High-power laser beam shaping using a metasurface for shock excitation and focusing at the microscale Yun Kai1 2Jet Lem1 2Marcus Ossiander3Maryna L. Meretska3Vyacheslav Sokurenko4

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High-power laser beam shaping using a metasurface for shock excitation and focusing at the

microscale

Yun Kai,1, 2, ∗Jet Lem,1, 2 Marcus Ossiander,3Maryna L. Meretska,3Vyacheslav Sokurenko,4

Steven E. Kooi,2Federico Capasso,3Keith A. Nelson,1, 2 and Thomas Pezeril1, 5, †

1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

2Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

3John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

4Kyiv Polytechnic Institute, National Technical University of Ukraine, 03056 Kyiv, Ukraine

5Institut de Physique de Rennes, UMR CNRS 6251, Université Rennes 1, 35042 Rennes, France

(Dated: July 18, 2023)

Achieving high repeatability and efﬁciency in laser-induced strong shock wave excitation remains a signif-

icant technical challenge, as evidenced by the extensive efforts undertaken at large-scale national laboratories

to optimize the compression of light element pellets. In this study, we propose and model a novel optical de-

sign for generating strong shocks at a tabletop scale. Our approach leverages the spatial and temporal shaping

of multiple laser pulses to form concentric laser rings on condensed matter samples. Each laser ring initiates a

two-dimensional focusing shock wave that overlaps and converges with preceding shock waves at a central point

within the ring. We present preliminary experimental results for a single ring conﬁguration. To enable high-

power laser focusing at the micron scale, we demonstrate experimentally the feasibility of employing dielectric

metasurfaces with exceptional damage threshold, experimentally determined to be 1.1 J/cm2, as replacements

for conventional optics. These metasurfaces enable the creation of pristine, high-ﬂuence laser rings essential

for launching stable shock waves in materials. Herein, we showcase results obtained using a water sample,

achieving shock pressures in the gigapascal (GPa) range. Our ﬁndings provide a promising pathway towards the

application of laser-induced strong shock compression in condensed matter at the microscale.

Shock waves have broad signiﬁcance across various ﬁelds,

such as materials science [1], physical chemistry [2, 3], as-

trophysics [4], medical therapies [5], and more. In partic-

ular, information regarding high-pressure equations of state

can be extracted through the study of shock propagation in

condensed matter. In classical laser-shock experiments, shock

waves are generated by delivering pulsed laser energy to a pla-

nar photoacoustic transducer layer deposited onto a sample.

The absorption of laser energy induces an out-of-plane shock

wave that travels into the sample. Commonly in these experi-

ments, the shock wave is probed after propagation through the

material at either a free surface or the interface of a transpar-

ent substrate. Such laser-induced shock wave techniques have

typically been conducted at large-scale facilities, where high-

energy laser pulses are readily available, often conveniently

coupled with coherent x-ray sources or other techniques that

enable advanced probing of the shock waves in samples.

Given comparable shock durations of several nanoseconds in

these experiments, the efﬁciency of laser-shock excitation can

be quantiﬁed as the ratio of achieved shock pressure to the

input laser pulse energy. Experimental campaigns conducted

at the LCLS and OMEGA laser facilities have consistently

revealed that the laser-shock excitation efﬁciency typically

ranges from 15 GPa/J to 100 GPa/J [6, 7]. Improving this efﬁ-

ciency is crucial for reaching the goal of achieving breakeven

fusion.

An alternative route towards shock wave experimentation is

homogeneous direct-drive techniques. In these experiments,

the sample itself serves as both the test material and shock

∗Corresponding author: ykai@mit.edu

†Corresponding author: pezeril@mit.edu

launching layer by making the material of interest optically

absorptive. Absorption of the laser energy leads to ablation of

the material, launching shock waves diverging from the exci-

tation region. This experimental geometry allows for the di-

rect visualization of shock waves propagating laterally in the

plane of the sample and is well-positioned for the application

of spectroscopic probes to investigate shock-induced phenom-

ena. Additionally, it allows the experimenter to shape the ex-

citation arbitrarily for varied experimental designs. One such

design demonstrated in our previous works[1, 8, 9], is based

on in-plane 2D focusing of shock waves. A converging shock

wave is launched by shaping the laser pulse into a ring, whose

pressure ampliﬁes as it reaches the focus. This experimental

geometry using a single laser ring has been shown to reach

excitation efﬁciencies as high as 104GPa/J, with pressures of

tens of GPa reached with pulse energies as low as a few mJs

[8]. This allows one to conduct high-pressure experimentation

with a commonplace low-cost tabletop laser ampliﬁer system

with the capability for rapid rearrangement and high through-

put experimentation (hundreds of shots per day).

The herein-described novel optical design is expected to

maintain or even exceed the shock excitation efﬁciency of 104

GPa/J reported in our previous work. Indeed, thanks to much

larger excitation areas with multiple laser ring excitations, we

hope to bypass the saturation or plateauing effect encountered

at increased laser ﬂuences. The two novel excitation schemes

that we describe herein, harness the fundamental principles

of energy focusing and speed matching for optimized shock

excitation efﬁciency. We have recently demonstrated the 1D

proof-of-concept of spatial tuning and superposition of mul-

tiple weak shock waves excited by an array of laser photoa-

coustic sources shaped as lines [10]. In this pioneering ex-

periments, we have shown that the optical device can excite

arXiv:2210.05750v3 [physics.optics] 17 Jul 2023

FIG. 1. (A) Dual Death Star setup to generate multiple time-delayed laser beams from a single input beam. The two “Death Star” cavities

are formed of elementary square-shaped mirrors and a partial reﬂector (PR) for each. The sequential time delay between pulses is governed

by the round-trip time of the Death Star cavity in the nanosecond range. (B) The matrix of n×n collinear beams that emerges from the Dual

Death Star setup can then be transmitted through a metasurface whose sophisticated 2D optical phase is calculated such that each of the beams

focuses at the microscale on the sample surface and forms a concentric ring of a different diameter.

×20 higher shock pressures as compared to a single source

that is limited by optical damage, and can maintain the high

efﬁciency of the linear excitation regime. The basic idea of

the novel optical design is based on the excitation of multiple

synchronized laser rings rather than a single ring. The oper-

ating principle of this technique is the superposition of mul-

tiple converging shock waves. The ﬁrst excitation will be the

largest ring. The second excitation will excite a second ring

with a smaller radius at a later inter-pulse time that matches

the shock propagation time. In this way, the second ring shock

is excited at the position of the previously launched ﬁrst con-

verging shock. This coherent multi-ring excitation is repeated

for as many laser rings as available. Combining the shock ve-

locity matching excitation and the 2D shock focusing should

lead to a nonlinear build-up of the traveling shock pressure.

Harnessing the power of both shock ampliﬁcation through 2D

focusing and shock velocity matching, one can expect signiﬁ-

cant increases in the achievable pressures [11].

In this study, we present a novel optical design termed the

dual “Death Star,” which enables the formation of an array of

multiple time-delayed beams in the nanosecond range, match-

ing the time scale of shock propagation in the sample. This

array of temporally and spatially spread beams, generated by

the dual “Death Star,” can be subsequently shaped and focused

onto the sample as concentric rings at the microscale. To cir-

cumvent the use of refractive optics with low optical damage

thresholds, which are unsuitable for high-energy pulsed lasers,

we propose an alternative approach utilizing phase elements

for shaping and focusing laser rings. Unlike conventional fo-

cusing elements, these phase elements alone could directly

produce multiple rings at the sample location. While opti-

cal phase masks have been employed to focus or shape high-

power laser beams at the millimeter scale [12–14], their milli-

metric resolution is inadequate for microscale shock waves. In

our work, we demonstrate the application of modern metasur-

faces [15–17], which exhibit a damage threshold of up to 1.1

J/cm2, as a viable implementation for generating microscale

laser-induced shock waves. Furthermore, we provide exper-

imental results obtained from water samples, demonstrating

the metasurfaces’ ability to launch shock waves with pressures

in the GPa range.

MULTI-RING CONCEPT: DUAL “DEATH STARS”

OPTICAL DESIGN

The Death Star cavity, originally used for high-frequency

(tens to hundreds of GHz) acoustic wave spectroscopy [18],

can be repurposed from its original use to obtain an array of

beams with nanosecond inter-time delay or more. The Death

Star operates with a four-mirror cyclic cavity, whose last mir-

ror is a partial reﬂector (PR). After traveling through the cav-

ity the PR allows part of the laser input pulse to exit the cavity

and horizontally offsets the reﬂected laser beam for another

round trip through the cavity. This leads to an output of n-

horizontally spaced laser pulses, with temporal delay set by

the Death Star round trip time. We will utilize two Death

Star cavities connected by a twisted periscope in the proposed

design. The ﬁrst Death Star generates a horizontal array of

n-pulses. The twisted periscope rotates this array by 90 de-

grees. This vertical array is input into the second Death Star

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High-powerlaserbeamshapingusingametasurfaceforshockexcitationandfocusingatthemicroscaleYunKai,1,2,∗JetLem,1,2MarcusOssiander,3MarynaL.Meretska,3VyacheslavSokurenko,4StevenE.Kooi,2FedericoCapasso,3KeithA.Nelson,1,2andThomasPezeril1,5,†1DepartmentofChemistry,MassachusettsInstituteofTechnology,Cambridg...

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High-power laser beam shaping using a metasurface for shock excitation and focusing at the microscale Yun Kai1 2Jet Lem1 2Marcus Ossiander3Maryna L. Meretska3Vyacheslav Sokurenko4

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