We develop an inverse-designed caustic approach to tailor nondiffracting structured lights that exhibit arbitrary intensity structures. Simultaneously, these lights can propagate in an accelerated manner along an arbitrary three-dimensional trajectory. The scheme inherently gives rise to caustics, which are intensity singularities in geometric optics. These types of structured lights possess sharp intensity shapes and exhibit a significant intensity gradient. Moreover, these types of structured nondiffracting lights exhibit structured orbital angular momentum. The proposed approach breaks the restriction of conventional nondiffracting light beams, which preserve fixed propagation trajectories and structures. We experimentally validate our theory prediction. These diverse accelerating nondiffracting light beams will pave the way for optically trapping and moving particles along arbitrary three-dimensional trajectories and are likely to result in applications in wavefront control, optical micromachining, and depth imaging.
REFERENCES
1.
J.
Durnin
, “
Exact solutions for nondiffracting beams. I. The scalar theory
,” J. Opt. Soc. Am. A
4
, 651
(1987
).2.
M. V.
Berry
and
N. L.
Balazs
, “
Nonspreading wave packets
,” Am. J. Phys.
47
, 264
(1979
).3.
G. A.
Siviloglou
,
J.
Broky
,
A.
Dogariu
, and
D. N.
Christodoulides
, “
Observation of accelerating Airy beams
,” Phys. Rev. Lett.
99
, 213901
(2007
).4.
S.
An
,
T.
Peng
,
S.
Yan
,
P.
Zhang
,
M.
Li
, and
B.
Yao
, “
Direct axial plane imaging of particle manipulation with nondiffracting Bessel beams
,” Appl. Opt.
60
, 2974
(2021
).5.
A.
Mathis
,
F.
Courvoisier
,
L.
Froehly
,
L.
Furfaro
,
M.
Jacquot
,
P. A.
Lacourt
, and
J. M.
Dudley
, “
Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams
,” Appl. Phys. Lett.
101
, 071110
(2012
).6.
T.
Vettenburg
,
H. I. C.
Dalgarno
,
J.
Nylk
,
C.
Coll-Llado
,
D. E.
Ferrier
,
T.
Cizmar
,
F. J.
Gunn-Moore
, and
K.
Dholakia
, “
Light-sheet microscopy using an Airy beam
,” Nat. Methods
11
, 541
(2014
).7.
A.
Chong
,
W. H.
Renninger
,
D. N.
Christodoulides
, and
F. W.
Wise
, “
Airy-Bessel wave packets as versatile linear light bullets
,” Nat. Photonics
4
, 103
(2010
).8.
Z.
Jiang
, “
Truncation of a two-dimensional nondiffracting cos beam
,” J. Opt. Soc. Am. A
14
, 1478
(1997
).9.
J. C.
Gutierrez-Vega
,
M. D.
Iturbe-Castillo
, and
S.
Chavez-Cerda
, “
Alternative formulation for invariant optical fields: Mathieu beams
,” Opt. Lett.
25
, 1493
(2000
).10.
M. A.
Bandres
,
J. C.
Gutierrez-Vega
, and
S.
Chavez-Cerda
, “
Parabolic nondiffracting optical wave fields
,” Opt. Lett.
29
, 44
(2004
).11.
V.
Arrizon
,
S.
Chavez-Cerda
,
U.
Ruiz
, and
R.
Carrada
, “
Periodic and quasi-periodic non-diffracting wave fields generated by superposition of multiple Bessel beams
,” Opt. Express
15
, 16748
(2007
).12.
R.
Vasilyeu
,
A.
Dudley
,
N.
Khilo
, and
A.
Forbes
, “
Generating superpositions of higher–order Bessel beams
,” Opt. Express
17
, 23389
(2009
).13.
D.
Liu
,
Y.
Zhang
,
X.
Hu
,
P.
Han
,
M.
Gu
, and
M.
Xiao
, “
Flexible tuning of nonlinear non-diffracting array beams using wavelengths and angles
,” Opt. Lett.
45
, 6106
(2020
).14.
V. V.
Kotlyar
,
A. A.
Kovalev
, and
V. A.
Soifer
, “
Asymmetric Bessel modes
,” Opt. Lett.
39
, 2395
(2014
).15.
W.
Yan
,
Y.
Gao
,
Z.
Yuan
,
Z.
Wang
,
Z.
Ren
,
X.
Wang
,
J.
Ding
, and
H.
Wang
, “
Non-diffracting and self-accelerating Bessel beams with on-demand tailored intensity profiles along arbitrary trajectories
,” Opt. Lett.
46
, 1494
(2021
).16.
J.
Baumgartl
,
M.
Mazilu
, and
K.
Dholakia
, “
Optically mediated particle clearing using Airy wavepackets
,” Nat. Photonics
2
, 675
(2008
).17.
L.
Li
,
T.
Li
,
S. M.
Wang
,
C.
Zhang
, and
S. N.
Zhu
, “
Plasmonic airy beam generated by in-plane diffraction
,” Phys. Rev. Lett.
107
, 126804
(2011
).18.
P.
Zhang
,
Y.
Hu
,
T.
Li
,
D.
Cannan
,
X.
Yin
,
R.
Morandotti
,
Z.
Chen
, and
X.
Zhang
, “
Nonparaxial Mathieu and Weber accelerating beams
,” Phys. Rev. Lett.
109
, 193901
(2012
).19.
I.
Kaminer
,
R.
Bekenstein
,
J.
Nemirovsky
, and
M.
Segev
, “
Nondiffracting accelerating wave packets of Maxwell's equations
,” Phys. Rev. Lett.
108
, 163901
(2012
).20.
I. D.
Chremmos
,
Z.
Chen
,
D. N.
Christodoulides
, and
N. K.
Efremidis
, “
Bessel-like optical beams with arbitrary trajectories
,” Opt. Lett.
37
, 5003
(2012
).21.
A.
Mathis
,
F.
Courvoisier
,
R.
Giust
,
L.
Furfaro
,
M.
Jacquot
,
L.
Froehly
, and
J. M.
Dudley
, “
Arbitrary nonparaxial accelerating periodic beams and spherical shaping of light
,” Opt. Lett.
38
, 2218
(2013
).22.
S.
Wei
,
Y.
Li
, and
D.
Ma
, “
Sculpting optical fields into caustic patterns based on freeform optics
,” Optica
10
, 1688
(2023
).23.
I. D.
Chremmos
,
Z.
Chen
,
D. N.
Christodoulides
, and
N. K.
Efremidis
, “
Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics
,” Phys. Rev. A
85
, 023828
(2012
).24.
P.
Vaveliuk
,
A.
Lencina
,
J. A.
Rodrigo
, and
O. M.
Matos
, “
Caustics, catastrophes, and symmetries in curved beams
,” Phys. Rev. A
92
, 033850
(2015
).25.
T.
Melamed
and
A.
Shlivinski
, “
Practical algorithm for custom-made caustic beams
,” Opt. Lett.
42
, 2499
(2017
).26.
A.
Zannotti
,
F.
Diebel
, and
C.
Denz
, “
Dynamics of the optical swallowtail catastrophe
,” Optica
4
, 1157
(2017
).27.
M. V.
Berry
and
C.
Upstill
, “
IV catastrophe optics: Morphologies of caustics and their diffraction patterns
,” Prog. Opt.
18
, 257
(1980
).28.
J.
Nye
and
F. J.
Wright
, “
Natural focusing and fine structure of light: Caustics and wave dislocations
,” Am. J. Phys.
68
, 776
(2000
).29.
M. V.
Berry
, “
The singularities of light: Intensity, phase, polarization
,” Light
12
, 238
(2023
).30.
H.
Teng
,
Y.
Qian
,
Y.
Lan
, and
Y.
Cai
, “
Abruptly autofocusing circular swallowtail beams
,” Opt. Lett.
46
, 270
(2021
).31.
C.
Lopez-Mariscal
and
K.
Helmerson
, “
Shaped nondiffracting beams
,” Opt. Lett.
35
, 1215
(2010
).32.
E.
Greenfield
,
M.
Segev
,
W.
Walasik
, and
O.
Raz
, “
Accelerating light beams along arbitrary convex trajectories
,” Phys. Rev. Lett.
106
, 213902
(2011
).33.
T.
Fukushima
, “
Numerical computation of inverse complete elliptic integrals of first and second kinds
,” J. Comput. Appl. Math.
249
, 37
(2013
).34.
Q.
Wang
,
Z.
Xia
,
J.
Zhao
,
X.
Zhang
,
C.
Tu
,
Y.
Li
, and
H.
Wang
, “
Tailoring nonuniform local orbital angular momentum density
,” Opt. Lett.
49
, 746
(2024
).35.
H. I.
Sztul
and
R. R.
Alfano
, “
The Poynting vector and angular momentum of Airy beams
,” Opt. Express
16
, 9411
(2008
).36.
M. S.
Soskin
,
V. N.
Gorshkov
, and
M. V.
Vasnetsov
, “
Topological charge and angular momentum of light beams carrying optical vortices
,” Phys. Rev. A
56
, 4064
(1997
).37.
Z.
Ren
,
Z.
Cheng
,
L.
Fan
,
R.
Sun
,
W.
Zhu
,
P.
Wan
,
B.
Dong
,
Y.
Lou
,
J.
Ding
,
X.
Wang
, and
H.
Wang
, “
Polarization-controlled generation of multiple orbital angular momentum modes
,” APL Photonics
9
(3
), 031304
(2024
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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