Letter pubs.acs.org/NanoLett
Optical Properties of Single Infrared Resonant Circular Microcavities for Surface Phonon Polaritons Tao Wang, Peining Li, Benedikt Hauer, Dmitry N. Chigrin, and Thomas Taubner* First Institute of Physics (IA), RWTH Aachen University, Aachen 52056, Germany ABSTRACT: Plasmonic antennas are crucial components for nanooptics and have been extensively used to enhance sensing, spectroscopy, light emission, photodetection, and others. Recently, there is a trend to search for new plasmonic materials with low intrinsic loss at new plasmon frequencies. As an alternative to metals, polar crystals have a negative real part of permittivity in the Reststrahlen band and support surface phonon polaritons (SPhPs) with weak damping. Here, we experimentally demonstrate the resonance of single circular microcavities in a thin gold film deposited on a silicon carbide (SiC) substrate in the mid-infrared range. Specifically, the negative permittivity of SiC leads to a well-defined, size-tunable SPhP resonance with a Q factor of around 60 which is much higher than those in surface plasmon polariton (SPP) resonators with similar structures. These infrared resonant microcavities provide new possibilities for widespread applications such as enhanced spectroscopy, sensing, coherent thermal emission, and infrared photodetectors among others throughout the infrared frequency range. KEYWORDS: Optical antenna, surface phonon polariton, circular microcavities, slot antenna, polar crystal, optical phonon
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part of the permittivity Re(εSiC) of SiC20 has a Lorentzian line shape with a sharp resonance around 793 cm−1 (12.6 μm), due to the excitation of transverse optical (TO) phonons (Figure 1a). In the Reststrahlen band, that is, between the transverse optical and longitudinal optical (LO) phonon frequency (969 cm−1, 10.32 μm), the Re(εSiC) is negative, similar to plasmonic materials below their plasma frequency. At frequencies higher than the LO phonon frequency the Re(εSiC) is positive, similar to a dielectric (Figure 1a). In this Letter we want to investigate a resonant cavity for SPhPs at the air/SiC interface. A circular microcavity is realized as a microsized hole in a thin gold film (40 nm) deposited on a SiC substrate (Figure 1b). These microsized holes are fabricated using the colloidal lithography method with different sphere diameters D (see Methods). In such a structure, two types of resonances may be expected: (i) SPhP resonances inside the microcavity in the spectral range where the real part of the SiC permittivity is negative (ωTO < ω < ωLO) and (ii) circular slot antenna resonances along the microcavity in spectral range where the real part of the SiC permittivity is positive (ω > ωLO). It should be noted that it is not recommended to fabricate these microsized holes by focused ion beam (FIB) milling because the crystalline properties of the SiC substrate may be destroyed by focused ion-beam implantation.21 The Fourier transform infrared (FTIR) reflectance spectra (see Methods) of a resonant microcavity with different
ptical antennas are designed to efficiently receive, transmit, or broadcast electromagnetic radiation at their resonance wavelength.1−3 In the visible frequency region, metallic nanostructures are widely used as optical antennas owing to the resonance of surface plasmons that are the collective oscillations of the surface charge density at the metal/ dielectric interface. 4 One commonly used structure of plasmonic antennas is a nanohole5 or microcavity in a metallic film with surface plasmon polariton (SPP) resonance.6−12 However, due to the high conductivity of metals at infrared frequencies, a similar microsized hole structure possesses resonant properties which strongly resemble ones of a conventional microwave antenna, not an plasmonic antenna with high field enhancement.13−15 Fortunately, in the infrared region, the SPP has a counterpart, the surface phonon polariton (SPhP), which is the coupling between the electromagnetic fields and optical phonons (lattice vibrations) of the polar crystal. Due to the low intrinsic loss, SPhPs, especially on silicon carbide (SiC), can provide sharp resonances in various geometries: The near-field coupling of a metallic tip in a scanning near-field microscope to a SiC surface yielded strongly enhanced signals and a sharp resonance;16 SPhPs on a SiC surface have been used for mid-infrared refractive index sensing;17 SiC nanodisks have been theoretically proposed to show a strong localized SPhP resonance;18 and very recently sharp localized SPhP resonances have been demonstrated on SiC nanopillar arrays.19 Thus, a resonant cavity for SPhPs supported by the interface of polar crystals (i.e., SiC) may be a good alternative for realizing widespread applications as plasmonic antennas frequencies. The optical properties of SiC make it an interesting alternative to metals at mid-infrared frequencies. The real © 2013 American Chemical Society
Received: June 4, 2013 Revised: October 4, 2013 Published: October 11, 2013 5051
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ing to both the positive permittivity and the negative permittivity responses of SiC. For example, for a 6 μm diameter microcavity, the two resonances are located at 10.18 μm (Re(εSiC) = 0.52) and 10.67 μm (Re(εSiC) = −1.62) in both experimental and simulated spectra. From the field distribution of the FDTD simulation (Figure 2b), it is clear that at 10.18 μm where the permittivity of SiC is positive, the field is mainly distributed along the edge of the cavity (at the air−gold interface), similar to the field distribution of a horizontal dipole induced in a nanohole (plasmonic antenna) in a gold film at visible frequencies.6 On the contrary, at 10.67 μm where the permittivity is negative, the field distribution is mainly inside the cavity (at the air/SiC interface) which is associated with a SPhP resonance of the circular microcavity. To further identify the physical origin of these SPhP resonances, near-field measurements were performed using scattering-type scanning near-field optical microscopy (sSNOM) at the resonance wavelengths of the circular microcavities. During the near-field measurements, two types of AFM (atomic force microscope) tips are used: metallic tips (Pt coated silicon tips) and dielectric tips (silicon tips). The metallic tip has been successfully used to map SPhP propagating on the air/SiC interface.22 The dielectric tip, however, has weaker coupling to the substrate and is often used to get reliable mapping of antenna near-field modes,23 although the signal is much lower. Figure 3a shows the infrared near-field amplitude and phase images of a 3 μm SiC microcavity at resonance wavelength 10.61 μm. The images reveal strong amplitude signals and a uniform phase distribution. These allow to identify this mode as a fundamental SPhP resonance, with a field distribution similar to the first mode (0, 1) of an optical fiber, LP01.24 To analyze the image contrast, we perform threedimensional FDTD simulations (see Methods) of the near-field distribution of a 3 μm SiC microcavity at the resonance wavelength of 10.61 μm. Compared to the experimental images, the simulated data clearly shows that the amplitude and phase of the z-component, |Ez| and φz, are probed. Note that the amplitude image is slightly asymmetric along the polarization direction (≈ 45° in the sample plane) because the incident angle θ of the infrared laser is around 60° to the surface normal in our s-SNOM setup.22 The angle is also used in our FDTD simulations. We notice that the experimental amplitude patterns using both metallic and dielectric tip are similar, which indicates that the resonance pattern is not influenced substantially by the AFM tip. This is because the used microcavities are much larger that the AFM tip. The simulated images (without tip) agree well with the experimental images, which also confirms that the tip does not influence the resonance pattern. Similarly, the infrared near-field amplitude and phase images of a 6 μm SiC microcavity at resonance wavelength 10.67 μm are shown in Figure 3b. The images reveal strong amplitude signals but nonuniform amplitude and phase distributions. Considering both amplitude and phase images, the mode inside the cavity could be identified as a higher order resonance mode (1, 1), similar to the field distribution of the second mode of an optical fiber, LP11.24 The resonance wavelength (FTIR spectra, Figure 2a) as a function of antenna diameter is shown in Figure 4 both for SPhP resonance and circular slot antenna resonance. It can be clearly seen that dependence of the resonance wavelength on diameter is qualitatively different for two type of modes. The resonance wavelength of the circular slot antenna resonance follows a typical Fabry−Perot condition25−27 mλ0 = 2neff(λ)D
Figure 1. Sketch and concept. (a) Real part permittivity of SiC. The inset shows the two response regions of SiC: positive and negative permittivity regions. (b) The schematic image of the SiC circular microcavity. The angle θ is the incident angle to the sample surface.
diameters are shown in Figure 2a. It is evident that for each spectrum there are two resonances which are blue-shifted as the diameter D decreases. To better understand the resonances, finite-difference time-domain (FDTD) simulated reflectance spectra (see Methods) are presented in Figure 2b, showing good agreement with the experimental results. Each simulated spectrum clearly represents two resonance modes correspond-
Figure 2. Far field measurements. (a) FTIR reflectance of the circular microcavities with different diameters. (b) FDTD simulated reflectance of the circular microcavities. In b, from top to down, the curves are for microcavity diameters 3.0, 3.8, 4.8, and 6.0 μm. The curves are shifted vertically to be seen clearly. The inset images are the simulated field distributions of Ez (real part field enhancement with respect to the incident field) at two resonance positions λ = 10.18 μm (positive permittivity of SiC) and λ = 10.67 μm (negative permittivity of SiC) of the 6 μm infrared antenna. 5052
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Figure 3. Near-field imaging of the SPhP resonances. (a) Near-field resonance pattern of a 3 μm microcavity at λ = 10.61 μm. The near-field SNOM images are recorded with a Pt tip and a Si tip and compared to a FDTD simulation. The upper panel shows the amplitude S3 of the SNOM images. The lower panel is the phase φ3. The FDTD simulated image shows the field enhancement with respect to the incident field (|Ez/E0|). (b) Near-field resonance pattern of a 6 μm microcavity at λ = 10.67 μm with the same information as part a.
from a metallic mirror and depends on the height of the cavity walls in the gold film.11 In Figure 4, it is also seen that for the cavity diameters smaller (larger) than 4.5 μm the fundamental (0, 1) (second order (1, 1)) mode is excited in the FTIR spectra in a good agreement with the near-field observation (Figure 3). An important quantity to describe the quality of the infrared resonator is the Q factor (ω0/fwhm, full-width at halfmaximum) of its resonances. From Figure 2, we estimate the Q factor of the circular slot antenna resonance to be about 10− 20. To avoid coupling to the broad resonance of the circular slot antenna mode and improve accuracy of the Q factors evaluation for the SPhP resonances, we do the reflection spectral measurement under grazing incidence (see Methods). Because of the large incident angle (θ ≈ 83°), the circular slot antenna resonance is largely eliminated from the spectra, so that only SPhP resonance is excited and detected as shown in Figure 5a. From these spectra, we calculate the Q factor of the SPhP cavity resonance to be about 50−70 (Figure 5b). It should be noted that as an intrinsic parameter to describe the
Figure 4. Resonance conditions. Lines are presented as the theoretical resonance wavelength as a function of microcavity diameter. For the circular slot antenna resonances, the solid green curve shows the fundamental mode (m = 1). For the SPhP resonances, solid blue and red lines show the first two modes (1, 0) and (1, 1). The square (round) dots present the experimental data of the slot antenna (SPhP) resonances. The dashed curves present higher order modes for the circular slot antenna resonances and SPhP resonances, correspondingly.
(m = 1, 2, 3...) for a fundamental mode (m = 1). Here the influence of the substrate is taken into account via the effective refractive index26,27 neff(λ) = ([1 + εSiC(λ)]/2)1/2. λ0 is the resonance wavelength, and D is the diameter of the hole. Due to the variation of SiC permittivity, the resonance wavelength of the slot antenna mode does not have a linear dependence on the diameter. The walls of the hole in gold film define the circular cavity for SPhP wave supported by the air/SiC interface. Modes of such a cavity are defined by the following resonance condition28 kSPhPD + φ = ρm,n, where kSPhP is the SPhP wavenumber29 kSPhP = k0(εSiC/(1 + εSiC))1/2, k0 is the free space wavenumber, φ is the phase increment upon the cavity boundary, and ρm,n is the mth zero-crossing of the nth Bessel function of the first kind Jn(ρ). In Figure 4, the first few modes of the cavity are plotted assuming a phase shift of −π/2. This negative phase increment, φ = −π/2, for the SPhP reflecting from the metallic cavity walls is similar to the negative phase shift for a plane wave reflecting
Figure 5. Q factor. (a) FTIR reflectance of these circular microcavities under grazing incidence. (b) The Q factor of the SPhP resonance (negative permittivity of SiC) and the circular slot antenna resonance (positive permittivity of SiC) as a function of the antenna diameter D. 5053
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antenna resonance properties the Q-factor of the SPhP resonance does not depend on the incident angle but depends on the permittivity of SiC and the thickness of the gold film. The Q factor of SPhP resonance is larger than that of the dipole-like slot antenna resonance (Q ∼ 10−20), Mie scattering (Q ∼ 10−30) of the SiC whiskers,30 and the SPP resonance (Q ∼ 10−20) with similar geometries.7−12 This large Q factor benefits from the weak damping of SPhP on the air/SiC interface.16−19 We also notice that the Q factor of our SPhP resonance is higher as compared to the theoretically proposed localized SPhP resonance (Q ∼ 50−60) of SiC nanodisks18 and in the same order as the localized SPhP resonance (Q ∼ 40− 135) of SiC pillar arrays.19 The Q factor of our circular microcavities may be further improved by increasing the height of the cavity11 or coupling the microcavities in an array.19 In conclusion, we have experimentally demonstrated the SPhP resonances of single circular microcavities in the midinfrared range. The microsized hole in a thin gold film deposited on SiC substrate acts as a resonant cavity for SPhPs. The infrared spectra clearly show two type resonance modes supported by the studied structure: circular slot antenna resonance (Q = 10−20) and SPhP resonances (Q = 50−70). Owing to the high field enhancement of the two types of resonances, surface-enhanced infrared absorption31−34 and near-field spectroscopy16,35 experiments using this simple structure are possible. Because the two types of resonances can be tuned, they have the opportunity to cover a certain frequency range in the mid-infrared region. Furthermore, by changing the SiC substrate to other polar crystals36 (such as InSb, GaN), the two types of resonances can cover other infrared frequency ranges. These microcavities may be fabricated with other geometries to realize infrared applications such as beaming,11 color filtering,12 waveguiding,37 lasing,38 and so on. These circular microcavities may also be fabricated with semiconductor materials (such as doped InAs) to realize SPP resonance in infrared frequencies.39,40 Moreover, these planar circular microcavities can be easily integrated with other components so that integrated SPhP devices41 at infrared frequencies may be realized in the near future. Methods. Sample Preparations. The SiC microcavities are fabricated using colloidal nanosphere lithography on a SiC 6-H substrate (CrysTec, Berlin, Germany). During the preparation, the SiC substrates are first dispersed with the polystyrene microspheres (Polyscience, Inc.) with different diameters (3, 3.5, 3.8, 4.0, 4.8, 5.0, 5.3, 6, 6.3, and 7 μm) before the deposition of 40 nm thick gold films. Then, the samples are immersed in a toluene solution to etch the polystyrene spheres for more than 24 h. After resolving the polystyrene spheres, circular microcavities with different diameters are ready for measurements. FTIR Reflectance Measurement. The FTIR reflectance spectra are taken with a Bruker Vertex 70 Fourier transform infrared (FTIR) spectrometer in combination with a Hyperion 2000 infrared microscope. The objective used for the measurements in Figure 2 has a 36 times magnification, and its numerical aperture is 0.5 with an incidence angle centered at about 23°. The FTIR spectra are recorded using a MCT (mercury cadmium telluride) detector with a polarizer. During the experiments, knife edge apertures are set to form a measurement area about 20 × 20 μm2. The background spectrum is measured with the same aperture size on the flat gold film more than 50 μm far away from the micocavities as a reference. The spectra shown in Figure 2 are normalized to this
reference. The noise level of the spectra corresponds to 200 scans with a resolution of 4 cm−1 . For the spectral measurements in Figure 5, the GIR (grazing incidence reflection) objective with a 15 times magnification is used. The incidence angle of the GIR objective is about 83°, and the measurement conditions are all the same as mentioned above except the spectra are averaged over 400 scans. FDTD Simulations. To simulate the reflectance and the nearfield field distributions in Figures 2b and 3, three-dimensional finite-difference time-domain (3D-FDTD) simulations are performed using Lumerical FDTD solution v8.5. Perfectly matched layers are defined as boundary conditions of our simulation volume at a distance with respect to the aperture antenna of at least one wavelength. According to our setup, the incident angle is set to 23° for Figure 2b and 60° for Figure 3. In the simulation, a fine mesh size of 2 nm × 2 nm × 1 nm is used for the antenna. The reflectance is recorded 10 μm above the antenna, and the near-field distribution is recorded 2 nm above the antenna. In Figure 2b, the real part images of Ez are shown for the two resonances of a 6 μm circular microcavity at λ = 10.18 μm (positive permittivity of SiC, circular slot antenna resonance) and λ = 10.67 μm (negative permittivity of SiC, SPhP resonance). In Figure 3, the amplitude and phase images are presented for the SPhP cavity resonance of the 3 and 6 μm microcavities at λ = 10.61 μm and λ = 10.67 μm, respectively. It should be noted that, in all FDTD simulations, no tip is included. The optical dielectric constant of gold is described by a Drude model34 with plasma frequency ωP = 1.367 × 1016 Hz and damping frequency γ = 1.257 × 1014 Hz. The optical dielectric function used for SiC20 is 2 ⎛ ⎞ ω 2 − ωTO ⎟ εSiC = ε∞⎜1 + 2 LO 2 ωTO − iωγ − ω ⎠ ⎝
where ε∞ = 6.7, ωTO = 793 cm−1, ωLO = 969 cm−1, and γ = 4.76 cm−1. Near-Field Spectral s-SNOM. Our scattering-type SNOM23,37 (Neaspec GmbH) is based on a tapping-mode atomic force microscope (AFM) in which the AFM tip (radius a ∼ 30 nm) is vibrating with an amplitude of about 40 nm at a tapping frequency Ω ≈ 270 kHz. To probe the near fields, the tip is illuminated by a tunable mid-infrared CO2 laser (ranging from 9.2 to 11.2 μm, Edinburgh instruments), and the backscattered light from the tip is collected. To suppress background scattering from the tip shaft and the sample, the detector signal is demodulated by higher harmonic nΩ (for the experiments shown in Figure 3 n = 3). By interferometric detection, near-field optical amplitude sn and phase φn are obtained.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Excellence Initiative of the German federal and state governments, the Ministry of Innovation of North Rhine-Westphalia, and the DFG under the SFB917. This work was also supported by the Defense Acquisition Program Administration of South Korea and the 5054
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Agency for Defense Development as a part of a basic research program under the contract UD110099GD.
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