1 Beyond Bounds on Light Scattering with Complex Frequency Excitations Seunghwi Kim1 Sergey Lepeshov2 Alex Krasnok3 and Andrea Alù14

2025-04-28 0 0 490.17KB 15 页 10玖币

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Beyond Bounds on Light Scattering with Complex Frequency Excitations

Seunghwi Kim1, Sergey Lepeshov2, Alex Krasnok3, and Andrea Alù1,4*

1Photonics Initiative, Advanced Science Research Center, City University of New York, New

York, New York 10031, USA

2DTU Electro, Department of Electrical and Photonics Engineering, Technical University of

Denmark, Ørsteds Plads 343, Kgs. Lyngby, DK-2800, Denmark

3Department of Electrical and Computer Engineering, Florida International University, Miami,

FL 33174, USA

4Physics Program, Graduate Center, City University of New York, New York, NY 10016, USA

*Corresponding author: aalu@gc.cuny.edu

Light scattering is one of the most established wave phenomena in optics, lying at the heart of

light-matter interactions and of crucial importance for nanophotonic applications. Passivity,

causality and energy conservation imply strict bounds on the degree of control over scattering

from small particles, with implications on the performance of many optical devices. Here, we

demonstrate that these bounds can be surpassed by considering excitations at complex

frequencies, yielding extreme scattering responses as tailored nanoparticles reach a quasi-steady-

state regime. These mechanisms can be used to engineer light scattering of nanostructures beyond

conventional limits for noninvasive sensing, imaging, and nanoscale light manipulation.

The study of light scattering by small particles has a long history [1], and it is the basis of a

disparate range of phenomena, from the color of the sky to the brightness of stained glasses.

Despite its well-established nature, engineering light scattering is not an outdated problem: it

remains of paramount interest in photonics [2,3], not only enabling new discoveries [4,5], but also

broadening the impact of nanophotonics for various applications, such as optical antennas [6],

imaging [7], optical tweezers and trapping [8,9].

Small nanoparticles are typically characterized by a broad donut-shape scattering pattern sustained

by their dominant dipolar fields. More exotic scattering features can be achieved in suitably

tailored nanoparticle geometries by carefully balancing electric and magnetic dipolar scattering,

yielding destructive interference in specific directions that make the scattering more directive. For

instance, scattering suppression in either the forward or backward direction can be obtained in

nanoparticles satisfying the Kerker conditions [10]. Magneto-electric, plasmonic [11] and high-

index dielectric (DNPs) [12,13] nanoparticles have been shown to support peculiar scattering

features, offering opportunities for light manipulation, and establishing the basis for the design of

metasurfaces and metamaterials. However, these exotic responses require careful design of the

nanoparticle geometries, and they emerge only at specific wavelengths as a function of the

available material dispersion. In addition, even when these conditions are met, the scattering from

nanoparticles remains limited by causality, passivity and energy conservation.

Consider, for instance, the problem of realizing a particle with directional backward scattering,

i.e., with minimized forward scattering cross-section

( )( )

2 1 0,

F n n

n a b







= + +



where

k=k

is the wavenumber of the incident wave,

is the multipolar order, and

and

are

electric and magnetic Mie scattering coefficients, corresponding to the amplitude of multipolar

scattered waves of order n [2,14]. We assume an



−

time convention under plane wave excitation

iˆ

in o

−

=kz

, where

is a unit vector. According to the optical theorem, the extinction cross-

section

ext



is proportional to the normalized forward scattering amplitude with polarization

parallel to the incident wave

( )

ˆ=e f k k

[2,15]:

( )

4ˆ

Im ,

ext abs scat



  

= + =  =





e f k k

(1)

where

abs



and

scat



are the absorption and scattering cross-sections,

is the unit polarization

vector of the incident wave, and

and

are the wave vectors of incident and scattered waves,

respectively. Eq. (1) indicates that

ext



must be zero if

( )

i0==f k k

, yet in a passive scatterer

0, 0

abs scat





, hence this condition can be met only if the scattered power is zero at all angles

[15-18]. For very small particles, a negligible – yet strictly nonzero – forward scattering can be

achieved, with most of the residual scattering distributed at other angles, as in the inset of Fig.

1(a), but a severe trade-off exists between total scattering and residual forward scattering,

consistent with Eq. (1) [16]. Passivity fundamentally limits how backward directive a scattering

pattern can be.

Active materials can be employed to overcome this limitation, since such particles can support

abs





, relaxing the constraint on zero forward scattering. Gain provides additional energy,

relaxing limitations that stem from power conservation, and offering a broader control over light

scattering. However, it is challenging to embed active media within nanophotonic systems, and

typically optical gain comes at the price of stringent bandwidth and stability limitations [19,20].

Moreover, active materials are characterized by unavoidable noise in the form of amplified

spontaneous emission or parasitic harmonics in the case of parametric gain [20], which hinder the

practical feasibility of active systems for several applications.

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1BeyondBoundsonLightScatteringwithComplexFrequencyExcitationsSeunghwiKim1,SergeyLepeshov2,AlexKrasnok3,andAndreaAlù1,4*1PhotonicsInitiative,AdvancedScienceResearchCenter,CityUniversityofNewYork,NewYork,NewYork10031,USA2DTUElectro,DepartmentofElectricalandPhotonicsEngineering,TechnicalUniversityofDen...

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1 Beyond Bounds on Light Scattering with Complex Frequency Excitations Seunghwi Kim1 Sergey Lepeshov2 Alex Krasnok3 and Andrea Alù14

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