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The intrinsic linewidth and angular dispersion of Surface Plasmon Polariton resonance of a micrometric metal mesh have been measured with a collimated mid-infrared beam, provided by an External Cavity tunable Quantum Cascade Laser. We show that the use of a collimated beam yields an observed resonance linewidth γ = 12 cm−1 at the resonance frequency ν0 = 1658 cm−1, better by an order of magnitude than with a non-collimated beam. The extremely narrow plasmon resonance attained by our mesh is then exploited to reconstruct, by varying the QCL angle of incidence θ, the angular intensity distribution f(θ) of a globar at the focal plane of a conventional imaging setup. We thus show that f(θ) is better reproduced by a Gaussian distribution than by a uniform one, in agreement with ray-tracing simulation.
© 2013 Optical Society of America
1. Introduction
In recent years, the optical properties of two-dimensional (2D) subwavelength hole arrays have attracted considerable interest, due to the role played by Surface Plasmon Polaritons (SPP) in enhancing the electromagnetic field in the proximity of the hole edges [1, 2]. This effect can be exploited for applications such as molecular sensing [3, 4], enhancement of nonlinear effects [5], or optical beam steering [6, 7]. Square metal meshes support plasmonic modes with electromagnetic frequency ranging from the millimeter waves to the visible range, the difference in the optical properties being mostly related to the variety of designs and the employed fabrication technologies. Plasmonic meshes display narrow resonant transmittance peaks with an asymmetric Fano profile resulting from the interference of the diffraction continuum with the discrete 2D grating modes [8]. In the mid-infrared range, the intrinsic linewidth is predicted to become extremely narrow [9], since the SPP and the light dispersion relations almost overlap and reinforce the interference with respect to the visible range. Fano resonances have been exploited e.g. for the optical detection of biomolecular layers [4, 10] and surface-enhanced mid-infrared spectroscopy [11–13, 15].
A degradation of the frequency selectivity of the 2D grating modes, hence of the asymmetry of the Fano lineshape, occurs when the response of the mesh is measured by large Numerical Aperture (NA) imaging systems, such as a microscope objective [16]. This degradation, which is due to the simultaneous excitation of resonances at different frequencies by infrared rays coming from a distribution of angles of incidence, can be reduced by using smaller-NA optics [17, 18]. However some authors [9, 19, 20] have pointed out that, in order to study the intrinsic lineshape and to measure the angular dispersion of SPPs, radiation in a single plane-wave eigenstate should be used (collimated beam). To our knowledge, such improvement has not been achieved in the infrared and millimeter wave ranges but only in the visible [19]. However, the fabrication tolerance of nano-scale focused ion-beam machines used to serially implement the individual subwavelength holes of the array [17], together with the scattering of plasmons by nanoscale roughness of the evaporated metal surface [21], provide lower bounds to the Fano linewidth displayed by meshes in the visible range.
In the present work, we propose an effective solution to the above described optics-fabrication trade-off by studying the transmittance of a metal mesh in the Mid-InfraRed range (MIR) with a collimated beam having a diameter of 2 mm. This is provided by an external-cavity Quantum Cascade Laser (EC-QCL) (Daylight solutions, tuning range 5.8–6.2 μm). EC-QCLs in other mid-infrared ranges were previously used either to study the spatial distribution of the radiation beamed by a subwavelength mesh [22] or to show that the radiation can be steered at selected angles beyond the mesh [7], if this is patterned in a suitable way. To do that, however, in both cases the laser beam was focused on a small area of the sample surface. We used Electron Beam Lithography (EBL) to implement a square array of sub-wavelength square holes on an aluminum film with very high precision over a millimeter-sized sample area, large enough for illumination with a collimated beam in the MIR. We then measured the transmittance spectrum with the EC-QCL, by also varying the angle of incidence. We obtained the angular dispersion of the SPP mode close to normal-incidence, which turned out to be in excellent agreement with theoretical predictions. The intrinsic Fano linewidth of the SPP resonance centered at ν0 = 1658 cm−1 was found to be γ = 12 cm−1. The high quality factor of the resonance is of advantage for MIR sensing applications as already demonstrated in [13]. As a novel field of application of metal meshes, we finally demonstrate that they can be used as momentum-space probes to infer on the angular intensity distribution of a non-collimated (thermal) MIR source. This subject has been treated by Heer et al. in [14] by use of three-dimensional finite-difference time-domain calculations. Here instead, this is done by using the mesh transmittance spectra recorded with the EC-QCL at variable angle of incidence as a basis set for reconstructing the plasmonic resonance lineshape as measured for several NA’s with a standard Fourier-Transform (FT-IR) spectrometer.
2. Experiment and results
The plasmonic mesh was fabricated by using a top-down high-resolution lithographic approach. EBL allowed for high precision patterning of square holes (840x840 nm wide, array pitch 1775 nm) over an area of 5x5 mm2. The ratio between the hole side and the array pitch, close to 1/2, provides a narrow linewidth toghether with a reasonably high trasmitted peak intensity of about 0.09 at ν ∼ ν0. The sub-wavelength holes array was lithographically defined by using electron beam direct writing on a resist polymer spun over a double-polished optical-grade Si(100) wafer. Metallic array was then obtained by evaporation of a low-resistivity 200nm-thick Al film, followed by lift-off with acetone soak. The Scanning Electron Microscope images (see (Fig. 1(a)) have shown that the hole design was reproduced 106 times in the array with the accuracy of 10 nm.
Fig. 1 a): SEM image of the 2D plasmonic mesh. b): Optical layout for transmission measurements with the tunable Quantum Cascade Laser source (QCL), the mesh (M), the MCT detector (D), and the attenuator, implemented by a polarizer of KRS5. The polarization direction of the laser beam (P) and the variable angle of incidence θ are also indicated. c): Optical scheme of the FTIR interferometer with the globar source, the diaphragm d, the variable iris, and the nitrogen-cooled MCT detector. The grey boxes represent the optics of the interferometer.
The optical setup for the transmittance measurements with the EC-QCL is shown in Fig. 1(b). The QCL source (Daylight Solutions Inc.) provides a collimated beam in TEM00 mode, linearly polarized as shown by the arrow in the figure, in the frequency range between 1580 – 1720 cm−1. The mesh M could be rotated around a vertical axis to change the angle of incidence θ, while keeping one side of the square mesh aligned with the polarization vector of the radiation. We remark that the residual divergence of 2 mrad of the laser beam directly coming from the cavity is negligible if compared with all other geometrical dimensions of the experiment. The intensity Im transmitted by the mesh and that, Is, transmitted by the bare Si substrate, were detected by a thermoelectric-cooled Mercury-Cadmium-Tellurium (MCT) detector and processed by a lock-in amplifier triggered by the repetition rate of the QCL source. In order to avoid saturation of the detector, the QCL was operated at a repetition rate of 10 KHz, with a 0.1% duty cycle and behind a KRS5 wire-grid polarizer which was rotated to regulate the radiation intensity on the detector. The frequency step of the tunable cavity was 1 cm−1. The whole setup was housed in a nitrogen-purged box in order to eliminate the MIR absorption from the atmosphere.
The transmittance spectra TQCL(θ, ν) = (Im/Is)QCL were collected by varying θ between 0° and 11°, with a step of 0.5°. Some of them, as obtained after a Savitski-Golay smoothing of the raw data, are reported in Fig. 2(a). The spectrum at θ = 0 shows a single resonance peak, whereas two poorly resolved peaks are visible for angles of incidence up to 1°. These peaks further split and shift towards higher and lower frequencies for increasing θ. A residual feature at about 1660 cm−1 is observed at any angle of incidence. The contour plot of Fig. 2(c) highlights the angle and frequency dependence of the TQCL(θ, ν) spectra. One may notice that the dashed lines in Fig. 2(c) converge, for θ → 0, toward the resonance value of 1658 cm−1 extracted from the fit the resonance line in Fig. 2(b) (see below). Due to its asymmetry, the resonance is slightly shifted with respect to the peak position (1652 cm−1).
Fig. 2 a): Transmittance spectra of the mesh illuminated by the QCL, for different angles of incidence θ; the arrows indicate the peak positions for θ = 00 (red arrow) and θ = 1.50 (yellow arrows); b): resonance at θ = 0 (dots) with its fit to Eq. (2) (solid line); c): angular dispersion of the SPP modes in a). The dashed lines are guides to the eye.
In order to assign the peaks in Fig. 2(a) and explain their angular dependence (Fig. 2(c)) one has to combine the dispersion of SPP modes at a single metallic-dielectric interface with the concept of momentum matching [16, 18, 23]. One thus obtains for a square hole-array the following dispersion relation:
where L is the mesh lattice constant, neff the real part of the refractive index at the Si - mesh interface and the integers (i, j) label the order of the resonance. We studied the first grating order with (i2 + j2) = 1 so that, at θ = 0, the resonance occurs at . Here , where εm = −160 and εs = 11.6 are the dielectric functions of the metal layer and of silicon, respectively, evaluated at the resonance frequency. We found neff = 3.26. The θ-dependent peak pair in Fig. 2 corresponds instead to the (positive) solutions of Eq. (1) at the orders (1,0) and (−1,0), while the undispersed peak around 1660 cm−1 is due to the degenerate frequencies at (0,1) and (0,−1). In turn, the resonance at normal incidence in Fig. 2(b) is well fit by the Fano lineshape [13]Remarkably, we obtain γ = 12 cm−1, a value much smaller than what reported by Limaj et al. in [13] on samples with identical structures but measured with a FT-IR setup. This result suggests that the quality factor of plasmonic meshes operating in the MIR is much higher than previously believed on the basis of different experiments, all performed with FT-IR setups [3, 12, 13, 24].
In order to confirm the above findings, we have placed the same mesh in the sample compartment of a FTIR interferometer (Bruker IFS66/v). The interferometer was equipped with a thermal source (globar) and a nitrogen-cooled MCT detector (see Fig. 1(c)). The pupil diameter d was chosen equal to the laser beam diameter (3 mm), and data were taken with 1 cm−1 resolution. An additional iris allowed us to change the marginal angle of incidence θmax between 0.50 and 5.50, and therefore NA = nsinθmax (where n = 1) between 0.01 and 0.1, while the average angle of incidence was kept at θ =0. In Fig. 3(a), selected TFTIR(ν) = (Im/Is)FTIR are reported for different θmax. At the highest NA the transmittance shows a broad and almost featureless band, peaked around 1638 cm−1. The width of the SPP resonance decreases from 30 cm−1 at NA = 0.1 to 14.5 cm−1 at NA = 0.01, where it is still slightly higher than that measured with the collimated QCL beam(see Fig. 4(a)). Therein, however, to obtain a comparable signal-to-noise ratio and spectral resolution we needed an acquisition time longer by a factor of 80, if compared to the entire EC-QCL wavelength scan. The NA-dependent broadening in Fig. 3(a) is mainly due to the four first-order resonances (0,1), (0,−1),(1,0), and (−1,0), which occur at different frequencies for any θ >0, being mixed for finite NAs. Indeed the full linewidth at NA = 0.1 in Fig. 3 (60 cm−1 is similar to the inter-peak spacing for θ = 5.50 in Fig. 2(c) (70 cm−1). The residual linewidth observed with the collimated beam may be partly due to the interaction between pairs of those modes.
Fig. 3 a): Transmittance of the mesh measured with a FTIR interferometer, for different values of the NA, from 0.1 to 0.01; b) and d): Spectra reconstructed from the variable-angle QCL data according to Eq. (3) and using a uniform (b) and Gaussian (d) intensity distribution (see insets). c): Ray-tracing simulation of the mesh transmittance for different NA. The insets show the f(θ) used for the reconstruction of the corresponding spectra.
Fig. 4 a): Transmittance of the metal mesh measured with the FTIR setup for NA = 0.01 (blue line) and 0.1 (red line) and compared with TQCL(θ = 0) (dashed). A comparable slope (straight lines) can be achieved only for NA = 0.01; b): average slope of the FTIR and QCL data at resonance vs. θmax.
The beam of the extended blackbody source is an unpolarized spherical wave which can be decomposed, in the focal plane, into a superposition of plane waves [25] labeled by a set of k vectors. Each of them can then be reproduced by one EC-QCL beam impinging with the same k, namely at a given angle θ, on the plasmonic mesh. Given the short temporal and spatial coherence [26] of the blackbody source, it may be assumed that each plane-wave sums up incoherently and independently according to the momentum-conservation rule for SPP excitation (see Eq. (1)). Therefore, the TQCL(θ, ν) spectra of Fig. 2 provide a suitable basis set for the TFTIR(ν) spectra, according to the relation
Here f(θ) must reproduce the angular intensity distribution of the blackbody radiation through the optical elements of the FTIR setup. It is worth to note that the symmetry properties of both the mesh and the incoming radiation reduce the variables of the theoretical model to a single degree of freedom (θ). In the following we will reproduce TFTIR(θmax, ν) by using the QCL spectra of Fig. 2(a) and three different trial functions for f(θ). To this aim, the right-hand side integral of Eq. (3) is sampled into a discrete sum of 128 terms obtained through linear interpolations in θ of the QCL spectra.We first considered a uniform intensity distribution within the range ±θmax, corresponding to an aberration-free optical path through the FTIR setup and an isotropic spherical emission from the blackbody. The reconstructed transmittance Tflat(θmax, ν) reported in Fig. 3(b) for the same NA’s as in Fig. 3(a) do not reproduce in detail the experimental data in Fig. 3(a). This should be expected, as optical aberrations affect the source beam profile in real FTIR systems. To account for these effects, we simulated the actual optical path by tracing 105 rays [27]. For each value of the iris diaphragm, histograms representing f (θ) at the focal plane have been obtained (see the inset of Fig. 3(c)). The Tray(θmax, ν) curves have been then computed by Eq. (3) and reported in panel (c). The agreement with the data in panel a) is considerably improved with respect to Fig. 3(b). Following the indications of ray tracing, in a third attempt we have used again the QCL data with a Gaussian distribution f (θ). Its standard deviation was fixed at based on statistical arguments. This approach leads to the TGauss(θmax, ν) transmittance reported in Fig. 3(d), where the agreement with Fig. 3(a) is quite satisfactory. Such agreement confirms a posteriori our assumption on the incoherent sum of laser beams.
A more quantitative comparison among the mesh response measured with the QCL, with the FTIR interferometer, and that reconstructed as reported above, can be done by determining the average slope of the different spectra at resonance. This parameter can indeed be assumed as a figure of merit for the evaluation of SPP-based devices. Fig. 4(a) shows the FTIR transmittance at the highest and the lowest NA, together with the QCL transmittance at normal incidence. The QCL spectrum (square at θmax = 0 in Fig. 4(b)) displays the highest slope, even larger than that of the FTIR spectrum at the smallest iris aperture (NA = 0.01) but with an acquisition time larger by a factor of 80.
The average slope <dT/dν> of Tflat, Tray and TGauss is reported In Fig. 4(b) vs. the iris aperture θmax, together with that of the the experimental TFTIR. The slope calculated with the flat angular distribution is systematically higher than TFTIR. Both the Gaussian distribution model and the ray tracing results provide a good agreement with the experimental data, except for the smallest NA where the TGauss reconstruction seems more adequate.
3. Conclusion
In summary, we have studied the mid-infrared transmittance spectra of a 2D plasmonic mesh as a function of the angle of incidence, by using the plane waves of an external-cavity Quantum Cascade Laser. At normal incidence we observed a Fano resonance even sharper than that obtained by a conventional interferometric apparatus working with NA = 0.01 and with an acquisition time longer by two orders of magnitude. This shows that in previous experiments performed with FTIR interferometers or microscopes the selectivity in frequency of plasmonic devices was deteriorated - and therefore underestimated - by the superposition of waves coming from a distribution of angles of incidence. The residual linewidth observed with the collimated beam (12 cm−1) can be considered the intrinsic linewidth of the plasmonic resonance. It may be partly due to the interaction between quasi-degenerate SPP modes. Moreover, we have demonstrated that spectra taken under arbitrary angular distribution from an incoherent thermal source can be reproduced by a suitable composition of the spectra taken with the QCL collimated beam. The angular distribution of the black body intensity n the focal plane, at the sample position, turned out to be Gaussian. The present observations with a collimated source open more encouraging perspectives to the applications of plasmonic meshes in the mid infrared than what was previously assumed.
Acknowledgments
We acknowledge support from the Italian Ministry of Research through programs “FIRB Futuro in Ricerca” (Grant No. RBFR08N9L9) and from Sapienza Universita’ di Roma through the program “Grandi Attrezzature 2011”.
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