This study explores exceptional points (EPs) in photonic crystals (PhCs) and introduces an experimental technique for their single-shot observation. Exceptional points are spectral singularities found in non-Hermitian systems, such as leaky PhC slabs. However, directly observing EPs in PhC systems using regular reflectivity spectroscopy is a considerable challenge due to interference between guided resonances and background signals. In this work, we present a simple, nondestructive technique that employs crossed polarizations to directly observe EPs in momentum-resolved resonant scattering. This approach effectively suppresses the background signal, enabling exclusive probing of the guided resonances where EPs manifest. Our results demonstrate the formation of EPs in both energy-momentum mapping and isofrequency imaging. All experimental findings align seamlessly with numerical simulations and analytical models. Our approach holds great potential as a robust tool for studying non-Hermitian physics in the PhC platform.

1.
R.
El-Ganainy
,
M.
Khajavikhan
,
D. N.
Christodoulides
, and
S. K.
Ozdemir
, “
The dawn of non-Hermitian optics
,”
Commun. Phys.
2
,
37
(
2019
).
2.
Q.
Yan
,
B.
Zhao
,
R.
Zhou
,
R.
Ma
,
Q.
Lyu
,
S.
Chu
,
X.
Hu
, and
Q.
Gong
, “
Advances and applications on non-Hermitian topological photonics
,”
Nanophotonics
12
,
2247
2271
(
2023
).
3.
H.
Nasari
,
G. G.
Pyrialakos
,
D. N.
Christodoulides
, and
M.
Khajavikhan
, “
Non-Hermitian topological photonics
,”
Opt. Mater. Express
13
,
870
(
2023
).
4.
A.
Li
,
H.
Wei
,
M.
Cotrufo
,
W.
Chen
,
S.
Mann
,
X.
Ni
,
B.
Xu
,
J.
Chen
,
J.
Wang
,
S.
Fan
,
C.-W.
Qiu
,
A.
Alù
, and
L.
Chen
, “
Exceptional points and non-Hermitian photonics at the nanoscale
,”
Nat. Nanotechnol.
18
,
706
720
(
2023
).
5.
I.
Rotter
, “
A non-Hermitian Hamilton operator and the physics of open quantum systems
,”
J. Phys. A
42
(
15
),
153001
(
2009
).
6.
N.
Okuma
and
M.
Sato
, “
Non-Hermitian topological phenomena: A review
,”
Annu. Rev. Condens. Matter Phys.
14
,
83
107
(
2023
).
7.
K.
Ding
,
C.
Fang
, and
G.
Ma
, “
Non-Hermitian topology and exceptional-point geometries
,”
Nat. Rev. Phys.
4
,
745
760
(
2022
).
8.
H.
Nasari
,
G.
Lopez-Galmiche
,
H. E.
Lopez-Aviles
,
A.
Schumer
,
A. U.
Hassan
,
Q.
Zhong
,
S.
Rotter
,
P.
LiKamWa
,
D. N.
Christodoulides
, and
M.
Khajavikhan
, “
Observation of chiral state transfer without encircling an exceptional point
,”
Nature
605
,
256
261
(
2022
).
9.
H.
Benisty
,
A.
Lupu
, and
A.
Degiron
, “
Transverse periodic P T symmetry for modal demultiplexing in optical waveguides
,”
Phys. Rev. A
91
,
053825
(
2015
).
10.
T.
Goldzak
,
A. A.
Mailybaev
, and
N.
Moiseyev
, “
Light stops at exceptional points
,”
Phys. Rev. Lett.
120
,
013901
(
2018
).
11.
J. B.
Khurgin
,
Y.
Sebbag
,
E.
Edrei
,
R.
Zektzer
,
K.
Shastri
,
U.
Levy
, and
F.
Monticone
, “
Emulating exceptional-point encirclements using imperfect (leaky) photonic components: Asymmetric mode-switching and omni-polarizer action
,”
Optica
8
,
563
569
(
2021
).
12.
A.
Schumer
,
Y. G. N.
Liu
,
J.
Leshin
,
L.
Ding
,
Y.
Alahmadi
,
A. U.
Hassan
,
H.
Nasari
,
S.
Rotter
,
D. N.
Christodoulides
,
P.
LiKamWa
, and
M.
Khajavikhan
, “
Topological modes in a laser cavity through exceptional state transfer
,”
Science
375
,
884
888
(
2022
).
13.
Z.
Lin
,
H.
Ramezani
,
T.
Eichelkraut
,
T.
Kottos
,
H.
Cao
, and
D. N.
Christodoulides
, “
Unidirectional invisibility induced by P T-symmetric periodic structures
,”
Phys. Rev. Lett.
106
,
213901
(
2011
).
14.
A.
Regensburger
,
C.
Bersch
,
M.-A.
Miri
,
G.
Onishchukov
,
D. N.
Christodoulides
, and
U.
Peschel
, “
Parity–time synthetic photonic lattices
,”
Nature
488
,
167
171
(
2012
).
15.
B.
Peng
,
S. K.
Özdemir
,
F.
Lei
,
F.
Monifi
,
M.
Gianfreda
,
G. L.
Long
,
S.
Fan
,
F.
Nori
,
C. M.
Bender
, and
L.
Yang
, “
Parity–time-symmetric whispering-gallery microcavities
,”
Nat. Phys.
10
,
394
398
(
2014
).
16.
B.
Peng
,
S. K.
Özdemir
,
S.
Rotter
,
H.
Yilmaz
,
M.
Liertzer
,
F.
Monifi
,
C. M.
Bender
,
F.
Nori
, and
L.
Yang
, “
Loss-induced suppression and revival of lasing
,”
Science
346
,
328
332
(
2014
).
17.
M.
Brandstetter
,
M.
Liertzer
,
C.
Deutsch
,
P.
Klang
,
J.
Schöberl
,
H. E.
Türeci
,
G.
Strasser
,
K.
Unterrainer
, and
S.
Rotter
, “
Reversing the pump dependence of a laser at an exceptional point
,”
Nat. Commun.
5
,
4034
(
2014
).
18.
L.
Feng
,
Z. J.
Wong
,
R.-M.
Ma
,
Y.
Wang
, and
X.
Zhang
, “
Single-mode laser by parity-time symmetry breaking
,”
Science
346
,
972
975
(
2014
).
19.
H.
Hodaei
,
M.-A.
Miri
,
M.
Heinrich
,
D. N.
Christodoulides
, and
M.
Khajavikhan
, “
Parity-time–symmetric microring lasers
,”
Science
346
,
975
978
(
2014
).
20.
M.
Shahmohammadi
,
M. J.
Süess
,
R.
Peretti
,
F.
Kapsalidis
,
A.
Forrer
,
M.
Beck
, and
J.
Faist
, “
Exceptional point singularities in multi-section DFB lasers
,”
New J. Phys.
24
,
053047
(
2022
).
21.
W.
Chen
,
S. K.
Özdemir
,
G.
Zhao
,
J.
Wiersig
, and
L.
Yang
, “
Exceptional points enhance sensing in an optical microcavity
,”
Nature
548
,
192
196
(
2017
).
22.
H.
Hodaei
,
A. U.
Hassan
,
S.
Wittek
,
H.
Garcia-Gracia
,
R.
El-Ganainy
,
D. N.
Christodoulides
, and
M.
Khajavikhan
, “
Enhanced sensitivity at higher-order exceptional points
,”
Nature
548
,
187
191
(
2017
).
23.
J.-H.
Park
,
A.
Ndao
,
W.
Cai
,
L.
Hsu
,
A.
Kodigala
,
T.
Lepetit
,
Y.-H.
Lo
, and
B.
Kanté
, “
Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing
,”
Nat. Phys.
16
,
462
468
(
2020
).
24.
A.
Pick
,
B.
Zhen
,
O. D.
Miller
,
C. W.
Hsu
,
F.
Hernandez
,
A. W.
Rodriguez
,
M.
Soljačić
, and
S. G.
Johnson
, “
General theory of spontaneous emission near exceptional points
,”
Opt. Express
25
,
12325
12348
(
2017
).
25.
L.
Ferrier
,
P.
Bouteyre
,
A.
Pick
,
S.
Cueff
,
N. H. M.
Dang
,
C.
Diederichs
,
A.
Belarouci
,
T.
Benyattou
,
J. X.
Zhao
,
R.
Su
,
J.
Xing
,
Q.
Xiong
, and
H. S.
Nguyen
, “
Unveiling the enhancement of spontaneous emission at exceptional points
,”
Phys. Rev. Lett.
129
,
083602
(
2022
).
26.
S.
Fan
and
J. D.
Joannopoulos
, “
Analysis of guided resonances in photonic crystal slabs
,”
Phys. Rev. B
65
,
235112
(
2002
).
27.
Y.
Liang
,
C.
Peng
,
K.
Sakai
,
S.
Iwahashi
, and
S.
Noda
, “
Three-dimensional coupled-wave model for square-lattice photonic crystal lasers with transverse electric polarization: A general approach
,”
Phys. Rev. B
84
,
195119
(
2011
).
28.
W.
Zhou
,
D.
Zhao
,
Y.-C.
Shuai
,
H.
Yang
,
S.
Chuwongin
,
A.
Chadha
,
J.-H.
Seo
,
K. X.
Wang
,
V.
Liu
,
Z.
Ma
, and
S.
Fan
, “
Progress in 2D photonic crystal fano resonance photonics
,”
Prog. Quantum Electron.
38
,
1
74
(
2014
).
29.
B.
Zhen
,
C. W.
Hsu
,
Y.
Igarashi
,
L.
Lu
,
I.
Kaminer
,
A.
Pick
,
S.-L.
Chua
,
J. D.
Joannopoulos
, and
M.
Soljačić
, “
Spawning rings of exceptional points out of Dirac cones
,”
Nature
525
,
354
358
(
2015
).
30.
P. M.
Kamiński
,
A.
Taghizadeh
,
O.
Breinbjerg
,
J.
Mørk
, and
S.
Arslanagić
, “
Control of exceptional points in photonic crystal slabs
,”
Opt. Lett.
42
,
2866
(
2017
).
31.
H.
Zhou
,
C.
Peng
,
Y.
Yoon
,
C. W.
Hsu
,
K. A.
Nelson
,
L.
Fu
,
J. D.
Joannopoulos
,
M.
Soljačić
, and
B.
Zhen
, “
Observation of bulk fermi arc and polarization half charge from paired exceptional points
,”
Science
359
,
1009
1012
(
2018
).
32.
D. A.
Bykov
and
L. L.
Doskolovich
, “
Cross-polarization mode coupling and exceptional points in photonic crystal slabs
,”
Phys. Rev. A
97
,
013846
(
2018
).
33.
S.-G.
Lee
and
R.
Magnusson
, “
Band flips and bound-state transitions in leaky-mode photonic lattices
,”
Phys. Rev. B
99
,
045304
(
2019
).
34.
L.
Lu
,
Q.
Le-Van
,
L.
Ferrier
,
E.
Drouard
,
C.
Seassal
, and
H. S.
Nguyen
, “
Engineering a light matter strong coupling regime in perovskite-based plasmonic metasurface: Quasi-bound state in the continuum and exceptional points
,”
Photonics Res.
8
,
A91
A100
(
2020
).
35.
T.
Wu
,
W.
Zhang
,
H.
Zhang
,
S.
Hou
,
G.
Chen
,
R.
Liu
,
C.
Lu
,
J.
Li
,
R.
Wang
,
P.
Duan
,
J.
Li
,
B.
Wang
,
L.
Shi
,
J.
Zi
, and
X.
Zhang
, “
Vector exceptional points with strong superchiral fields
,”
Phys. Rev. Lett.
124
,
083901
(
2020
).
36.
M. W.
McCutcheon
,
G. W.
Rieger
,
I. W.
Cheung
,
J. F.
Young
,
D.
Dalacu
,
S.
Frédérick
,
P. J.
Poole
,
G. C.
Aers
, and
R. L.
Williams
, “
Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities
,”
Appl. Phys. Lett.
87
,
221110
(
2005
).
37.
M.
Galli
,
S. L.
Portalupi
,
M.
Belotti
,
L. C.
Andreani
,
L.
O'Faolain
, and
T. F.
Krauss
, “
Light scattering and fano resonances in high-q photonic crystal nanocavities
,”
Appl. Phys. Lett.
94
,
071101
(
2009
).
38.
E. C.
Regan
,
Y.
Igarashi
,
B.
Zhen
,
I.
Kaminer
,
C. W.
Hsu
,
Y.
Shen
,
J. D.
Joannopoulos
, and
M.
Soljačić
, “
Direct imaging of isofrequency contours in photonic structures
,”
Sci. Adv.
2
,
e1601591
(
2016
).
39.
Y.
Nazirizadeh
,
U.
Lemmer
, and
M.
Gerken
, “
Experimental quality factor determination of guided-mode resonances in photonic crystal slabs
,”
Appl. Phys. Lett.
93
,
261110
(
2008
).
40.
Y.
Nazirizadeh
,
J. G.
Müller
,
U.
Geyer
,
D.
Schelle
,
E.-B.
Kley
,
A.
Tünnermann
,
U.
Lemmer
, and
M.
Gerken
, “
Optical characterization of photonic crystal slabs using orthogonally oriented polarization filters
,”
Opt. Express
16
,
7153
7160
(
2008
).
41.
H.
Lüder
,
M.
Paulsen
, and
M.
Gerken
, “
Photonic crystal slab between orthogonal polarizers: Details on the guided mode resonance wavelength
,”
Opt. Quantum Electron.
52
,
180
(
2020
).
42.
P. B.
Deotare
,
M. W.
McCutcheon
,
I. W.
Frank
,
M.
Khan
, and
M.
Lončar
, “
High quality factor photonic crystal nanobeam cavities
,”
Appl. Phys. Lett.
94
,
121106
(
2009
).
43.
R.-M.
Ma
,
H.-Y.
Luan
,
Z.-W.
Zhao
,
W.-Z.
Mao
,
S.-L.
Wang
,
Y.-H.
Ouyang
, and
Z.-K.
Shao
, “
Twisted lattice nanocavity with theoretical quality factor exceeding 200 billion
,”
Fundam. Res.
3
,
537
543
(
2023
).
44.
D.
Bajoni
,
D.
Gerace
,
M.
Galli
,
J.
Bloch
,
R.
Braive
,
I.
Sagnes
,
A.
Miard
,
A.
Lemaître
,
M.
Patrini
, and
L. C.
Andreani
, “
Exciton polaritons in two-dimensional photonic crystals
,”
Phys. Rev. B
80
,
201308
(
2009
).
45.
N. H. M.
Dang
,
S.
Zanotti
,
E.
Drouard
,
C.
Chevalier
,
G.
Trippé-Allard
,
M.
Amara
,
E.
Deleporte
,
V.
Ardizzone
,
D.
Sanvitto
,
L. C.
Andreani
,
C.
Seassal
,
D.
Gerace
, and
H. S.
Nguyen
, “
Realization of polaritonic topological charge at room temperature using polariton bound states in the continuum from perovskite metasurface
,”
Adv. Opt. Mater.
10
,
2102386
(
2022
).
46.
G.
Capraro
,
M.
Lipkin
,
M.
Möller
,
J.
Bolten
, and
M. C.
Lemme
, “
Phase mask pinholes as spatial filters for laser interference lithography
,”
Adv. Photonics Res.
4
,
2300225
(
2023
).
47.
ThorLab
. “
Bandpass filter tutorial.

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