Letter pubs.acs.org/NanoLett
Colossal Absorption of Molecules Inside Single Terahertz Nanoantennas Hyeong-Ryeol Park,† Kwang Jun Ahn,‡ Sanghoon Han,§ Young-Mi Bahk,† Namkyoo Park,§ and Dai-Sik Kim*,† †
Center for Subwavelength Optics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea Global Frontier Center for Multiscale Energy Systems, Seoul National University, Seoul 151-742, Korea § Photonic Systems Laboratory, School of EECS, Seoul National University, Seoul 151-744, Korea ‡
S Supporting Information *
ABSTRACT: Molecules have extremely small absorption cross sections in the terahertz range even under resonant conditions, which severely limit their detectability, often requiring tens of milligrams. We demonstrate that nanoantennas tailored for the terahertz range resolves the small molecular cross section problem. The extremely asymmetric electromagnetic environment inside the slot antenna, which finds the electric field being enhanced by thousand times with the magnetic field changed little, forces the molecular cross section to be enhanced by >103 accompanied by a colossal absorption coefficient of ∼170 000 cm−1. Tens of nanograms of small molecules such as 1,3,5trinitroperhydro-1,3,5-triazine (RDX) and lactose drop-cast over an area of 10 mm2, with only tens of femtograms of molecules inside the single nanoslot, can readily be detected. Our work enables terahertz sensing of chemical and biological molecules in ultrasmall quantities. KEYWORDS: Terahertz nano, terahertz molecule sensing, terahertz absorption, terahertz absorption coefficient, terahertz cross section, terahertz nanoantenna electric field E, and magnetic field H, the Fermi’s golden rule states that the energy loss per unit time is proportional to μ2E2, which depletes from the incident energy flux S⃗ = E⃗ × H⃗ * (= EH). Therefore, the quantum mechanical absorption cross section σ can be written as follows:36
T
he demand for new chemical and biological sensing has been dramatically increasing in optical,1−3 infrared,4,5 terahertz (THz),6−8 or microwave9 regimes. Especially, the emergence of diverse materials, including organic- and biomolecules that respond resonantly to the THz waves, raises the possibility of sensitive THz detection.10−12 For improving sensitivities, various THz molecule sensing techniques utilizing parallel plate waveguide,13,14 microresonator,15 and frequency filter,16−19 have been developed, mostly by increasing the effective interaction length.20 Recently, plasmonic nanoantennas,21−23 which support collective resonances with strong local field in the infrared frequencies,24 have been suggested as a tool for the molecular detection, enhancing absorption signals of molecules around the antennas by 4−5 orders of magnitude.25−27 However, these tools have intrinsic limitations to measure the absolute absorptivity and cross section of their respective molecules due to the greater quantitative uncertainties of the reacting molecules in and around the positive-mold antennas and the lack of simple measure for energy and field enhancements. Meanwhile negative slot antennas28 allow simple and precise analysis of the electromagnetic fields over the whole aperture, both in terms of energy and field enhancements.29−35 When a molecule with a dipole moment μ is subject to an electromagnetic wave with intensity (Poynting vector) S, © 2013 American Chemical Society
σ=
ℏω 2π 2 2 2π 2 E2 μ E ρ(ℏω0) 0 = μ ρ(ℏω0)ℏω0 ℏ S ℏ S
(1)
where ρ(ℏω0) is the density of states, ω0 and S are the resonant angular frequency and the Poynting vector of the incident light, respectively (See Supporting Information for further details). In free space, (E2/S) = (E/H) = Z0 (Z0 = 377 Ω), and therefore σ = (2π/ℏ)μ2ρ(ℏω0)ℏω0Z0. Inside a terahertz nanoslot antenna (Figure 1a),37−39 however, the case is strikingly different although eq 1 is still valid. Dictated by the boundary condition of the metal slot, the electromagnetic wave is strongly perturbed, and the resultant electric field is enhanced by orders of magnitudes, in contrast to the magnetic field which deviates little from the incident value, within a factor of two.40,41 This extremely asymmetric electromagnetic environment in turn forces the cross section of the molecules to Received: January 29, 2013 Revised: February 20, 2013 Published: February 26, 2013 1782
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Figure 1. (a) The giant absorption cross section of RDX (1,3,5-trinitroperhydro-1,3,5-triazine) molecules inside a THz nanoslot antenna is induced by an asymmetric electromagnetic environment with E/Z0H ratio of about 103. The p-polarized terahertz pulses with polarization perpendicular to the long axis of the rectangle are normally incident on the sample. (b) Absorption spectrum using 1 mg of RDX molecules onto the bare quartz substrate. (c) Transmission spectra for RDX amounts ranging from 2 μg to 200 μg onto the bare quartz. (d) Transmission spectra for a single THz nanoslot antenna, having dimensions of the length 90 μm, the width 50 nm, and the metal thickness 50 nm, without and with RDX ranging from 40 ng to 2 μg.
Figure 2. (a, Left) Schematic of a single THz nanoslot antenna with a length of l = 90 μm, a width of w, and a thickness of h. (Right) SEM images of some of our slot samples with w = 50, 500, 1000, and 5000 nm from left to right. (b) Normalized resonant transmissions measured at 0.87 THz for all the slots: w = 50 nm (h = 50 nm), 100, 200, 500, 1000, and 5000 nm (h = 100 nm), with the RDX amounts ranging from 0 to 2 μg. (c) Peak absorption coefficients and cross sections of RDX molecules inside slots, plotted against the width w (red squares). The fit (black dashed line) indicates a 1/w dependence. (d) The schematic diagram of the molecular cross section characteristics for three types of asymmetric electromagnetic environments of E/Z0H = 1, 103, and 105.
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Figure 3. (a) SEM images of two nanoslot antennas with different lengths of 90 and 150 μm, having resonances of 0.9 THz and 0.5 THz, respectively. (b) Transmission spectra through the two nanoslot antennas without and with RDX amounts ranged from 0 to 2 μg. (c) Absorption spectrum using 1.5 mg lactose molecules onto the bare substrate. The peak absorption at 0.54 THz is well-matched to the fundamental resonance of the 150 μm length nanoslot antenna. (d) Transmission spectra for the 150 μm length nanoslot antenna with lactose amounts ranged from 0 to 1 μg.
enhancement factor follows ∑ = (E2/Z0S) ∝ (l/w), as expected from an analytical calculation based on modal expansion26,29 (for more details, see Supporting Information), we vary the nanoantenna width. Single THz slot antennas with fixed l = 90 μm and varying widths (w) in thin gold films with the thickness of h were fabricated using a focused ion beam machine on a 500 μm thick quartz substrate, as shown in Figure 2a (left), with their resonance peaks at around 0.87 THz. Figure 2a (right) presents SEM images of some of our slot samples with w = 50, 500, 1000, and 5000 nm from left to right. The RDX molecules were filled inside the nanoslot by simple drop casting over an area of ∼8 mm2. The solutions were diluted from the RDX standard solution (Accustandard, Inc.) containing 1 mg/mL of RDX in acetonitrile/methanol.13 It is emphasized that although the RDX solutions from 0.02 to 2 μL were drop-cast over the said area, actually participating are only a few tens to hundreds of femtograms inside the slot. Figure 2b shows normalized resonant transmissions measured at 0.87 THz for the slots: w = 50 nm (h = 50 nm), 100, 200, 500, 1000, and 5000 nm (h = 100 nm), with the increasing RDX amounts up to 2 μg. For most of the samples, the transmission decrease saturates at ∼0.1 μg of RDX, consistent with the RDX film thickness t ∼ h. From these data, using the Beer’s law, we obtain the absorption coefficient α thereby the absorption cross section σ through α = σN = −(1/t)ln(T/T0). The number density of dried molecules is estimated as N = 4.93 × 1021cm−3, and T and T0 are the transmissions with and without RDX molecules, respectively. Figure 2c plots absorption coefficient and cross sections as a function of the antenna width w. The experimentally obtained α and σ are inversely proportional to w as expected, and are a few thousand times larger than the bulk values shown in Figure 1b, also consistent with what we predict from the ∑ ∝(l/w) dependence using our theoretical calculation.
become larger by a huge factor ∑ = (E2/Z0S) = (E/Z0H), at least 3 orders of magnitude, resulting in the absorption coefficient α reaching the colossal value of >100 000 cm−1. To probe absorption cross sections of molecules in THz region, we perform THz time-domain spectroscopy40,42,43 for the frequencies ranging from 0.3 to 2.0 THz. In Figure 1b, it was found that the drop-cast 1 mg RDX (1,3,5-trinitroperhydro-1,3,5-triazine) molecules over an area of ∼80 mm2 on the bare quartz have the most prominent absorption peak near 0.83 THz, in agreement with the previous free space THz measurements.44,45 It should be noted, as shown in Figure 1c, that we really do need 1 mg of RDX to get meaningful decrease in transmission- there is little change between 2 μg to 200 μg on the bare quartz. For observing small quantities of the molecules as promised by the unique electromagnetic environments of the slot antenna, we first designed a single THz nanoantenna with a large length/width ratio of l/w = 90 μm/50 nm =1800, to have 3 orders of magnitudes of electric field enhancement.29 The resonance wavelength of the antenna satisfies the condition λres = 2neffl, where neff is the effective index of refraction of the antenna−substrate composite.29,31 The length is designed to match one of the RDX absorption bands, about 0.8 THz, attributed to molecular conformations or a weak hydrogen bond between two RDX molecules.46,47 The contribution of the direct transmission through the unpatterned gold film is subtracted when obtaining the transmission spectra through the single nanoantennas. Strikingly, when we put RDX molecules into the metallic substrate with tailored nanoslot in the middle, as shown in Figure 1a, we start to see significant decrease in the resonant transmission intensity already for the amount of 40 ng spread over a sample area of 8 mm2, amounting to 22 fg inside the slot cavity (Figure 1d). For the amount of 2 μg RDX molecules, the resonance is almost gone. To see if the cross section 1784
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The maximum α and σ are, respectively, 170 000 cm−1 and 3.6 × 10−17 cm2 for the 50 nm width slot, about 2800 times larger than the values on the bare substrate. Hereby, it is possible to estimate how much more energy a single molecule inside the slot absorbs compared with the bare substrate. Since the absorbed power per molecule is σS, we need to approximate the Poynting vector enhancement as well: from the electric field enhancement of 2500 experimentally measured through the Kirchhoff formalism39,40,48 (see Supporting Information for further detail), we estimate the Poynting vector enhancement of ∼2900.29,49 The molecular absorption enhancement is therefore 2800 × 2900 ≈ 8 × 106. This is also in good quantitative agreement with the absorption enhancements estimated by PEC calculations and FDTD simulations (see Supporting Information). As made evident by these findings, because electric field E is much more enhanced than magnetic field Z0H inside the slot, it should be possible to amplify the molecular cross section inside the slot antenna further by closing the width even more (Figure 2d, middle). In this situation, only the ratio of E to Z0H, not the absolute power of the excited light is important to modulate the cross section. Using an ultimate nanoslot with a width of below 1 nm, it would be possible to reach 105 of the E/Z0H ratio necessary to induce the enhanced molecular cross section to approach the actual molecular size of ∼10−14 cm2 = 1 nm2 (Figure 2d, right). We now explore the possibility of extending our method to encompass any molecules with resonances in terahertz. We manufacture two single THz nanoslot antennas with the same width of 120 nm, same thickness of 100 nm, and different lengths l = 90 and 150 μm, having the resonances at 0.9 THz and 0.5 THz, respectively (Figure 3a). In stark contrast to the 90 μm length slot antenna, spectra for the 150 μm length slot antenna change little, as shown in Figure 3b. We put lactose molecules, which have substantial cross section near 0.5 THz (Figure 3c),50 into the 150 μm length slot antenna. The change in transmission is as dramatic as the RDX case (Figure 3d), and we deduce an enhanced absorption coefficient of 164,000 cm−1 demonstrating the generality of our terahertz nanoslot technology. In summary, we have demonstrated the molecular cross section and absorption coefficient enhancement created by the asymmetric electromagnetic environment with E/Z0H ratio of over 103 inside nanoslots. Up to 2800 enhancement of absorption cross section of RDX molecules, leading to the giant molecular absorption enhancement of 8 × 106, enables detection of extremely small quantities near 40 ng (22 fg inside the slot). With orders of magnitudes improved sensitivities and demonstrated generality, our method could pave the way toward THz intermolecular fingerprinting of target molecules, as well as ultrasmall quantity THz spectroscopy of chemicals and biological molecules in their developmental stages.
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simulations. This material is available free of charge via the Internet at http://pubs.acs.org.
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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 National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (SRC, No: 2008-0062255) (GRL, No: K20815000003) (Others, No: 2010-0029648, 2011-0019170, 2011-0020209), and Hi Seoul Science/Humanities Fellowship from Seoul Scholarship Foundation. We thank J. Y. Rhie for technical assistance with sample fabrication.
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ASSOCIATED CONTENT
S Supporting Information *
Derivation of quantum mechanical absorption cross section. Terahertz time-domain measurement and estimation of field enhancements. Analytical calculation based on modal expansion with slot antenna array. Molecular absorption enhancements inside slot antenna array in a PEC film estimated by the analytical model. Molecular absorption enhancements inside slot antenna array in a real metal film estimated by the FDTD 1785
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