The growing need for new and reliable surface sensing methods is arousing interest in the electromagnetic excitations of ultrathin films, i.e., to generate electromagnetic field distributions that resonantly interact with the most significant quasi-particles of condensed matter. In such a context, Bloch surface waves turned out to be a valid alternative to surface plasmon polaritons to implement high-sensitivity sensors in the visible spectral range. Only in the last few years, however, has their use been extended to infrared wavelengths, which represent a powerful tool for detecting and recognizing molecular species and crystalline structures. In this work, we demonstrate, by means of high-resolution reflectivity measurements, that a one-dimensional photonic crystal can sustain Bloch surface waves in the infrared spectral range from room temperature down to 10 K. To the best of our knowledge, this is the first demonstration of infrared Bloch surface waves at cryogenic temperatures. Furthermore, by exploiting the enhancement of the surface state and the high brilliance of infrared synchrotron radiation, we demonstrate that the proposed BSW-based sensor has a sensitivity on the order of 2.9 cm-1 for each nanometer-thick ice layer grown on its surface below 150 K. In conclusion, we believe that Bloch surface wave-based sensors are a valid new class of surface mode-based sensors for applications in materials science.
The growing need for new and reliable surface sensing methods is arousing interest in the electromagnetic excitations of ultrathin films, i.e., to generate electromagnetic field distributions that resonantly interact with the most significant quasi-particles of condensed matter. In such a context, Bloch surface waves turned out to be a valid alternative to surface plasmon polaritons to implement high-sensitivity sensors in the visible spectral range. Only in the last few years, however, has their use been extended to infrared wavelengths, which represent a powerful tool for detecting and recognizing molecular species and crystalline structures. In this work, we demonstrate, by means of high-resolution reflectivity measurements, that a one-dimensional photonic crystal can sustain Bloch surface waves in the infrared spectral range from room temperature down to 10 K. To the best of our knowledge, this is the first demonstration of infrared Bloch surface waves at cryogenic temperatures. Furthermore, by exploiting the enhancement of the surface state and the high brilliance of infrared synchrotron radiation, we demonstrate that the proposed BSW-based sensor has a sensitivity on the order of 2.9 cm-1 for each nanometer-thick ice layer grown on its surface below 150 K. In conclusion, we believe that Bloch surface wave-based sensors are a valid new class of surface mode-based sensors for applications in materials science.
Infrared (IR) spectroscopy is a powerful
tool to investigate the
properties of most significant quasi-particles in condensed matter
by detecting their spectral “fingerprints”, i.e., their
vibrational absorption lines.[1,2] As is well known, the
relevant range of wavelengths is from 2.0 to 25 μm, i.e., the
mid-IR region (MIR).In the present work, we intend to demonstrate
the potential of
a novel surface-enhanced IR spectroscopy scheme for application in
low-dimensionality condensed matter systems at cryogenic temperatures,
down to 10 K. The proposed scheme exploits the strong field localization
provided by Bloch surface waves (BSWs) sustained at the interface
between a finite one-dimensional photonic crystal (1D-PC) and vacuum.
From this perspective, many applications can be expected for BSWs,
like the extension of our precedent work on low-dimensional topological
insulators[3] and the application to the
study of other features of low-dimensional systems, such as phonon
overtones and combination bands in hybrid perovskites,[4] Dirac-like dispersion of electronic states in doped graphene[5] and spectroscopy under extreme conditions as
in planetary atmospheres.[6]In the
last few decades, several strategies to improve the MIR
capability to sense at the micro/nanoscale were developed and applied
to a large number of practical issues, ranging from medical diagnostics
to the detection of environmental pollution.[2,7,8] Several methods make use of the strong electromagnetic
field confinement occurring at the interface between different materials[9,10] to detect molecular species in the proximity of structural boundaries.[11,12] A large number of MIR sensors were actually fabricated, based for
example on surface phonon polariton annihilation/creation in semiconductors,[13−15] non-neutral graphene,[16,17] and metals.[18−20]Among such classes of novel sensors, dielectric heterostructures
housing a 1D-PC have been recently investigated.[2,21] In
a 1D-PC, the refractive index modulation along the stacking direction
defines an optical lattice and, accordingly, the dispersion of light
propagating inside the 1D-PC[22] is strongly
distorted, as demonstrated by the appearance of a photonic band (PB)
structure. PC and their photonic band (PB) have been a very intensively
investigated research field.[23−25] Less attention was paid to the
excitation of BSWs at the surface of a finite PC, particularly to
the electromagnetic modes localized at the boundary between a truncated
1D-PC and an external homogeneous medium.[22] Similar to surface plasmon polaritons, BSWs are characterized by
an electric field envelope, which decays exponentially both inside
the 1D-PC and the external medium.[22,26,27] BSW-based sensors working in the visible range showed
enhanced resolution for the detection of molecular species in a wide
range of applications.[28−30] Surprisingly, the interest toward BSWs in the MIR
region has increased only recently,[2,21] driven by
the need for overcoming the sensitivity shortcomings of MIR spectroscopy,
when applied to very thin films, and on the track of previously proposed
methods, such as photoexpansion[31] and grazing-angle
spectroscopy with polarized IR beams.[3,32−35] The 1D-PC geometry offers options to design and optimize for specific
applications.[36] The PB of a 1D-PC has been
demonstrated to be robust and tolerant to a significant amount of
deviation from the designed structure.[37−39] A threshold level of
disorder in 1D-PCs has been found in ref (40): σth ≈
(Δω/3ωc)1/2, where σth is the width of
a Gaussian distribution of the optical lengths of the PC period and
Δω and ωc are the photonic band gap width
and photonic band gap central frequency, respectively. Below the threshold,
the photonic band gap is stable in the presence of disorder.[40] As far as we know, the robustness of surface-enhanced
1D-PC sensing schemes at extreme temperatures needed for the investigation
of MIR excitations in low-dimensional systems has not been tested
so far. This study is then the first mandatory step for the application
of BSWs to such a field, an important test for the 1D-PC fabrication
technology, and the possibility to integrate the scheme with the peculiar
properties of the IR radiation emerging from the AILES beamline of
the SOLEIL synchrotron.[41]In addition
to that, but not less important, this work demonstrates
experimentally the BSW molecular sensing capability to detect molecular
fingerprints at cryogenic temperatures, using water vapor as a molecular
species, which condensates into a thin ice layer onto the 1D-PC surface
even under moderately high vacuum conditions. We demonstrate that
BSWs are sensitive to molecular layers of a few nanometers added on
the top surface, with a phenomenological behavior that can be directly
attributed to the water vapor–ice sublimation cycle.
Materials and Methods
1D-PC Materials and Design
The materials of choice
to fabricate the 1D-PC are CaF2 and ZnS; both show high
transparency and a convenient refractive index mismatch in the MIR
spectral range. Based on the literature values of the respective refractive
indices,[42,43] the geometry of the 1D-PC was designed and
tuned to the MIR wavelength range by means of several rounds of numerical
simulations (see Section S1 of the Supporting
Information (SI)). The designed layer structure was CaF2(substrate)/[ZnS(200 nm)/CaF2(2300 nm)]2/ZnS(50
nm)/vacuum, which can sustain BSWs with a suitable dispersion, which,
in agreement with the literature,[40] is
stable toward the random inhomogeneities of the thicknesses of the
layers arising from fabrication uncertainty (see Section S1 and Figure S.2 of the SI).1D-PCs were fabricated
by thermal evaporation in a high-vacuum chamber, with a limiting pressure
of 5 × 10–7 Torr, equipped with two evaporation
sources.[44] CaF2 and ZnS layers
could therefore be deposited without breaking the vacuum from granulated
materials (UMICORE, purity 99.99%) using molybdenum boats. They were
deposited on CaF2-truncated prisms, purchased from Korth
Kristalle, with a 55° base angle and designed to operate in a
Kretschmann–Raether (KR) configuration under total internal
reflection (TIR) conditions[45] (see Figure a). We preliminarily
deposited a 20 nm thick CaF2 layer on the CaF2 substrates to improve adhesion and avoid delamination of the first
ZnS layer. The main issue in the deposition of multilayers is strain
accumulation that increases with the layer thickness and may cause
undesirable buckling and bending.[46,47]
Figure 1
(a) Sketch
of the Kretschmann–Raether configuration. The
prism is quoted and the radiation wavevector has been decomposed in its parallel, β, and perpendicular, , components. (b) Scanning electron
microscopy (SEM) image of the focused ion beam (FIB) milled cross-section
of the deposited 1D-PC and a sketch of the transverse geometry with
measured layer thicknesses. (c) R(θ,λ)
reflectance map according to the transfer-matrix method (TMM) calculation
for σ polarization. The black and red lines are the photonic
band edges (BEs), calculated for the infinitely extended 1D-PC. The
surface waves (SWs) and the band-edge (BE) modes appear as dark reflectance
lines. In the insets, we plot the square modulus of the electric fields
of the modes, superimposed on the 1D-PC refractive index distribution.
The external medium is vacuum.
(a) Sketch
of the Kretschmann–Raether configuration. The
prism is quoted and the radiation wavevector has been decomposed in its parallel, β, and perpendicular, , components. (b) Scanning electron
microscopy (SEM) image of the focused ion beam (FIB) milled cross-section
of the deposited 1D-PC and a sketch of the transverse geometry with
measured layer thicknesses. (c) R(θ,λ)
reflectance map according to the transfer-matrix method (TMM) calculation
for σ polarization. The black and red lines are the photonic
band edges (BEs), calculated for the infinitely extended 1D-PC. The
surface waves (SWs) and the band-edge (BE) modes appear as dark reflectance
lines. In the insets, we plot the square modulus of the electric fields
of the modes, superimposed on the 1D-PC refractive index distribution.
The external medium is vacuum.Preliminary test samples and the final 1D-PC were
characterized
by dual-beam focused ion beam (FIB) milling cross-sectional analysis,
scanning electron microscopy (SEM), and near-normal incidence reflectance.
SEM inspection of CaF2/ZnS/CaF2 test structures
deposited on CaF2 substrates appeared undamaged even after
immersion in liquids and after strong ultrasound treatments.[21]The SEM image of the FIB cross-section
of a 1D-PC deposited on
the prism is shown in Figure b (for details see Section S2 in
the SI). The first CaF2 (∼20 nm) adhesion layer
is not visible in the image, while one can clearly distinguish the
1D-PC structure composed of the two ZnS/CaF2 binary units
(dark yellow and green in the lateral sketch, respectively) and the
final 35 nm thick ZnS defect layer (dark yellow). From the image,
we retrieved the effective 1D-PC geometry Prism/ZnS(1)/CaF2(1)/ZnS(2)/CaF2(2)/ZnS/vacuum with measured thicknesses of 0.200(±0.015)/2.50(±0.07)/0.205(±0.025)/2.45(±0.10)/0.035(±0.020)
μm, respectively. The 1D-PC surface profile, according to atomic
force microscopy, had a root mean square (rms) roughness Rq of ∼ 32 nm (see Section S3 of the SI). The periodic 1D-PC defines the photonic band structure
of the multilayer, whereas the additional top defect layer is used
to fine-tune the BSW dispersion. Moreover, the temperature-dependency
of the material refractive indices is considered through the temperature-dependent
Sellmeier model reported in refs (42) and (43) for CaF2 and ZnS, respectively. In particular,
we evaluated that the refractive indices at a wavelength of 2.1 μm
(ν = 4.76 × 103 cm–1) and
at room temperature (298 K) are 2.26 for ZnS[43] and 1.42 for CaF2.[42] However,
we found (see Section S4 of the SI) that
the refractive indices of the ZnS and CaF2 layers of the
1D-PC are reduced due to the materials’ porosity. The effect
of the porosity was studied by fitting the stack reflectance measured
at near-normal incidence (about 8°) with unpolarized light. Making
use of a Maxwell Garnett model,[48] we evaluated
the void/full ratio of the materials, which was approximately 1–2%
for ZnS and 18 ± 2 and 21 ± 3% for CaF2(1) and CaF2(2) layers, respectively. Such porosity
values correspond to a refractive index of 2.25 for the ZnS layers
and 1.348 and 1.335, respectively, for the CaF2(1) and CaF2(2) layers.Based on the real
1D-PC geometry and materials’ optical
properties, the room temperature numerical simulation of the reflectance R(θ,λ) was carried out by a proprietary transfer-matrix
method (TMM) MATLAB code.[26] The numerical
simulations refer to the Kretschmann–Raether configuration
shown in Figure a,
which was used experimentally to excite the BSW. As is known,[45] BSWs can be excited only under TIR conditions
for the prism/vacuum interface.[22] In the
following, β and are the parallel and perpendicular components of the incidence
wavevector , with respect to the 1D-PC
interfaces, and σ and π refer to the transverse electric
and transverse magnetic polarizations, respectively.The proposed
1D-PC sustains both σ and π BSW modes;[21] however, in the π-polarized BSW case,
the field enhancement is small due to its weak localization. We will
therefore focus on the σ-polarized BSWs, both experimentally
and theoretically (details of the π case are given in Section S6 of the SI). In Figure c, we show the calculated 1D-PC reflectance R(θ,λ), in the MIR wavelengths range (1 μm
< λ < 8 μm) and in a wide range of incidence angles
θ inside the prism, including the TIR edge (40° < θ
< 80°). Moreover, in the same (θ,λ) plane, we
plot, with red and black solid lines, the PB edges for σ-polarization,
as calculated by means of an iterative plane wave eigensolver method.[23,49] In such a calculation, an infinite 1D-PC was assumed, with CaF2 and ZnS layers’ thickness corresponding to the mean
of the values found by SEM for the fabricated layers. The lines plotted
with the same color are the band edges of the same nth order band, where the propagation inside the 1D-PC is permitted.Beyond the TIR angle, the dispersion curves (Figure c) relate to different σ-polarized
modes propagating along the 1D-PC structure, whose nature is identified
by the insets showing the plots of the square modulus of the electric
field together with the refractive-index profile n(x). From the simulation, we can see that the 1D-PC
can sustain BSWs in both the first (low frequencies surface waves,
SWLF) and in the second (high frequencies surface waves,
SWHF) photonic band gap. In particular, the SWLF modes can be excited at wavelengths lower than 6 μm and in
the angular range of 47° < θ < 69°, with an
intensity profile that decays exponentially from the interface with
vacuum. Further, we estimate the field intensity enhancement, fσ, for the BSW, through the ratiowhere |EBSW|σ2 and |E0|σ2 are the
maximum field intensities under TIR
excitation at resonant angle θBSW, for either the
1D-PC-coated prism or the bare prism, respectively. The maximum enhancement fσ ∼ 27 is obtained at λ =
3.0 μm for θBSW = 60.4°. Moreover, the
1D-PC also admits band-edge modes which are labeled with acronyms
BE1, and BE2; for such modes, the field is localized inside the 1D-PC;
indeed, BE1, in the 1D-PC first permitted PB show their maximum intensity
inside the ZnS(2) layer, whereas the BE2 is pinned at the
CaF2(1) layer.
Experimental Method
In Figure , we sketch
the apparatus used to experimentally
characterize the deposited 1D-PC. We perform high-resolution reflectivity
measurements using the SOLEIL synchrotron source, on the AILES beamline.
A schematic sketch is shown in Figure a.[41]
Figure 2
(a) Sketch of the AILES
beamline at SOLEIL synchrotron which exploits
a series of mirrors (M) to handle the radiation. With permission from
ref (41), we reproduced
a portion of Figure 4. Copyright 2006 Elsevier B.V. (b) Sketch of
the experimental apparatus. Infrared synchrotron source (IR-SS), plane
mirror (PM), focusing mirror (FM), iris (I), compartments window (CW),
Kretschmann–Raether (KR) configuration, polarizer (P), cryoscopic
compartment (CC), and bolometer (B).
(a) Sketch of the AILES
beamline at SOLEIL synchrotron which exploits
a series of mirrors (M) to handle the radiation. With permission from
ref (41), we reproduced
a portion of Figure 4. Copyright 2006 Elsevier B.V. (b) Sketch of
the experimental apparatus. Infrared synchrotron source (IR-SS), plane
mirror (PM), focusing mirror (FM), iris (I), compartments window (CW),
Kretschmann–Raether (KR) configuration, polarizer (P), cryoscopic
compartment (CC), and bolometer (B).The measurements have been performed using a Bruker
IFS 125 HR
interferometer equipped with a KBr beamsplitter and liquid He-cooled
detectors (Figure a, S). In the present experiments, we used a cryoscopic chamber (CC)
allowing measurements of reflectivity at variable angles, θ
(grazing-angle reflectivity setup[50]), and
temperatures, T. The prism, with or without the 1D-PC,
was mounted on the closed cycle cryogenerator whose cold finger is
thermally connected to the custom-made sample holder. The temperature
cycles are created and controlled by a custom LabView code. Moreover,
the position of the sample holder can be finely adjusted to compensate
for any contraction at low temperatures.The sample compartment
of the interferometer is used here to host
the optics, which redirects the radiation to the cryoscopic chamber.
In Figure b, we sketch
the grazing-incidence optical setup assembled to excite the BSW.[50] The synchrotron IR radiation was collimated
and focused by means of a series of planar (PM) and focusing (FM)
gold mirrors. The spot size was reduced by means of an iris (∼1
mm, I), and the IR radiation was collected and collimated by means
of a mirror system specularly mounted with respect to the input mirrors.
On the path, a σ-polarizer (P) was inserted. The interferometer
and the cryoscopic compartments are connected by an input and an output
chamber window (CW) transparent to IR and visible radiations. The
probe laser beam can therefore tunnel through the 1D-PC and efficiently
excite the BSWs at the free 1D-PC/vacuum interface, as sketched in Figure a. The temperature
in the cryostat compartment was measured by means of a thermocouple
located about 2 cm above the sample, by ensuring a temperature measurement
uncertainty of ±2 K.Finally, although the ultimate vacuum
in the interferometer can
be reduced to 10–4 mbar, the sample compartment,
of dimensions 262 mm × 184 mm × 162 mm, can be improved
to 10–6 mbar, to reduce absorption due to residual
gases. This pumping has been carried out by means of a set of mechanical
and turbo-molecular pumps.[50]
Results
and Discussion
The spectral intensity I(ν,T) of the σ-polarized radiation
reflected by a sample was collected
at the incidence angle θ0 = 65.0 ± 0.9°
and at temperature T, with a spectral resolution
of 0.25 cm–1. It is noteworthy that the incidence
angle could be affected by a systematic error too, due to the difficulty
in aligning the sample inside the chamber, which was estimated to
be less than 1°. In Figure a, we show the I(ν,T) spectra for either a 1D-PC-coated CaF2 prism (solid
lines) or a reference bare CaF2 prism (dashed lines), obtained
at three different temperatures. For both types of samples, the following
thermal cycle procedure was adopted: starting from 300 K, the temperature
was gradually reduced to 100 K and suddenly increased up to 250 K,
to ensure maximum evacuation of the chamber and, eventually, to forewarn
for any alignment issue induced by uncompensated thermal contraction/expansion.
Once completed this preliminary procedure, the temperature was lowered
to 10 K and the reflectance was measured, in the order, at 10, 50,
100, 150, 200, 250, and 300 K. The experimental session has a duration
of 3 h for each polarization.
Figure 3
(a) Reflected intensity spectra I(ν,T) obtained at three different temperatures:
(dash) bare
CaF2 prism (reference), (solid) 1D-PC-coated CaF2 prism. (b) R(ν,T) reflectance
spectra in the BSW excitation region: (dot) experiment, (solid) fit
with the TMM simulation. Except for the case at T = 300 K, the curves are vertically shifted for convenience. Absorbance
spectra in the OH-stretch region, for bare CaF2 prism (c)
and of the 1D-PC-coated CaF2 prism (d).
(a) Reflected intensity spectra I(ν,T) obtained at three different temperatures:
(dash) bare
CaF2 prism (reference), (solid) 1D-PC-coated CaF2 prism. (b) R(ν,T) reflectance
spectra in the BSW excitation region: (dot) experiment, (solid) fit
with the TMM simulation. Except for the case at T = 300 K, the curves are vertically shifted for convenience. Absorbance
spectra in the OH-stretch region, for bare CaF2 prism (c)
and of the 1D-PC-coated CaF2 prism (d).In Figure a, we
show with light gray bands two spectral regions of our interest, on
which we shall focus the data analysis. In the first region, around
4.7 × 103 cm–1, the excitation of
BSWs is witnessed by the appearance of dips in the reflectance measured
for the 1D-PC-coated prism. In the second region, around 3.25 ×
103 cm–1, we observed absorption dips
related to the OH-stretching band.Figure b shows
details of the region around 4.7 × 103 cm–1, in which the experimental reflectance curves R(ν,T) (dots) obtained at different temperatures
are plotted with an arbitrary offset with respect to the 300 K measurement
for the sake of clarity. The R(ν,T) curves were obtained by normalizing the experimental data to the
reference curves obtained with the bare prism. The solid lines are
the fits obtained with the TMM simulations. The results show that
the 1D-PC continues sustaining BSWs down to 10 K without any damage
to the dielectric stack, such as delamination, demonstrating their
appeal for applications in extreme environmental conditions, such
as space optics and spectroscopy, for example, absorption spectroscopy
in planetary atmospheres.[6] The observed
frequency shift of the resonant dip with temperature indicates a perturbation
of the refractive index of either the external medium or the 1D-PC
itself, giving rise to a change in the BSW dispersion. We ascribe
the shift primarily to the condensation of residual water vapor in
the vacuum chamber to a thin ice layer at the surface of the 1D-PC
at low temperatures and secondarily to the presence of residual condensed
water inside the 1D-PC pores at higher temperatures. During the thermal
cycle, the resonant frequency (νBSW) gradually shifts
as T increases from 10 K. However, an abrupt discontinuity
is observed above 200 K since ice sublimation takes place and retrieves
the real part of the refractive index on the top of the 1D-PC to that
of vacuum.The continuous growth of the thin ice film all along
the experiments
is confirmed by the analysis of the reflectance in the OH-stretching
spectral region around 3.25 × 103 cm–1. The increasing thickness of the water ice should not be surprising.
As often happens in cryogenic measurements, albeit under high vacuum
conditions, the presence of water is unavoidable. In this particular
case, the main parameter which affects the ice sedimentation is the
time (about 2 h) in which the sample stands below the ice sublimation
temperature. In Figure c,d, we plot the absorbance of either the bare or the 1D-PC-coated
prism using the respective spectra acquired at 300 K as a reference
assuming that the samples’ surfaces are dry at 300 K. The presence
of an OH-stretching absorption peak is evident below the ice sublimation
temperature at the chamber operation pressure Ts ∼ 160 K;[51] above Ts, the A curves are flat as
confirmed by the curve at 200 K. The absorbance A is larger for the bare prism than the 1D-PC-coated one, approximately
by a factor 7, due to the interference of the multiple reflections
of the incidence wave at the multilayered structure interfaces (Bragg
condition), which gives rise to a lower value of the field intensity
at the 1D-PC top surface at 3.25 × 103 cm–1 (λ = 3.08 μm), as confirmed by the TMM calculations
reported in Section S5 of the SI.From the data shown in Figure d, we could evaluate the thickness of the ice film.
Assuming that all facets of the prism are coated with an ice film
of the same thickness, using the literature values for the temperature-dependent
absorption coefficient of amorphous ice at the most intense OH band,[52] and simulating by the TMM the reflectance of
the 1D-PC-coated prism, we evaluated that the thickness of the ice
layer was about 5.1, 8.3, 15.5, and 21.6 nm, for the consecutive measurements
taken at 10, 50, 100, and 150 K, respectively.The values of
the ice layer thickness were used to calculate the
fitting curves by the TMM, as shown in Figure b. As for the CaF2 and ZnS, the
ice layer has been modeled through its refractive index dispersion
between 1.1 and 2.6 μm at each temperature.[52] For completeness, we considered the possibility that the
material thicknesses could change due to the thermal dilatation/contraction,
but the coefficient of thermal expansion of the materials is very
low for temperatures lower than the ice sublimation temperature; therefore,
we considered it to be negligible. Moreover, to best fit the amplitude
of the experimental curves with the simulated ones, we tuned the imaginary
part of the CaF2 refractive index by retrieving a value
almost constant in temperature in the order of 5 × 10–5. The agreement between the simulated curves and the experimental
data until 150 K is very good and shows that the perturbation of the
surface refractive index due to the thin ice layer can be efficiently
detected by measuring the shift of the BSW resonance at νBSW. Such a result assesses the sensing performances of the
BSW mode sustained by the 1D-PC. In Figure a, we plot the experimental
νBSW values with their uncertainty (δνBSW) as a function of the estimated ice film thickness tice. Data are aligned along a straight line,
whose slope is the experimental sensitivity of the BSWs toward the
ice film thickness . Data are in good agreement with
the TMM
simulation shown as a solid line in Figure b, which predicts a linear dependency with
a slope of −2.60 ± 0.05 cm–1/nm, as
shown in Figure a.
Finally, we evaluated the sensor limit of detection as the water thickness
variation (Δtmin) for which the
observed BSW resonance frequency variation (ΔνBSW) is 3 times δνBSW, i.e., Δtmin = 3δνBSW/Sexp = 1.9 ± 0.3 nm. For the sake of completeness,
at νBSW = 4.76 × 103 cm–1 (λBSW = 2.1 μm) and θBSW = θ0, we calculated that the field enhancement
is equal to fσ ∼ 9 and the
penetration length of the electric field in a vacuum is about lλ0σ = (2k)−1 = 230 nm.
Figure 4
(a) Plot of the BSW peak frequency, νBSW, versus
the ice layer thickness for the experimental (black dots) and the
simulated (red dots) cases. (b) Region of the (β̃,ω̃)
plane where the experimental BSW modes are localized: (dark gray)
calculated BSW dispersion (SWLF), (light gray) dispersion
of the propagating electromagnetic waves in the prism at the fixed
incidence angle θ, (dot) BSW experimental dispersion data with
error bars, (red dashed) dispersion when the CaF2(2) porosity is changed in its interval of confidence.
(a) Plot of the BSW peak frequency, νBSW, versus
the ice layer thickness for the experimental (black dots) and the
simulated (red dots) cases. (b) Region of the (β̃,ω̃)
plane where the experimental BSW modes are localized: (dark gray)
calculated BSW dispersion (SWLF), (light gray) dispersion
of the propagating electromagnetic waves in the prism at the fixed
incidence angle θ, (dot) BSW experimental dispersion data with
error bars, (red dashed) dispersion when the CaF2(2) porosity is changed in its interval of confidence.The I(ν, T) curves
recorded
at temperatures larger than 150 K still show a BSW resonance that,
upon complete sublimation of the ice layer, shifted back to larger
frequencies (measurement at T = 250 K). We observe
extra shifts at 200 and 300 K, in opposite directions, that we cannot
explain in the framework of the same model. Above the sublimation
temperature, the irregular displacement of the Bloch surface wave
spectral position can be due to the possible presence of water or
other impurities in the voids that characterize the 1D-PC. Although
at low temperatures the behavior of the water ice can be easily predicted,
it is not the same for water confined into micro-nanoporosity.[53] Therefore, we cannot formulate a hypothesis
for describing what happens at temperatures higher than the ice sublimation
temperature.Finally, a detail of the 1D-PC PB structure of
the nominal multilayer
stack introduced above is mapped in the (β̃,ω̃)
plane for σ-polarization in Figure b, where β̃ = βΛ/2π
is the normalized parallel component of the wavevector, ω̃
= ωΛ/2πc is the normalized angular frequency, and
Λ = 2.54 μm is the 1D-PC periodic unit thickness. A portion
of a permitted band for light propagation is filled in gray, while
the white filled area corresponds to the first photonic band gap for
the electromagnetic radiation. The calculated dispersion of the BSW
modes (SWLF) is plotted in dark gray solid line and, for
the sake of clarity, we plot a grid of dotted line where each of them
corresponds to a fixed incidence angle θ, i.e., the dispersion
of the propagating electromagnetic waves in the prism. In the same
plane, we plotted the BSW dispersion retrieved from the experiments
(colored point labeled with the measurement temperature), with its
experimental error bar due to the incidence angle uncertainty. The
1D-PC optical properties are very sensitive to the material porosity
variation and, in particular, to the CaF2(2) layer porosity, which is evaluated in the order of 21%, as reported
above. To take into account the uncertainty of the material porosity,
in the same graph, we plot the BSW mode dispersion calculated when
the CaF2(2) porosity is ranging between 18 and
24% (red dashed-dotted lines). Despite the uncertainty of the material
porosity, BSWs are robust, and their observation is well reproduced
by our model.
Conclusions
In this work, we have
successfully demonstrated
the use of sensors
based on BSWs in the mid-IR with a scheme based on the detection of
both the real and the imaginary part variations of the materials’
refractive index placed on the top surface of the 1D-PC.For
the first time to our knowledge, it has been demonstrated the
possibility to sustain BSWs on a 1D-PC made of CaF2 and
ZnS layers, in the mid-IR spectral range, down to low temperatures.
Although the measurements have been performed at pressures on the
order of 10–6 mbar, we observed the formation of
a water ice layer, whose thickness does not exceed 30 nm. We have
exploited this effect to demonstrate that the spectral dip associated
with the BSWs is able to detect the deposition of a nanometric layer
on top of the 1D-PC, through variations of both the real and imaginary
parts of the refractive index, which gives rise, respectively, to
a shift of the spectral position and to variations of the depth/width
of the dip. Ultimately, we estimated that the proposed BSW-based sensor
has a sensitivity on the order of 2.9 cm–1 for each
nanometer of icy water added to its top surface for a temperature
lower than 150 K.
Authors: Daniel Rodrigo; Odeta Limaj; Davide Janner; Dordaneh Etezadi; F Javier García de Abajo; Valerio Pruneri; Hatice Altug Journal: Science Date: 2015-07-10 Impact factor: 47.728
Authors: Aleksei Anopchenko; Agostino Occhicone; Riccardo Rizzo; Alberto Sinibaldi; Giovanni Figliozzi; Norbert Danz; Peter Munzert; Francesco Michelotti Journal: Opt Express Date: 2016-04-04 Impact factor: 3.894
Authors: Daniel Rodrigo; Andreas Tittl; Odeta Limaj; F Javier García de Abajo; Valerio Pruneri; Hatice Altug Journal: Light Sci Appl Date: 2017-06-02 Impact factor: 17.782