto it one of these small
gallium-arsenide photocells. Metasurfaces have been sent
to space. That’s cool.>>Yeah.>>To do what?>>I’m not really sure,
it’s like [inaudible].>>Yeah.>>How long does
the inverse design process take? Is it parallelizable and what do you think the prospects are since we’re a bunch of
computer scientists here. A lot of us are computer scientists. What do you think the prospects
are for coming up with better optimization algorithms and
improving efficiency that way.>>So that’s a really
good question up. This particular simulation
took around one day on our workstation computer
and that’s like one of the new AMD 12-core processors, and it’s GPU accelerated or the matrix vector multiplication is GPU accelerated with some NVIDIA. I think it’s a Titan XP. So this took around
a day and that was rigorously simulating all
of these spheres together. One way to get this better, was actually something we’ve
been thinking about is, instead of simulating
an entire structure- so when we simulate
these entire structure together, we get the accurate result. But if we wanted to cut some corners, one thing that we can
consider doing is actually splitting this into
a different simulation regions. So we can simulate
these small sections of this, and that’s easily parallelizable. You can simulate
large sections of these. That actually reduces the time that it takes for
your iterative solver to->>That would very much be
like FMM methods, right?>>That’s multiple?>>Yes.>>Yeah.>>If this is 2D, roughly. This [inaudible] stand
beneath each other at all?>>No.>>No. So then that
is like a quad tree. You’re doing a quad tree like subdividing this into
four sections and so on.>>Yeah. So I think
you would actually want to have some overlapping, maybe some window that has
some kind of constant change.>>Yeah. Actually, FMM would do
full interactions between them. So you’re not isolating them at all.>>Okay.>>It’s just a way of organizing the compute so that you can
go in and multiple series. So the guy on the upper left corner, will have a low order
angular interaction, like you have a lower and lower
order angular resolution.>>Right.>>In the how you represent
the interaction between them.>>Do you ignore that interaction
or do you still-.>>Interaction is included, but it’s just that’s the central idea of FMM that you can actually
do in cross and interactions, but in a login and compute y respecting say double
precision or you specify the precision and it will do
it, respecting that precision. So I think you have your analytic solutions for
each sphere that you want to use, but you could import a FMM
like ideas into this. Because you’re also doing
single frequency and that’s natively where
FMM was designed.>>Right.>>So there’s definitely room to use those ideas for what you want.>>Right. I don’t
know much about FMM, but I do know that
the authors of the paper, of the Versailies,
were thinking about it and they were talking about
it in their GitHub chat. I was like, okay. Cool.>>Right. Because I’m imagining
if it’s taking a day, then a lot of your work is going into this dense matrix of interactions
between all of these things.>>Right.>>Which is why you are
proposing like target finding it and ignoring some introductions, but FMM will give you actually good results without
ignoring those introductions.>>Is FMM easily parallelizable?>>People have been working
on that for a while.>>Okay.>>It boils down to a sparse
matrix vector multiplication, but that’s when you use
BEM as the foundation. You start with a boundary
element formulation and then apply FMM ideas.>>Right.>>But you would start
with analytics solutions and then apply FMM ideas, but I think they still apply.>>Okay.>>But it’s all based
on multiple series of the baby equation and
all that business, which would still apply to you.>>This is all
non-convex optimization. So I’ve been using
L-BFGS just because it doesn’t give me oscillations
and that’s fine for me for now.>>What’s L-BFGS?>>It’s a quasi Newton method. It’s like you do a gradient descent which is just go in the direction
of your gradient. L-BFGS stores the history of the gradient descents and it
approximates your second derivative. So if you’re really close to
the minimum, you go faster. Also has some like,
what is it called? Trust region methods, so that your figure of merit never increases
if you’re trying to minimize. So it has like an adjustable step
size that it does automatically. There’s other update methods
that people have been thinking. I’ve used Nestor OBS gradient
for a little while. There’s some people that have
told us to use Stochastic method. One way that’s like
maybe a little far off, but I went to a D-Wave talk recently and they were
talking about optimization. I was like, hey, maybe I could
think about how D-Wave could help. That’s something I’ve been
interested in is like using D-Wave.>>[inaudible] right?>>Yeah.>>Sorry. D-Wave is
similar meanings, right?>>Yeah.>>Yeah.>>Quantum simulated.>>It’s a bit what
they using holographs. That’s what I was going to
ask is how nonlinear is this. So if you take one ball
out of this system, can you easily up substract its contribution
to your reconstruction, to your field, or
once you take a ball, you have to calculate
the whole thing again?>>So if I take a single sphere
out of this matrix, the system of equations that
I’m solving is changed, and I need to calculate again, yes.>>Well, there’s global optimization, that’s the philosophy anyway.>>Because we pull up and
everything is linear. So you can say, I’m
flipping one pixel.>>Yeah.>>So I’m just calculating
the contribution of that pixel.>>That’s what we were
saying earlier that the following modeling that’s
the built-in assumption. The idea of this approach to things
is not ignored and all that.>>This is still a linear system. It’s just highly coupled and
maybe if there was a way that you could resolve
the coupling somehow. That’s interesting. I never thought about it that way.>>Is it possible that you
can get something out of instead of like assuming these are
all on a transparent substrate?>>These are simulated in a space.>>Oh okay.>>Yeah.>>So they’re simulated in space. Well, I was wondering
is it possible that you could use hemispheres, metallic backplane and
use it for reflection?>>Right. So isn’t that the
same as what I’m doing.>>Well, it could be and it
could be easier to fabricate. It could be more efficient.>>Oh, okay. I see what
you’re saying. So I can’t actually simulate flat boundaries. This code doesn’t
actually support that.>>Or you could just say
it’s a perfect mirror.>>Yeah. I could
simulate something like a reflection of this pillar set. Yeah. That’s totally.>>I had a more general
question building on that. Have people looked
at like all this is full for refractive materials, have people looked at
reflective metal surface, are there uses for that like making a nice mirror that
solved the features?>>Yes.>>That is something cool for you.>>The original chromatic
aberration paper that use dispersion engineering, actually used reflective mirror, because that’s actually a really
easy way to double your phi. Because now usually light travels one way and it comes right back out. That’s one way that you could double the phase compensation and then
not have a very high thickness. There’s been other interesting ideas. One of the cool things
that’s come out recently is it’s a spin preserving mirror. So normally, when you have right-hand circular light
and it reflects off, it becomes left, but they have it, so they’ve made a mirror such that its right-hand circuit polarize
and it reflects back right, and it doesn’t reflect
left or something. I’m not sure about
what it does to left.>>Interesting. We’ve done that
with the [inaudible] LC materials.>>Okay.>>Or something similar I
didn’t have exactly that.>>So where is the emphasis
in the field now? Is it on better
computational methods? Is it on better materials? Where do people see the biggest
possible improvement coming from.>>So I think more recently, there’s been a lot of work towards
system level metal surfaces. So like these retro reflectors, these angle of compensating things. Right now that’s a harder problem
in these tunable systems. There is a significant push towards inverse design and that’s part
of the push that I’m part of. I don’t think that
many people are exploring computational imaging
paved metal surfaces, because there hasn’t been very much research that’s been done with these. But that’s very much
one of the emphasis. One of the major emphasis of our lab is that we
really want to pair this computational
intrepidity technique with these metal surfaces
and do this co-optimization. In addition, there’s a lot of interesting ideas
in non-linear optics. So these metal surfaces, if someone had a non-linear material, you can achieve
some phase-matching condition, and people have shown
that you can get some high non-linear enhancements
for these metal surfaces. There’s some really cool work
doing engineered disorder, but I think it’s more moving towards the system level
integrations, and like the vertical stacking and I think it’s actually
moving towards volume optics. But maybe slowly and in addition
to these inverse design methods.>>You’re graduating, so for example, I’m very interested in
collaboration, who should I talk to?>>Our commissioner.>>Okay.>>Or the other two people that
are very much at the top of the list are Andrei Faraon at
Caltech or Faraon at Caltech, and Federico Capasso at Harvard. If you’re interested in
the metallic surfaces which I didn’t talk about at all, Vladimir Shalaev at Purdue
is really interesting. Then there’s also Boltasseva,
Alexandra Boltasseva there. Naomi Halas at Duke does
some interesting plasmonic stuff. There’s this group in China
that recently made this. There’s the line universities on this list mostly in
Taiwan and Nanjing. So I guess this guy too Nanfang Yu, he’s in Columbia doing
this kind of stuff. I think he mostly works more on infrared optics right now
and not as much invisible.>>We’re going to try
to get her here later in the summer, so make sure. We’ll keep you posted on that. Okay. Well, it that’s it. There’s no more questions. Thank you very much, that was a very detailed and helpful for us to understand
a lot of these issues.>>Yeah. Thank you.>>Yeah.

Design and Optimization of Dielectric Metasurfaces
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  • September 4, 2019 at 10:37 am
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    Simple switch-case will be able to describe only one mobile movement, quite advanced…

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