Sculpting Narrowband Fano Resonances Inherent in the Large-area Mid-infrared Photonic Crystal Microresonators for Spectroscopic Imaging

Fourier transform infrared (FT-IR) imaging spectrometers are almost universally used to record microspectroscopic imaging data in the mid-infrared (mid-IR) spectral region. While the commercial standard, interferometry necessitates collection of large spectral regions, requires a large data handling overhead for microscopic imaging and is slow. Here we demonstrate an approach for mid-IR spectroscopic imaging at selected discrete wavelengths using narrowband resonant filtering of a broadband thermal source, enabled by high-performance guided-mode Fano resonances in one-layer, large-area mid-IR photonic crystals on a glass substrate. The microresonant devices enable discrete frequency IR (DF-IR), in which a limited number of wavelengths that are of interest are recorded using a mechanically robust instrument. This considerably simplifies instrumentation as well as overhead of data acquisition, storage and analysis for large format imaging with array detectors. To demonstrate the approach, we perform DF-IR spectral imaging of a polymer USAF resolution target and human tissue in the C−H stretching region (2600−3300 cm −1). DF-IR spectroscopy and imaging can be generalized to other IR spectral regions and can serve as an analytical tool for environmental and biomedical applications. FTIR imaging of wheat endosperm cell walls in situ reveals compositional and architectural heterogeneity related to grain hardness, " Combined Fourier-transform infrared imaging and desorption electrospray-ionization linear ion-trap mass spectrometry for analysis of counterfeit antimalarial tablets, " Anal. Spectroscopic FTIR imaging of water species in silicic volcanic glasses and melt inclusions: An example from the Izu-Bonin arc, " J. Detection and tracking of gas clouds in an urban area by imaging infrared spectroscopy, " Proc. SPIE 8743, 874317 (2013). High-resolution Fourier-transform infrared chemical imaging with multiple synchrotron beams, " Nat. High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data, " Biochim. Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing, " Appl. Discrete frequency infrared microspectroscopy and imaging with a tunable quantum cascade laser, " Anal. Design and performance of a planar array infrared spectrograph that operates in the 3400 to 2000 cm −1 region, " Appl. Experimental observation of photonic-crystal emission near a photonic band edge, " Appl. Three-dimensional photonic-crystal emitter for thermal photovoltaic power generation, " Appl. Controlled thermal emission of polarized infrared waves from arrayed plasmon nanocavities, " Appl. Thermal emission of two-color polarized infrared waves from integrated plasmon cavities, " Appl. Photonic crystal enhanced narrow-band infrared emitters, " Appl. Phys. High …


Introduction
Mid-infrared (mid-IR) spectroscopic imaging is an emerging combination of fundamental vibrational absorption spectroscopy and microscopy that provides a powerful analytical tool for visualizing the molecular content of a sample without the use of dyes, stains or destructive procedures [1].Over the last 15 years, numerous applications including those in polymer composites, forensics, environmental science, geology, human tissue pathologies, palaeontology and plants have been reported [1][2][3][4][5][6][7][8][9].Almost all mid-IR imaging data acquired today are using Fourier transform infrared (FT-IR), in which a specimen is illuminated by broadband radiation using a Michelson interferometer.In this setup, intensity values at the detector are recorded at each of thousands of specific positions of the moving mirror and a Fourier transform is used to convert the time-domain signal to the frequency-domain spectrum.FT-IR imaging spectrometers are high-precision instruments but necessitate the acquisition of a continuous absorption spectrum over a large bandwidth.Despite the strengths of interferometer-based data acquisition [10], alternative approaches could be beneficial for many applications.The need to scan an entire interferogram/time and resulting large data sizes can become crippling limitations, especially as the spatial resolution of microspectroscopic imaging increases [11,12].For many routine applications, such as environmental monitoring and industrial process control, only a small portion of the spectrum contains useful information, and a more rapid, robust, and inexpensive instrument than an FT-IR spectrometer would be most appropriate.In cases where the relevant spectral wavelengths are known, a simpler imaging approach to acquire only these data would enable spectroscopic imaging to be applied in settings that have thus far been impossible.For example, multiple studies show that only a few wavelengths over the broad mid-IR range are required to provide all the information required for tissue histopathology [13,14], which can potentially be speeded up if only these frequencies could be recorded.This alternate approach to the dominant FT-IR imaging approach is emerging as a viable alternative and is termed discrete frequency IR (DF-IR) spectroscopic imaging [1].A significant topic of interest in this area is the development of a variety of devices for discrete frequency illumination, including selective emitters and resonant filters in mid-IR, and their optimal integration into an imaging system.
The major capabilities required from these devices are to produce narrow-bandwidth (typically requiring a resolving power λ peak /Δλ > 50 for mid-IR spectroscopy of condensed matter and tissues [13][14][15], where λ peak and Δλ are the peak wavelength and the linewidth of the narrowband radiation respectively) and wavelength-tunable mid-IR radiation.Tunable quantum cascade lasers (QCLs) have shown such promise but their use has primarily been for gas sensing and spectroscopy thus far [16][17][18].Their expense and spatial coherence introducing optical effects that make high-resolution microscopic imaging challenging with simple instrumentation [19] likely imply that QCLs will be used for complex, high-end instrumentation.A simpler approach would be to utilize a grating/slit monochromater to select desired wavelengths [20].However, the spatial-spectral convolution and lack of high grating diffraction efficiency over a broad spectral range would make instrumentation extremely challenging to design and operate.Selective mid-IR thermal emission from tungsten photonic crystals (PCs) [21,22], plasmonic nanocavity arrays [23,24], plasmonic crystals [25][26][27][28][29], patterned steel [30], and metamaterials [31,32] have also been studied but the bandwidths are not narrow enough (λ peak /Δλ ≤ 11) for spectroscopy applications.Narrow thermal emission can be achieved by using surface-phonon polaritons in a silicon carbide (SiC) periodic structure [33], Mie resonances in a SiC optical antenna [34], and semiconductor multiple-quantum-well PCs [35], but they operate in a small spectral range and/or have undesired sidebands in the vicinity of the main emission peaks.In summary, no practical technologies exist to perform generalized DF-IR spectroscopic imaging.
We sought to develop an approach in which mid-IR radiation at selective wavelengths could be obtained from narrowband filtering of the commonly-used, inexpensive broadband incandescent source used for mid-IR spectroscopy today.While static Bragg filters comprised of quarter-wave stacks of alternating dielectric thin films [36] are alternatives in principle, producing a series of filters with only slightly different thin film stacks is prohibitive in cost and fabrication complexity.In contrast, silicon-based PC slabs [37], subwavelength plasmonic aperture arrays [38][39][40][41], and double-layered plasmonic crystals [42] show selective mid-IR resonant filtering but either have low peak-background contrast ratio or tend to have wide resonance bandwidths.Here we report the design and demonstration of mid-IR highperformance PC resonant filters that are based on guided-mode-type Fano resonances [43].We term this class of dielectric microresonant structures guided Fano resonators (GFRs).Compared to the aforementioned selective thermal emission and filtering methods, GFRs here are capable of exhibiting single reflection peak, narrow linewidth (λ peak /Δλ ~100), and high peak-background contrast ratio in the spectral region around the C−H stetching vibrational mode (wavenumber ν = 2600−3300 cm −1 ).Since spectroscopic measurements require more than one filter, we sought to co-fabricate a series of GFRs that are designed with different resonant wavelengths upon a single glass substrate as a 'filter wheel'.This approach considerably simplifies fabrication while imparting exquisite control needed over the wide bandwidth.The planar design of our one-layer devices has a feature size of ~1 µm, thus their fabrication is not a challenge for available photolithography and deposition/etching tools.Finite element method (FEM) electromagnetic computation and a Fano interference model are reported to model the devices and validate experimental spectra.Finally, the GFR filter wheel is incorporated into a new DF-IR imaging instrument.DF-IR imaging is validated using a polymer (SU-8) USAF resolution target against FT-IR imaging in the C−H stretching region and the potential of rapid IR imaging in pathology is demonstrated by breast tissue imaging.

Underlying principles and analytical design of high-contrast-ratio, narrowband GFRs
Figure 1(a) presents a schematic illustration of the GFR for mid-IR spectroscopy and imaging.Our device is comprised of a single layer of IR-transparent (for light of wavelength λ < 6 µm), periodically structured silicon nitride (Si 3 N 4 ) thin film on top of a soda lime (SL) glass substrate.The depth of the subwavelength structure (d 1 ) determines the resonance bandwidth [44].The layer thickness d 2 and the period Λ control the peak-background ratio, lineshape, and spectral location of the resonance, thereby enabling facile design and flexibility in fabrication by combinations of values.When illuminated by a broadband source, the coupling between the incident light and the periodic subwavelength structure may occur in two ways.(i) Incident light at λ couples to the discrete in-plane guided mode supported by the structure via ± 1st-order Bragg scattering described by the momentum-matching condition: where k mode is the wavevector of a specific guided mode, x is the unit vector in the x direction, k 0 is the wavevector for the incident light (|k 0 | = 2π/λ), θ i is the angle of incidence (θ i = 0° is chosen for single-peak resonance in the present work), and G x is the reciprocal lattice vector (|G x | = 2π/Λ).The mechanism creates a sharp resonance peak in the spectra (resonant Wood's anomalies) [45][46][47].(ii) Incident light couples to the continuum broadband vertical Fabry−Pérot (F−P) microcavity [48], as illustrated in Fig. 1(b).Processes (i) and (ii) take place simultaneously, leading to a total reflectivity spectrum, R(ν), expressed as a phenomenological Fano interference model [45,49] given as where R(ν) is an interference effect of the continuum direct contribution (with amplitude a c ) and the discrete Lorentzian resonance (with amplitude b r , resonance wavenumber ν res , and bandwidth Δν) with a phase difference φ.Within an appropriate spectral range, the slowlyvarying continuum a c (ν) can be expressed approximately as , where a 0 , a 1 , and a 2 are fit parameters.When ν = ν res , the ratio of the power in the guided resonance to that in the continuum background is P r /P c = |b r /a c (ν res )| 2 [50].A resonance spectrum with a symmetric lineshape occurs when the phase difference φ = 0 [49] or a c = 0 [45].When , the incident wave does not satisfy the momentum-matching condition and cannot be coupled into the guided mode.Thus, only the continuum F−P multiple reflections determine the background reflectance.When res ν ν ν − ≤Δ , the reflected wave is the interference of the guided mode and F−P reflections, exhibiting an asymmetric Fano lineshape [45,49].The coherent interference between a discrete narrow-linewidth and broadband contributions originates from atomic physics [51], and has been observed in a variety of photonic/plasmonic micro-and nano-systems [43,[52][53][54][55][56][57].
A figure of merit for spectroscopic sensing, which depends on separating the peak reflectance of the resonance (R peak ) from the continuum reflectance in the vicinity of the resonance (R vicinity ), is proposed here as a contrast ratio (CR): Ideally, a GFR for spectroscopy must have a high CR and therefore a low R vicinity .Second, a guided resonance must occur at a targeted wavelength.Therefore, it is essential to assure that the in-plane guided mode is not cut off when layer thicknesses are optimized for low continuum reflectance.Here, based on these considerations we use an efficient analytical methodology in designing narrowband GFRs.The Si 3 N 4 slab thickness determines both the broadband continuum F−P reflection and the guided mode dispersion k mode (ν).By ignoring the periodically structured surface to a first approximation for GFRs with a narrow linewidth, the GFR structure becomes an equivalent flat thin-film slab of effective thickness t slab = d 2 + d 1 /2, whose F−P reflectivity (R F-P ) and guided mode cutoffs can be computed separately using the propagation matrix method [58,59] and dielectric waveguide theory [59], respectively (see Appendix A and B for the methods).
Figure 1(c) presents the analytically calculated R F-P spectrum of the equivalent flat thinfilm slab for normal incidence and cutoff wavenumber of several lowest-order guided modes as a function of t slab .In our GFRs, fundamental guided modes TE 0 and TM 0 are employed for resonances in the C−H stretching region, and therefore this spectral range for a t slab has to be above the cutoffs for TE 0 and TM 0 modes.Additionally, the higher-order modes are designed to be cut off in the C−H stretching region in order to display a single resonance peak [44].Thus, the spectral range for a t slab must be below the cutoffs for TE 1 and TM 1 modes.At the same time, high CR requires small R vicinity near the spectral location of resonance, which suggests locating the C−H stretching region for a t slab between two ridges of high R F-P in Fig. 1(c).Here, we choose t slab = 730 nm (yellow dashed line in Fig. 1(c)) for low R F-P around 2800−3300 cm −1 and fundamental-mode (TE 0 or TM 0 ) operation.After engineering both broadband F−P reflection and guided mode cutoffs, the structure period Λ is determined analytically based on the momentum-matching condition (Eq.( 1)) in order to locate resonances in the targeted spectral region.Predicting Λ for a given ν res using Eq.(1) requires knowing dispersion curves of k mode (ν), which are plotted in Fig. 1(d) for TE 0 and TM 0 guided modes (calculated with Eq. ( 9) and (10) in Appendix B).The dispersion curves start from the cutoff condition on the substrate light line (k mode = k 0 n SL ) and approach the slab light line (k mode → k 0 n SiN ) for high-wavenumber limit.Normally-incident IR radiation above the air light line acquires a momentum of 2π/Λ in the x direction and then couples to the guided mode dispersion k mode (ν) based on the momentum-matching condition |k mode (ν)| = k mode (ν) = 2π/Λ, which determines and predicts Λ for a given ν res (as illustrated in the inset of Fig. 1(d)).As shown in Fig. 1(e), the analytically predicted period Λ is plotted as a function of resonance wavenumber for TE and TM polarizations, showing good agreement with the reflectivity map computed with FEM (COMSOL Multiphysics) for a physical structure for comparison, where d 1 is chosen to be 300 nm for a narrow resonance bandwidth of ~30 cm −1 at 2700−3200 cm −1 [44].To compare with the results of analytical predictions the same refractive indices (n SiN = 2.02 and n SL = 1.47) were used in the FEM computation in Fig. 1(e).FEM computation also verifies low continuum background that is predicted by the analytical approach in Fig. 1(c) in the vicinity of the C−H stretching region.Thus, we provide an analytical framework for design of high-efficiency narrowband GFRs.

Experimental realization and validation of large-area narrowband high-CR mid-IR GFRs
The dispersion diagram in Fig. 1(d) indicates that the spectral position of the resonance is sensitive to the angle of incidence based on Eq. (1).For example, Fig. 2 shows the effect of varying angle of incidence (θ i ) on the reflectance spectra of the GFR, indicating that offnormal incident light results in two reflectance peaks compared to the case at normal incidence.Therefore, our GFRs are designed for collimated normal incidence instead of tight focusing on a small area.This necessitates a practical constraint that the area of a resonator structure be large to collect enough light.
Based on these constraints and the desired spectral range of 2700−3200 cm −1 in mid-IR, we fabricated a group of (seven) large-area (>20 × 20 mm 2 ) GFRs on a 4-inch soda lime glass substrate.First, a Si 3 N 4 thin film with a thickness of ~880 nm was deposited on soda lime glass (Mark Optics) by plasma-enhanced chemical vapor deposition (Mesc Multiplex PECVD, STS) at a pressure of 900 mTorr, temperature of 300 °C, and gas flow rates of 1960, 80, and 50 cm 3 /min for N 2 , SiH 4 , and NH 3 respectively.AZ 5214-E was used as positive tone photoresist (PR) for photolithography and was spun coat on Si 3 N 4 at 4000 rpm for 45 s.Following prebake at 110 °C for 60 s to remove moisture, PR was exposed to UV (λ = 405 nm) radiation at 21.6 mW/cm 2 for 9.6 s through a chrome mask.Then PR was developed in AZ 327 MIF (metal ion free) for 32 s followed by treatment with oxygen plasma (Jupiter III, March Instruments) at 600 mTorr under 100 W for 3 min.After hard bake at 120 °C for 2 min, the Si 3 N 4 layer was then etched using CF 4 reactive ion etching (Freon/O 2 RIE, PlasmaLab) at a pressure of 35 mTorr under 90 W for 5.3 min to achieve an etch depth of ~300 nm.Finally, residual PR was removed using acetone in an ultrasonic bath for 5 min followed by piranha cleaning (H 2 SO 4 :H 2 O = 3:1) for 2 min.The fabricated structures are shown in the optical image (Fig. 3(a)) and scanning electron microscopy (SEM) top view image (top right inset of Fig. 3(a)).The cross-sectional height profiles of the fabricated GFRs were analyzed with an atomic force microscope (AFM) (Dimension 3000, Digital Instruments) in tapping mode using a monolithic silicon tip with 30-nm-thick aluminum reflex coating (Budget Sensors), as shown in Fig. 3(b).Based on AFM measurements the structure parameters Λ, f, θ 1 , θ 2 , and d 1 of the fabricated GFRs were evaluated (Table 1).In addition, each structure is resonant with two orthogonal polarizations of incident light, enabling TE and TM modes of each structure to double the number of available filter wavelengths.Figure 3(c) shows the measured and calculated far-field reflectance at normal incidence for a representative resonator (GFR-3) along with the zoomed-in spectra in the vicinity of resonances for all GFRs.Far-field spectra were measured by using a Fourier-transform spectrometer (Vertex 70, Bruker), and reflectance values were evaluated by normalizing the spectral response of a GFR to that of a gold mirror.Two complementary approaches were pursued here to model the measured results.FEM simulations are used to compute the farfield reflectance spectra and the near-field electric field amplitude (|E/E inc |) distribution of the GFRs.Dispersion and optical absorption of the materials [60,61] and structural parameters extracted from AFM measurements (Table 1) were used in the FEM computation in Fig. 3(c).Here we used FEM to 'fit' our measured reflection spectra data, and d 2 was the only fit parameter.A proper value of d 2 , as listed in Table 1, was obtained for each structure by matching the resonance wavenumber in the FEM-computed TM-polarized spectrum to the experimental value.To explain the lineshape of the resonance as the result of Fano interference effect, experimental reflection spectra are fitted to Eq. ( 2).The resonance bandwidth, lineshape of resonance, and off-resonance reflectance in the measured far-field reflection spectra closely match FEM predictions.

Table 1. Structural parameters of the fabricated GFRs
The off-resonance background reflectance in Fig. 3(c) originates from continuum F−P multiple reflections, as described in the Fano interference model (Eq.( 2)).The fabricated narrowband GFRs here have a corresponding t slab of ~730 nm (Table 1), and exhibit a minimum continuum reflectance of ≤10% at 2800−3300 cm −1 in the experimental spectra, showing good agreement with the theoretical predictions of R F-P presented in Fig. 1(c) for an equivalent flat thin-film slab.As a result, the off-resonance background in the measured reflectivity spectra of GFRs is increased outside this spectral range.The width of this lowbackground spectral range can be enlarged and the background reflection can be further suppressed by incorporating additional layers for broadband antireflection coating [62].
Because of high R peak at resonance, the interference of the downward incident wave and upward reflected wave at resonance creates obvious standing wave patterns along the z direction in air, as seen in the near-field |E/E inc | distribution in Fig. 3(d).The on-resonance |E/E inc | distribution for TE polarization shows two maxima per unit cell within the slab in the in-plane (x) direction due to interference of guided waves propagating in opposite ( ± x) directions, confirming the momentum-matching condition (that is, |k mode | = 2π/Λ at resonance) [63].Combining both high R peak and low R vicinity of ~5−8%, our one-layer resonant filters possess a CR (listed in Table 2) of 9.8−13.7 and 9.4−14.8for TM and TE polarization respectively, showing >200% increase of CR than devices reported previously [64] (as seen in Fig. 4).Additionally, it is interesting to note that the very simple GFRs here show λ peak /Δλ and CR values comparable to that of recently developed narrowband mid-IR thermal emitters, based on rod-type two-dimensional PC structures comprising 13 pairs of quantum-well epitaxial layers [65], which are much more complicated.The measured far-field reflectance spectra of the fabricated GFRs and the fit with the Fano interference model match very well, from which values for [ν res , Δν, Q, P r /P c , φ] are determined and listed in Table 2.For guided Fano resonance, the phase difference (φ) goes to zero and the lineshape becomes symmetric when the direct F−P reflectivity reaches minimum [49,66].Our GFRs here are designed to have low F−P background; consequently, φ is small for fabricated resonators.
Table 2. Value of resonance wavenumbers (ν res ), linewidth (Δν), quality factor (Q), ratio of the powers in the Lorentzian resonance to in the direct continuum background (P r /P c ), the relative phase difference between these two channels (φ), and contrast ratio (CR) by a fit with Eq. ( 2) of the experimental spectra in Fig. 3(c)

A GFR-based instrument and DF-IR spectroscopic imaging
where I sample is the transmitted IR intensity through the sample, I ref is the reference IR intensity through the unmodified IR-transparent substrate, and I db is the dark-background IR intensity due to ambient radiation when the input port of the microscope is closed.Until now, there has not been a report of spectroscopic imaging using Fano-type narrowband radiation in the mid-IR.Hence, we validate our microscopy setup with a SU-8 polymer USAF target.The USAF resolution target is made of a patterned layer (~10 µm thick) of SU-8 polymer (MicroChem) on a polished barium fluoride (BaF 2 ) substrate (ISP Optics), fabricated using the conventional protocol of photolithography.
Although SU-8 is transparent in the visible region of the spectrum, as seen in the optical image in Fig. 6(a), it contains distinctive absorption bands in the C−H stretching region.As shown in Fig. 6(b), DF-IR absorbance images clearly demonstrate the spatial fidelity and spectral content of the target.The BaF 2 area has A DF-IR ≈0 because it is IR transparent.In addition to 'Absorption ON/OFF' imaging, it is also interesting to investigate DF-IR absorbance as a function of discrete wavelengths.Figure 6(c) shows a series of DF-IR absorbance images and their corresponding spectra using a set of GFRs.The spectral densities of the GFR-reflected IR beam (colored in Fig. 6(c)) were characterized by coupling the beam to a Bruker Vertex 70 spectrometer.The IR absorbance spectra of the SU-8 resolution target (grey in Fig. 6(c)) were measured with a FT-IR imaging microspectrometer (620-IR, Varian) equipped with a MCT FPA detector and a 15 × Schwarzschild objective and condenser with a NA of 0.4 to provide IR spectral images with a ~725 µm field of view and a spatial resolution of ca.5.65 µm × 5.65 µm.The FT-IR absorbance values (A FT-IR ) were evaluated by converting the ratio of single beam spectra to an appropriately acquired reference spectrum using Beer-Lambert law.As seen in Fig. 6(c), the DF-IR absorbance of the three SU-8 bars gradually gets higher/lower when the peak of the GFR-reflected IR beam enters/exits the IR absorption bands of SU-8. Figure 6(d) shows the absorbance spectrum measured by DF-IR imaging, compared to a corresponding FT-IR measurement.The data agree reasonably with the discrepancy arising from the Fano lineshape, the finite linewidth, and background reflectance of the GFRs and differences in optical setup between the two systems [68,69].To address the discrepancy due to GFR characteristics, we developed a simple model to quantitatively explain the DF-IR spectrum.Based on Eq. ( 4), the modeled DF-IR absorbance can be written as where S beam (ν) represents the measured spectral density of the narrowband IR beam (colored in Fig. 6(c)), and A FT-IR (ν) represents a measured FT-IR absorption spectrum (grey in Fig. 6(c) and 6(d)).T cond (ν) and T obj (ν) are the transmittance spectra of the condenser and the objective lens, respectively (see Fig. 7).The integrations in the denominator and the numerator represent the transmission IR intensity through a thin layer of sample and the reference IR intensity through the air, respectively.As shown in Fig. 6(d), the measured and modeled DF-IR absorbance spectra match very well.Therefore, the DF-IR system and its performance can be predicted, analyzed, and understood.For QCL-based IR spectral imaging [19], S beam (ν) has a delta-function-like spectrum, and therefore according to Eq. ( 5) we have A DF-IR ≈A FT-IR and imaging with high spectral sensitivity.For GFR-based IR spectral imaging, S beam (ν) has a finite linewidth Δν (due to coupling of the resonant guided mode to radiation channels outside the GFR) and background intensity (due to continuum F−P reflection of GFRs and the broadband incandescent IR source used), as shown in Fig. 6(c).Accordingly, A DF-IR is an average absorbance weighted by the Fano-like spectrum of S beam (ν) according to Eq. ( 5), leading to A DF-IR ≤ A FT-IR when ν res is within the IR absorption bands of the sample ('Absorption ON' state) and A DF-IR ≥ A FT-IR when ν res is outside the IR absorption bands ('Absorption OFF' state), respectively.As a result, the DF-IR spectrum here shows a spectral sensitivity less than the FT-IR counterpart, with the peak A DF-IR value ~2 times larger than the 'Absorption OFF' A DF-IR as shown in Fig. 6(d).Despite of this fact, engineering of narrow-bandwidth GFRs for low background reflectance and high CR in the vicinity of the spectral range of interest (Section 2.1 and 2.2) is the key to successfully observing the DF-IR spectroscopic contrast here that cannot be seen if using the devices reported previously (Fig. 4).The spectral sensitivity of the GFR-based DF-IR can be further enhanced by using narrowband multilayered GFRs with wideband antireflection design.
In addition to comparisons of the DF-IR and FT-IR spectra, the DF-IR absorbance spatial profiles of the three SU-8 bars (Fig. 6(e)) are compared to the case measured with a FT-IR imaging microspectrometer (Fig. 6(f)).The height of profiles reflects value of the local DF-IR absorbance, and the sudden increase of absorbance at the edges is due to light scattering [19,70], which is more apparent in DF-IR measurement due to the higher NA used.It is notable that in contrast to the QCL-based IR imaging system [19] where spatial coherence of laser introduces undesired fringe patterns into microscopic images, the GFR-based DF-IR instrument described here shows imaging quality comparable to that of the conventional FT-IR imaging.
The GFR-enabled DF-IR instrument also allows for the investigation of the IR absorption spectra of biological specimens.Figure 8(a) shows the optical image of an unstained human breast tissue sample (US Biomax), with a zoomed-in area of epithelium shown in the right inset.Breast tissue consists of complex microstructures which may have dissimilar IR response for different optical polarizations.In order to focus on the optical absorption and not on polarization, here we probed DF-IR absorbance of tissue using narrowband IR beam with the same polarization (TM) reflected by the GFR wheel.Figure 8(b) shows measured DF-IR and FT-IR absorbance spectra at the indicated location in Fig. 8(a), along with the corresponding S beam (ν) spectra for GFRs used.The trend of the DF-IR absorbance spectrum of breast tissue matches that of the FT-IR spectrum.In the top inset of Fig. 8(b), the FT-IR image at 2938 cm −1 (corresponding to ν res of GFR-7) shows generally higher absorbance than the FT-IR image at 3014 cm −1 (corresponding to ν res of GFR-5).In comparing DF-IR images as shown in Fig. 8(c), we observe that the same contrast can be seen in DF-IR images that is observed in FT-IR imaging data as shown in Fig. 8(b).Notably, we see that the epithelium can be readily discernible with just one frequency.Of course, use of other frequencies and spectral features can be used to refine this visualization and provide complete histopathological imaging.

Conclusion
By fully grasping the underlying principle and carefully designing, we sculpted optical properties of mid-IR GFRs for narrow bandwidth and high CR, which showed of critical importance in DF-IR spectroscopic measurements.The collective set of results indicates that the concept and method of the DF-IR spectroscopic imaging can be applied not only to study of condensed matter materials but also to biological applications.While different type of tissue cells have similar mid-IR absorption spectra in the C−H stretching region, they show dissimilar spectral features in the fingerprint mid-IR region (1000−1600 cm −1 ), where optimal discrete spectral regions have been discovered for automated cancer pathology [13,71].Therefore, once an appropriate set of narrowband high-CR GFRs at those characteristic wavelengths are made, IR cancer pathology will benefit from efficiency and robust instrumentation of the GFR-based DF-IR technology.Looking forward, in conjunction with development of high-performance IR photodetectors and GFRs in other regions of the mid-IR spectrum, GFR-based DF-IR technology opens a number of new opportunities for mid-IR spectroscopy.In addition to efficient spectral imaging, GFR-based DF-IR technology could also make video-rate imaging measurements possible for a variety of applications.
for the TE m mode, and for the TM m mode; α air and α SL are the decay constants in the transverse (z) direction in air and in the soda lime substrate, respectively, and are defined as When cutoff, decay constant vanishes in the substrate region, leading to α SL = 0 and k mode = k 0 n SL .Then the cutoffs can be determined from Eq. ( 9) and (10).

Fig. 1 .
Fig. 1.Principle and design of mid-IR narrowband high-contrast-ratio GFRs.(a) Schematic diagram defining the orientation and polarization of incident light and the structural parameters of the GFR.TE, transverse electric.TM, transverse magnetic.(b) Incident mid-IR radiation gets reflected via two channels presented in the structure, Lorentzian narrow-linewidth guided resonance and broadband Fabry−Pérot (F−P) reflection.(c) Computed F−P reflectance spectra vs. thickness for a flat thin-film slab with an effective thickness t slab = d 2 + d 1 /2 and refractive indices n SiN = 2.02 and n SL = 1.47 at normal incidence.Cutoff curves of the several lowestorder guided modes are combined with the reflectance contours for design of GFRs.(d) Calculated dispersion curves of the two fundamental guided modes, TE 0 and TM 0 , in a flat thin-film slab with t slab = 730 nm.Higher-order modes TE 1 and TM 1 have cutoff wavenumbers of 5984 and 6935 cm −1 , respectively, and are beyond the frequency range here.The inset illustrates how to determine Λ for a given ν res based on a dispersion curve.(e) Analytically predicted Λ vs. resonance wavenumber (white dashes) near the C−H stretching region.FEMcomputed reflectance maps for a physical structure with [θ 1 , θ 2 , f, d 2 , d 1 ] = [55°, 55°, 0.35, 580 nm, 300 nm] (corresponding to t slab = 730 nm) are overlaid for comparison.

Fig. 3 .
Fig. 3. Large-area mid-IR GFRs with narrow bandwidth and high CR.(a) Optical image of a set of large-area GFRs built on a 4-inch soda lime glass substrate.Top right inset: SEM image of a fabricated structure.(b) AFM cross-sectional profiles, vertically offset for clarity.The 3-D AFM topography image of the structure 7 (GFR-7) is shown in the top inset.(c) Measured and FEM-computed far-field reflectance spectra of a representative device (GFR-3) when a TMpolarized (top) or TE-polarized (bottom) light is normally incident, along with the zoomed-in spectra in the vicinity of the resonances of all GFRs as shown in the inset.Each experimental spectrum is also fitted with the Fano interference model (Eq.(2)).(d) FEM-computed electric field amplitude (|E/E inc |) distributions in a unit cell of the GFR-3 at the indicated spectral locations in (c).

Fig. 4 .
Fig. 4. Comparison of measured spectra of the GFRs in the present work and the devices reported previously [64] for (a) TE polarization and (b) TM polarization.(Reproduced with permission from [64].Copyright 2010 American Chemical Society.)

Figure 5 (
Figure5(a) schematically illustrates the GFR-based instrument constructed for DF-IR imaging.Broadband IR emission from a SiC incandescent source is collimated by an off-axis parabolic mirror.Two circular apertures used to filter divergent IR radiations reduce the optical beam diameter to ~17 mm.Polarization of the beam is controlled by a wire-grid polarizer.Narrowband IR beam reflected by a GFR is directed toward the microscope by a beam splitter.After the beam enters the microscope, it is condensed through an IR aspheric lens (NT68-245, Edmund Optics) with a NA of 0.63 before passing though the sample, and then the transmitted beam is collected by an objective lens (#390028, LightPath) with a NA of 0.56.Images are captured by a liquid-nitrogen-cooled mercury cadmium telluride (MCT) 128 × 128 pixel focal plane array (FPA) detector (SBF161, Santa Barbara Focalplane) with a wide detection range (ν = 1000−5000 cm −1 or λ = 2−10 µm).Given the large spectral range compared to other forms of spectroscopy, a major challenge is that even small out-of-band contributions can overwhelm in-band signals.A broadband pass filter (BBP-3000-3900c nm, Spectrogon) is employed to reject IR radiation outside 2500−3300 cm −1 (λ = 3.3−4.0µm).Both the GFR wheel mounting stage and the sample stage are motorized and controlled by a personal computer.Figure5(b) shows measured spectral densities[67] of the broadband incandescent IR source and the GFR-reflected narrow-bandwidth IR beam.Rotating the motorized mounting stage brings a specific GFR into the beam path, enabling rapid wavelength tuning.The DF-IR absorbance (A DF-IR ) at any discrete frequency (ν res of the GFR) using a GFR filter is evaluated as

Fig. 5 .
Fig. 5. (a) Schematic of GFR-based DF-IR spectroscopic imaging microscopy.Bottom inset: motorized GFR wheel mounting stage.Right inset: narrowband IR radiation passes through a sample under test.NA, numerical aperture.(b) IR spectra at the indicated beam locations in (a).

Fig. 6 .
Fig. 6.DF-IR spectroscopic imaging of a USAF resolution target made of SU-8 polymer.Optical microscopic image (a) and mosaic DF-IR absorbance images (b) of a USAF resolution target (group 3, element 3, 4, and 5) when the resonance of the GFRs is outside (left, using TEpolarized GFR-6) or within (right, using TE-polarized GFR-1) the IR absorption bands of SU-8 polymer.(c) A series of DF-IR absorbance images of the area defined by the yellow dashed square in (b) using a set of GFRs made and their corresponding spectra (colored: measured IR spectral density of the beam before entering the microscope; grey: measured FT-IR absorbance spectra of SU-8 polymer at the position denoted by the red cross in the top left inset of (c)).Scale bar 100 µm.(d) Measured (averaged over 3 × 3 pixels, with error bars indicating ± 1 standard deviation, N = 9) and calculated DF-IR absorbance spectra of SU-8 polymer at the location denoted by the red cross in the top left inset of (c), along with the measured FT-IR absorbance spectrum at the same place.Fitted resonance wavenumbers in Table 2 were used to determine the spectral positions of DF-IR data set.(e) Measured DF-IR absorbance profiles along the red line in the inset.The DF-IR image in the inset is the same as the one for TEpolarized GFR-1 shown in (c).(f) Measured FT-IR absorbance image of the same area and FT-IR absorbance profile along the red line at 2908 cm −1 , which is close to the resonance wavenumber of the TE-polarized GFR-1.

Fig. 8 .
Fig. 8. DF-IR spectral imaging of human breast tissue.(a) Optical images of an unstained human breast tissue specimen.(b) DF-IR absorbance spectrum (top) at the location marked by the green cross in (a) probed by narrowband IR beam reflected by the TM-polarized GFR wheel (IR spectral density S beam (ν) shown in the bottom).FT-IR absorbance spectrum at the same location and FT-IR absorbance images of the area defined by the red square in (a) at 2938 cm −1 and 3014 cm −1 (corresponding to ν res of TM-polarized GFR-7 and GFR-5, respectively) are also provided in the top for reference.Scale bar 50 µm.(c) DF-IR absorbance imaging, showing higher absorbance of tissue for GFR-7 (purple) than the value for GFR-5 (orange).
a Q = ν