We report on the performance and inherent artifacts of k-space optical microscopy for the study of periodic arrays of nanoparticles under the various illumination configurations available on an inverted optical microscope. We focus on the origin of these artifacts and the ways to overcome or even benefit from them. In particular, a recently reported artifact, called the “condenser effect,” is demonstrated here in a new way. The consequences of this artifact (which is due to spurious reflections in the objective) on Fourier-space imaging and spectroscopic measurements are analyzed in detail. The advantages of using k-space optical microscopy to determine the optical band structure of plasmonic arrays and to perform surface plasmon resonance experiments are demonstrated. Potential applications of k-space imaging for the accurate lateral and axial positioning of the sample in optical microscopy are investigated.
References
1.
M. A.
Lieb
, J. M.
Zavislan
, and L.
Novotny
, “Single-molecule orientations determined by direct emission pattern imaging
,” J. Opt. Soc. Am. B
21
, 1210
–1215
(2004
).2.
J. A.
Kurvits
, M.
Jiang
, and R.
Zia
, “Comparative analysis of imaging configurations and objectives for Fourier microscopy
,” J. Opt. Soc. Am. A
32
, 2082
–2092
(2015
).3.
R.
Biehl
and T.
Palberg
, “Real space and Fourier microscopy of colloidal suspensions confined to a parallel plate geometry
,” Rev. Sci. Instrum.
75
, 906
–914
(2004
).4.
I.
Sersic
, C.
Tuambilangana
, and A. F.
Koenderink
, “Fourier microscopy of single plasmonic scatterers
,” New J. Phys.
13
, 083019
(2011
).5.
J. F.
Galisteo-López
, M.
López-García
, A.
Blanco
, and C.
López
, “Studying light propagation in self-assembled hybrid photonic-plasmonic crystals by Fourier microscopy
,” Langmuir
28
, 9174
–9179
(2012
).6.
Y.
Fontana
, G.
Grzela
, E. P. A. M.
Bakkers
, and J. G.
Rivas
, “Mapping the directional emission of quasi-two-dimensional photonic crystals of semiconductor nanowires using Fourier microscopy
,” Phys. Rev. B
86
, 245303
(2012
).7.
G.
Lozano
, T.
Barten
, G.
Grzela
, and J. G.
Rivas
, “Directional absorption by phased arrays of plasmonic nanoantennae probed with time-reversed Fourier microscopy
,” New J. Phys.
16
, 013040
(2014
).8.
P.
Arora
and A.
Krishnan
, “Fourier plane colorimetric sensing using broadband imaging of surface plasmons and application to biosensing
,” J. Appl. Phys.
118
, 233105
(2015
).9.
F. J.
García de Abajo
, “Colloquium: Light scattering by particle and hole arrays
,” Rev. Mod. Phys.
79
, 1267
–1290
(2007
).10.
B.
Lamprecht
, G.
Schider
, R. T.
Lechner
, H.
Ditlbacher
, J. R.
Krenn
, A.
Leitner
, and F. R.
Aussenegg
, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance
,” Phys. Rev. Lett.
84
, 4721
(2000
).11.
S.
Linden
, J.
Kuhl
, and H.
Giessen
, “Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction
,” Phys. Rev. Lett.
86
, 4688
–4691
(2001
).12.
V. G.
Kravets
, F.
Schedin
, and A. N.
Grigorenko
, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles
,” Phys. Rev. Lett.
101
, 087403
(2008
).13.
B.
Auguié
and W.
Barnes
, “Collective resonances in gold nanoparticle arrays
,” Phys. Rev. Lett.
101
, 143902
(2008
).14.
B.
Auguié
and W. L.
Barnes
, “Diffractive coupling in gold nanoparticle arrays and the effect of disorder
,” Opt. Lett.
34
, 401
–403
(2009
).15.
B.
Auguié
, X. M.
Bendaña
, W. L.
Barnes
, and F. J.
García de Abajo
, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate
,” Phys. Rev. B
82
, 155447
(2010
).16.
A. G.
Nikitin
, A. V.
Kabashin
, and H.
Dallaporta
, “Plasmonic resonances in diffractive arrays of gold nanoantennas: Near and far field effects
,” Opt. Express
20
, 27941
–27952
(2012
).17.
A. G.
Nikitin
, T.
Nguyen
, and H.
Dallaporta
, “Narrow plasmon resonances in diffractive arrays of gold nanoparticles in asymmetric environment: Experimental studies
,” Appl. Phys. Lett.
102
, 221116
(2013
).18.
L.
Langguth
, D.
Punj
, J.
Wenger
, and A. F.
Koenderink
, “Plasmonic band structure controls single-molecule fluorescence
,” ACS Nano
7
, 8840
–8848
(2013
).19.
G.
Lozano
, G.
Grzela
, M. A.
Verschuuren
, M.
Ramezani
, and J. G.
Rivas
, “Tailor-made directional emission in nanoimprinted plasmonic-based light-emitting devices
,” Nanoscale
6
, 9223
–9229
(2014
).20.
L.
Langguth
, A. H.
Schokker
, K.
Guo
, and A. F.
Koenderink
, “Plasmonic phase-gradient metasurface for spontaneous emission control
,” Phys. Rev. B
92
, 205401
(2015
).21.
D. K. G.
de Boer
, M. A.
Verschuuren
, K.
Guo
, A. F.
Koenderink
, J. G.
Rivas
, and S. R.-K.
Rodriguez
, “Directional sideward emission from luminescent plasmonic nanostructures
,” Opt. Express
24
, A388
(2016
).22.
V.
Mikhailov
, G. A.
Wurtz
, J.
Elliott
, P.
Bayvel
, and A. V.
Zayats
, “Dispersing light with surface plasmon polaritonic crystals
,” Phys. Rev. Lett.
99
, 083901
(2007
).23.
H.
Gao
, J. K.
Hyun
, M. H.
Lee
, J.-C.
Yang
, L. J.
Lauhon
, and T. W.
Odom
, “Broadband plasmonic microlenses based on patches of nanoholes
,” Nano Lett.
10
, 4111
–4116
(2010
).24.
F. M.
Huang
, T. S.
Kao
, V. A.
Fedotov
, Y.
Chen
, and N. I.
Zheludev
, “Nanohole array as a lens
,” Nano Lett.
8
, 2469
–2472
(2008
).25.
F.
van Beijnum
, P. J.
van Veldhoven
, E. J.
Geluk
, M. J. A.
de Dood
, G. W t
Hooft
, and M. P.
van Exter
, “Surface plasmon lasing observed in metal hole arrays
,” Phys. Rev. Lett.
110
, 206802
(2013
).26.
A. H.
Schokker
and A. F.
Koenderink
, “Lasing at the band edges of plasmonic lattices
,” Phys. Rev. B
90
, 155452
(2014
).27.
T. W.
Ebbesen
, H. J.
Lezec
, H. F.
Ghaemi
, T.
Thio
, and P. A.
Wolff
, “Extraordinary optical transmission through sub-wavelength hole arrays
,” Nature
391
, 667
–669
(1998
).28.
T.
Thio
, H. F.
Ghaemi
, H. J.
Lezec
, P. A.
Wolff
, and T. W.
Ebbesen
, “Surface-plasmon-enhanced transmission through hole arrays in Cr films
,” J. Opt. Soc. Am. B
16
, 1743
–1748
(1999
).29.
Q.
Yu
, P.
Guan
, D.
Qin
, G.
Golden
, and P. M.
Wallace
, “Inverted size-dependence of surface-enhanced Raman scattering on gold nanohole and nanodisk arrays
,” Nano Lett.
8
, 1923
–1928
(2008
).30.
M. E.
Stewart
, C. R.
Anderton
, L. B.
Thompson
, J.
Maria
, S. K.
Gray
, J. A.
Rogers
, and R. G.
Nuzzo
, “Nanostructured plasmonic sensors
,” Chem. Rev.
108
, 494
–521
(2008
).31.
C.
Valsecchi
and A. G.
Brolo
, “Periodic metallic nanostructures as plasmonic chemical sensors
,” Langmuir
29
, 5638
–5649
(2013
).32.
M.-C.
Estevez
, M. A.
Otte
, B.
Sepulveda
, and L. M.
Lechuga
, “Trends and challenges of refractometric nanoplasmonic biosensors: A review
,” Anal. Chim. Acta
806
, 55
–73
(2014
).33.
J.
Li
, J.
Ye
, C.
Chen
, L.
Hermans
, N.
Verellen
, J.
Ryken
, H.
Jans
, W.
Van Roy
, V. V.
Moshchalkov
, L.
Lagae
, and P.
Van Dorpe
, “Biosensing using diffractively coupled plasmonic crystals: The figure of merit revisited
,” Adv. Opt. Mater.
3
, 176
–181
(2015
).34.
P.
Singh
, “SPR biosensors: Historical perspectives and current challenges
,” Sens. Actuators, B
229
, 110
–130
(2016
).35.
B.
Spackova
, P.
Wrobel
, M.
Bockova
, and J.
Homola
, “Optical biosensors based on plasmonic nanostructures: A review
,” Proc. IEEE
104
, 2380
–2408
(2016
).36.
W. L.
Barnes
, T. W.
Preist
, S. C.
Kitson
, J. R.
Sambles
, N. P. K.
Cotter
, and D. J.
Nash
, “Photonic gaps in the dispersion of surface plasmons on gratings
,” Phys. Rev. B
51
, 11164
–11167
(1995
).37.
S. C.
Kitson
, W. L.
Barnes
, and J. R.
Sambles
, “Surface-plasmon energy gaps and photoluminescence
,” Phys. Rev. B
52
, 11441
–11445
(1995
).38.
S. C.
Kitson
, W. L.
Barnes
, and J. R.
Sambles
, “Full photonic band gap for surface modes in the visible
,” Phys. Rev. Lett.
77
, 2670
–2673
(1996
).39.
E.
Devaux
, T. W.
Ebbesen
, J.-C.
Weeber
, and A.
Dereux
, “Launching and decoupling surface plasmons via micro-gratings
,” Appl. Phys. Lett.
83
, 4936
–4938
(2003
).40.
A.
Drezet
, A.
Hohenau
, A. L.
Stepanov
, H.
Ditlbacher
, B.
Steinberger
, F. R.
Aussenegg
, A.
Leitner
, and J. R.
Krenn
, “Surface plasmon polariton Mach-Zehnder interferometer and oscillation fringes
,” Plasmonics
1
, 141
–145
(2006
).41.
A.
Drezet
, D.
Koller
, A.
Hohenau
, A.
Leitner
, F. R.
Aussenegg
, and J. R.
Krenn
, “Plasmonic crystal demultiplexer and multiports
,” Nano Lett.
7
, 1697
–1700
(2007
).42.
B.
Stein
, J.-Y.
Laluet
, E.
Devaux
, C.
Genet
, and T. W.
Ebbesen
, “Surface plasmon mode steering and negative refraction
,” Phys. Rev. Lett.
105
, 266804
(2010
).43.
B.
Stein
, E.
Devaux
, C.
Genet
, and T. W.
Ebbesen
, “Self-collimation of surface plasmon beams
,” Opt. Lett.
37
, 1916
–1918
(2012
).44.
D.
Canneson
, E. L.
Moal
, S.
Cao
, X.
Quélin
, H.
Dallaporta
, G.
Dujardin
, and E.
Boer-Duchemin
, “Surface plasmon polariton beams from an electrically excited plasmonic crystal
,” Opt. Express
24
, 26186
–26200
(2016
).45.
A.
Yang
, Z.
Li
, M. P.
Knudson
, A. J.
Hryn
, W.
Wang
, K.
Aydin
, and T. W.
Odom
, “Unidirectional lasing from template-stripped two-dimensional plasmonic crystals
,” ACS Nano
9
, 11582
–11588
(2015
).46.
A.
Abbas
, M. J.
Linman
, and Q.
Cheng
, “New trends in instrumental design for surface plasmon resonance-based biosensors
,” Biosens. Bioelectron.
26
, 1815
–1824
(2011
).47.
M.
Sarkar
, M.
Besbes
, J.
Moreau
, J.-F.
Bryche
, A.
Olivéro
, G.
Barbillon
, A.-L.
Coutrot
, B.
Bartenlian
, and M.
Canva
, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a Kretschmann configuration
,” ACS Photonics
2
, 237
–245
(2015
).48.
H. A.
Atwater
and A.
Polman
, “Plasmonics for improved photovoltaic devices
,” Nat. Mater.
9
, 205
–213
(2010
).49.
D.
Dominguez
, N.
Alharbi
, M.
Alhusain
, A. A.
Bernussi
, and L. Grave de
Peralta
, “Fourier plane imaging microscopy
,” J. Appl. Phys.
116
, 103102
(2014
).50.
D. B.
Desai
, M. M. S.
Aldawsari
, B. M. H.
Alharbi
, S.
Sen
, and L.
Grave de Peralta
, “Comprehensive study of unexpected microscope condensers formed in sample arrangements commonly used in optical microscopy
,” Appl. Opt.
54
, 7781
(2015
).51.
D. B.
Desai
and L.
Grave de Peralta
, “Optical condensers formed in wet-mounting setup
,” Appl. Opt.
54
, 3580
(2015
).52.
D.
Dominguez
, M.
Alhusain
, N.
Alharbi
, A.
Bernussi
, and L. Grave
de Peralta
, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit
,” Plasmonics
10
, 1337
–1344
(2015
).53.
J.-F.
Bryche
, R.
Gillibert
, G.
Barbillon
, M.
Sarkar
, A.-L.
Coutrot
, F.
Hamouda
, A.
Aassime
, J.
Moreau
, M.
Lamy de la Chapelle
, B.
Bartenlian
, and M.
Canva
, “Density effect of gold nanodisks on the SERS intensity for a highly sensitive detection of chemical molecules
,” J. Mater. Sci.
50
, 6601
–6607
(2015
).54.
J.-F.
Bryche
, R.
Gillibert
, G.
Barbillon
, P.
Gogol
, J.
Moreau
, M.
Lamy de la Chapelle
, B.
Bartenlian
, and M.
Canva
, “Plasmonic enhancement by a continuous gold underlayer: Application to SERS sensing
,” Plasmonics
11
, 601
–608
(2016
).55.
Y.
Chu
, E.
Schonbrun
, T.
Yang
, and K. B.
Crozier
, “Experimental observation of narrow surface plasmon resonances in gold nanoparticle arrays
,” Appl. Phys. Lett.
93
, 181108
(2008
).56.
G. F.
Iriarte
, J. G.
Rodriguez-Madrid
, and F.
Calle
, “Fabrication of sub-100 nm IDT SAW devices on insulating, semiconducting and conductive substrates
,” J. Mater. Process. Technol.
212
, 707
–712
(2012
).57.
Y.
Wang
, M.
Abb
, S. A.
Boden
, J.
Aizpurua
, C. H.
de Groot
, and O. L.
Muskens
, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling
,” Nano Lett.
13
, 5647
–5653
(2013
).58.
S.
Cao
, E.
Le Moal
, F.
Bigourdan
, J.-P.
Hugonin
, J.-J.
Greffet
, A.
Drezet
, S.
Huant
, G.
Dujardin
, and E.
Boer-Duchemin
, “Revealing the spectral response of a plasmonic lens using low-energy electrons
,” Phys. Rev. B
96
, 115419
(2017
).59.
J.
Homola
, S. S.
Yee
, and G.
Gauglitz
, “Surface plasmon resonance sensors: Review
,” Sens. Actuators, B
54
, 3
–15
(1999
).60.
R. M. A.
Azzam
, “Phase shifts that accompany total internal reflection at a dielectric - dielectric interface
,” J. Opt. Soc. Am. A
21
, 1559
–1563
(2004
).61.
R. M. A.
Azzam
, “Phase shifts in frustrated total internal reflection and optical tunneling by an embedded low-index thin film
,” J. Opt. Soc. Am. A
23
, 960
–965
(2006
).62.
L.
Salomon
, F.
de Fornel
, and P. M.
Adam
, “Analysis of the near field and the far field diffracted by a metallized grating at and beyond the plasmon resonance
,” J. Opt. Soc. Am. A
16
, 2695
–2704
(1999
).63.
A.
Hohenau
, J. R.
Krenn
, F. J.
Garcia-Vidal
, S. G.
Rodrigo
, L.
Martin-Moreno
, J.
Beermann
, and S. I.
Bozhevolnyi
, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films
,” Phys. Rev. B
75
, 085104
(2007
).64.
S.
Lal
, S.
Link
, and N. J.
Halas
, “Nano-optics from sensing to waveguiding
,” Nat. Photonics
1
, 641
–648
(2007
).65.
E.
Yablonovitch
, “Inhibited spontaneous emission in solid-state physics and electronics
,” Phys. Rev. Lett.
58
, 2059
–2062
(1987
).66.
D.
Brissinger
, L.
Salomon
, and F.
De Fornel
, “Unguided plasmon-mode resonance in optically excited thin film: Exact modal description of Kretschmann-Raether experiment
,” J. Opt. Soc. Am. B
30
, 333
–337
(2013
).67.
C.
Fallet
, T.
Novikova
, M.
Foldyna
, S.
Manhas
, B.
Haj Ibrahim
, A.
De Martino
, C.
Vannuffel
, and C.
Constancias
, “Overlay measurements by Mueller polarimetry in back focal plane
,” J. Micro/Nanolithog. MEMS, MOEMS
10
, 033017
(2011
).68.
S.
Liu
, W.
Du
, X.
Chen
, H.
Jiang
, and C.
Zhang
, “Mueller matrix imaging ellipsometry for nanostructure metrology
,” Opt. Express
23
, 17316
–17329
(2015
).69.
V.
Ferreras Paz
, S.
Peterhnsel
, K.
Frenner
, and W.
Osten
, “Solving the inverse grating problem by white light interference Fourier scatterometry
,” Light Sci. Appl.
1
, e36
(2012
).70.
N.
Kumar
, P.
Petrik
, G. K. P.
Ramanandan
, O. E.
Gawhary
, S.
Roy
, S. F.
Pereira
, W. M. J.
Coene
, and H. P.
Urbach
, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry
,” Opt. Express
22
, 24678
–24688
(2014
).71.
H. F.
Talbot
, “LXXVI. Facts relating to optical science. No. IV
,” London Edinburgh Dublin Philos. Mag. J. Sci.
9
, 401
–407
(1836
).72.
L.
Rayleigh
, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith
,” London Edinburgh Dublin Philos. Mag. J. Sci.
11
, 196
–205
(1881
).73.
W.
Li
, H.
Li
, B.
Gao
, and Y.
Yu
, “Investigation on the plasmon Talbot effect of finite-sized periodic arrays of metallic nanoapertures
,” Sci. Rep.
7
, 45573
(2017
).74.
L.
Zhu
, R.
Badugu
, D.
Zhang
, R.
Wang
, E.
Descrovi
, and J. R.
Lakowicz
, “Radiative decay engineering 8: Coupled emission microscopy for lens-free high-throughput fluorescence detection
,” Anal. Biochem.
531
, 20
–36
(2017
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
