Science - USA (2020-05-22)

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The recent development of brilliant pulsed

x-ray sources has generated new opportuni-

ties for time-resolved diffraction experi-

ments in the femtosecond regime. The ex-

periment of Yang et al. is an ED experiment

performed at the SLAC-MeV-UED facility ( 11 )

on a target gas of pyridine. The pump laser

launches a nonstationary wave packet on the

potential-energy surface of the S 1 (np*) ex-

cited state. Large-angle elastic scattering en-

codes information on the nuclear structure,

whereas small-angle inelastic scattering is

sensitive to electron correlation. In the elec-

tronic ground state of pyridine, the localized

n orbital is doubly occupied, which results

in strong so-called dynamical electron cor-

relation (the two electrons try to avoid each

other). In the S 1 (np*) excited state, these two

electrons occupy spatially separated orbitals,

which reduces dynamical electron correla-

tion. The population of the S 1 (np*) state can

be detected by the reduction of the small-

angle inelastic electron scattering signal in

the excited state.

Yang et al. extracted the nuclear struc-

tural dynamics from the simultaneously

measured large-angle elastic ED, using algo-

rithms that were developed earlier for sta-

tionary ED. Specifically, the main geometric

parameters are the average bond length of

the C 5 N ring and the dihedral angle repre-

senting the distortion of one of the atoms

out of the plane of the six-membered ring.

The transient structure confirms the preful-

venic distortion predicted earlier by ab ini-

tio calculations (see the figure). The time-

resolved ED data unequivocally reveal that

the decay of the population of the S 1 (np*)

state and the distortion of the ring occur on

the same time scale of ~300 fs, resolving a

decades-old puzzle in molecular spectros-

copy. This work of Yang et al. represents a

milestone on the path toward the character-

ization of photochemical events with simul-

taneous complete resolution in time as well

as in atomic structure. j

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10.1126/science.abb9937

TOPOLOGICAL OPTICS

Solitons and topological waves

A laser-fabricated waveguide array creates a nonlinear

medium that supports solitons

By Mark J. Ablowitz andJustin T. Cole

T

he intense coherent emission from

lasers enabled the study of light

propagation in nonlinear media,

which spurred many important ap-

plications. More recently, the study

of electromagnetic wave propaga-

tion in periodic media, where linear band

structures play an important role, has ad-

vanced in new directions. By breaking cer-

tain symmetries, such as time reversal, the

medium can support so-called

“topologically protected” modes

that possess uncommon robust-

ness to material defects. Theory

has suggested that certain non-

linear waves can inherit the

topology of associated linear

waves. On page 856 of this is-

sue, Mukherjee and Rechtsman

( 1 ) describe experiments where

such nonlinear waves, called

solitons, can now be observed

in the bulk of photonic topo-

logical media. These localized

waves exhibit cyclotronic mo-

tion as the light propagates

down a specifically engineered waveguide.

When a different mode is considered—one

with trivial topology—the waves no longer

circulate but remain essentially fixed in

their initial spatial distribution.

Investigations of solitons trace their

roots back to 1834, when naval architect

John Scott Russell first recognized their

remarkable character in the Union Canal

near Edinburgh, Scotland ( 2 ). This wave

was not oscillatory; it was a solitary sur-

face wave that propagated over surpris-

ingly long distances (2 to 3 km) with fixed

form. Some years later, mathematicians

described this solitary wave in terms of ap-

proximate equations derived from the gov-

erning water-wave equations. For nearly

70 years, this was essentially

all that was known theoreti-

cally. The situation changed

in 1965 ( 3 ) when it was found

that two such solitary waves

have extraordinary interac-

tion properties. Their interac-

tion is elastic in nature, and

the two waves exit the interac-

tion with the same amplitude

and speed with which they

entered. Such solitary waves

were termed solitons.

This paper motivated ma-

jor research studies in both

mathematics and physics. In

mathematics, it gave rise to a new field of

study: integrable nonlinear wave systems.

These are nonlinear partial differential

equations that are exactly solvable and pos-

sess an infinite number of symmetries and

conservation laws. In physics, researchers

have observed solitary waves and solitons

not only in water waves and nonlinear op-

tics but also in plasmas, electrical circuits,

Department of Applied Mathematics, University of

Colorado, Boulder, CO 80309, USA. Email: mark.ablowitz@

colorado.edu; [email protected]

Light propagates down the waveguide and

cyclically returns to its initial state. If the

mode was nontopological, it would start and

remain in a state like the leftmost fgure.

The system is initialized

by injecting light (yellow)

into a waveguide (shown

as gray without light).

Light injection Rotating solitons

“Theory has

suggested

that certain

nonlinear waves

can inherit

the topology

of associated

linear waves.”

Tracking a topological soliton

Five snapshots (left to right) show a topological soliton as it propagates down an array of waveguides laser-

fabricated by Mukherjee and Rechtsman. The waveguide is fabricated in such a way that as adjacent waveguides

come close together, the light transfers in a counterclockwise fashion from one waveguide to the next.

22 MAY 2020 • VOL 368 ISSUE 6493 821

Published by AAAS