Ultrasensitive molecular absorption detection using metal slot antenna arrays

We theoretically study the transmission reduction of light passing through absorptive molecules embedded in a periodic metal slot array in a near infrared wavelength regime. From the analytically solved transmitted light, we present a simple relation given by the attenuation length of light at the resonance wavelength of the slot antennas with respect to the spectral width of the resonant transmission peak. This relation clearly explains that the control of the transmission reduction even with very low absorptive materials is possible. We investigate also the transmission reduction by absorptive molecules in a real metallic slot antenna array on a dielectric substrate and compare the results with finite difference time domain calculations. In numerical calculations, we demonstrate that the same amount of transmission reduction by a bulk absorptive material can be achieved only with one-hundredth thickness of the same material when it is embedded in an optimized Fano-resonant slot antenna array. Our relation presented in this study can contribute to label-free chemical and biological sensing as an efficient design and performance criterion for periodic slot antenna arrays. © 2015 Optical Society of America OCIS codes: (050.0050) Diffraction and gratings; (280.4788) Optical sensing and sensors; (250.5403) Plasmonics; (300.1030) Absorption. References and links 1. C. A. Balanis, Antenna Theory : Analysis and Design (John Wiley, Hoboken, 2005). 2. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011). 3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 4. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. 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Introduction
Antennas are electromagnetic (EM) devices which enable the communication between remote senders and receivers by transforming electric signals into electromagnetic waves and vice versa [1].By virtue of highly progressed nanofabrication technique, divers shapes and functionalities of antennas have been investigated for a wide frequency range from terahertz (THz) to visible frequencies [2].Highly conductive metals, also considered to be suitable material for antennas in near infrared (NIR) and visible frequencies, show a distinctive resonance property called as surface plasmon (SP) [3].Due to its smaller mode volume than that of the photon at a same frequency, it is possible to concentrate EM energy into a space overcoming the diffraction limit.As a result, the functionality of antennas is not confined to communication but extended to enhancing the light-matter interaction in linear [4] and nonlinear regimes [5].
Especially, label-free chemical and biological detections [6][7][8][9][10][11][12][13] and active transmission/reflection control of light using antennas [14] are very promising applications.While the former is usually accomplished by measuring antenna's resonance peak shift caused by the re-Fig.1.The sample geometry considered in this study.A periodic array of rectangular apertures perforated in a thin metal film is attached on a dielectric substrate.Each aperture has a same dimension of l × w × h (length×width×height) and the array has periods L x and L y along the x-and the y-axis.The dielectric constants of the substrate, the metal, molecules in the metal cavity, and the incident region are denoted as ε 3 , ε m , ε 2 , and ε 1 , in respective.
fractive index of targeted substances, the latter depends on the reduction of the resonant transmission/reflection by the absorption of surrounding materials, which can be controlled by an external stimuli.The fundamental design and performance criteria of antenna's sensitivity for a material detection is well understood by the figure of merit (FOM), the resonance peak shift per unit change of the refractive index (nm/RIU) with respect to the spectral width of the resonance peak [15].The sensitivity explained by the FOM inspires the antennas containing the Fano resonance in order to utilize its relatively narrow spectral width [16,17].A similar consideration is also requested for the decrease of the resonance peak value but has not been systematically discussed so far as we aware.
The aim of this report is to provide a clear criterion so that an efficient design of antenna arrays is allowed in the aspect of the absorption.We present an analytical form of the EM wave transmitted through (reflected from) an array of slot antennas perforated in a thin metal film, and investigate the decrease of the resonance transmission depending on the absorption of the material embedded in slot antennas (see Fig. 1).Although our analytical model based on Rayleigh expansion model (REM) is only valid for perfect electric conductor (PEC), it can be applied to real metals by including the surface impedance boundary approximation presented in [18].The numerical results from our models are compared with finite difference time domain (FDTD) simulations [19].It has already been demonstrated that single and arrays of ultranarrow slot antennas fabricated in thin metal films could be utilized for both purposes in THz regime [9,14].We demonstrate that such an ultrasensitive detection of molecular absorption can be accomplished in NIR and visible frequency regimes, when the attenuation length of light at the resonance wavelength of a slot antenna array is a comparable order of the spectral width of the resonant transmissio/reflection peak.

Mathematical model
In this section, we derive an analytical model for the transmitted light through a periodic array of rectangular slot antennas perforated on a thin metal film on a dielectric substrate, as depicted in Fig. 1.The apertures which have a same spatial dimension of a length l, a width w, and a height h are periodically arranged with periods L x and L y along the x-and the y-axis.The dielectric constants in the incident region (z > h/2), in the cavity (−h/2 ≤ z ≤ h/2), and in the substrate region (z < −h/2) are expressed by ε 1 , ε 2 , and ε 3 , in respective.
Our analytical model is derived with the same approach presented in [20][21][22] where the metal film is considered as PEC.For p-polarized incident plane wave (the magnetic field is parallel to the slot antenna length), the electromagnetic fields in three regions can be written by where with the wave number of the incident plane wave The wave number-dependent transmission and reflection coefficients f y , f z , g y , and g z and amplitudes inside the cavity A and B can be obtained by Dirichlet and Neumann boundary condition [23] at the input (z = h/2) and the output aperture plane (z = −h/2).Then, the Poynting vector of the transmitted wave through the slot array at the output aperture (z = −h/2) is written by where the incident power I 0 , the self-energy at the input/output aperture W j ( j = 1, 3), and D are defined as In the same manner, the Poynting vector of the reflected light at the input aperture (z = h/2) is obtained as The derived transmission of an array of slot antennas Eq. ( 8) has exactly the same form of the transmission of single slot antennas except for different definitions of I 0 , W j , and β [22].
Our PEC model can easily be extended to the one for real metals by considering surface impedance boundary conditions (SIBC) inside the slot aperture [24], as already discussed in single slots [25], an array of rectangular holes [18], and slit arrays [26].In this case, β must be numerically obtained by fulfilling the equation [25] tan and an additional impedance value Z s = 1/ √ ε m must be included.Although our PEC model is not suitable for a wavelength range from visible to NIR where the finite skin depth of real metals is not negligible, we can estimate with it how much transmission decrease could be expected with a simple approximation of Eq. ( 10) and (12).For slot antennas perforated in a very thin metal film and surrounded by air, we can use the following approximations, sin(β h) ≈ β h, cos(β h) ≈ 1, and decomposing the self energy into the radiative (G r ) and the evanescent mode (12).Then, Eq. ( 8) is simplified to With a complex ε 2 = ε r + iε i , it is rewritten to Equation ( 16) has exactly the same form of the Lorentzian line shape.Furthermore, it indicates that the spectral width of the transmission spectrum for ε i = 0 is determined by the radiative mode contribution of the self-energy (G r ), as explained for low dimensional semiconductors [27].At resonance (i.e.,the imaginary part of the denominator goes to zero), the transmission with an absorptive ε 2 normalized by the transmission without the absorption (T /T 0 ) is given by The normalized transmission Eq. ( 17) presents an intuitive physical explanation: a substantial decrease of the transmission peak can be measured when the attenuation length of light at the resonance wavelength in the cavity is a comparable order of the spectral width of the resonant transmission peak.

Numerical results and discussions
In this numerical study we are suppose to detecting a very low absorptive and transparent artificial material (ε = 1 + 0.01i).If such a material should be detected by a conventional light where k = 2π/λ in is the wave number, κ the imaginary value of the refractive index of the material, and L the material thickness.We show in the followings that the same transmission reduction can be obtained only with the 1/100 thickness of the same material if it is embedded in an optimized slot antenna array.
Since our studies are mainly focused in NIR wavelength regime, the aperture size is fixed to l = 350 nm, w = 50 nm, and h = 100 nm.It is well known that the maximum transmission of single PEC slot antennas occurs at the wavelength corresponding approximately to the twice the antenna length (λ 0 = 2l = 700 nm) [21], which is clearly seen in Fig. 2(a) (single).However, the transmission of periodic slot antenna arrays is controlled by the periods of slot antennas as well.For instances, by pushing the period L x near λ 0 (L x = 850 nm), a new strong and narrow transmission peak can be induced very close to the Rayleigh anomaly position (λ a 1,0 = 850 nm) as found in Fig. 2

(a) (array).
With these single and array of slot antennas, we investigate the transmission change when the slot antennas are filled by the low absorptive material (ε 2 = 1 + 0.01i).While about 10% reduction of the transmission peak value is observed with the single PEC antenna, over 20% reduction of the maximum transmission is calculated by the slot antenna array.Although the attenuation length in the metal cavity (k 0 hIm[ε 2 ]) is same for both cases, the larger transmission reduction presented by the slot antenna array is attributed to the smaller spectral width (G r ) compared to that of the single slot antenna, as explained by Eq. ( 17).
In Fig. 2(b) we perform the same calculations by replacing PEC with Au.The wavelengthdependent dielectric constant of Au is obtained from [28].Compared to the results of the PEC antenna array, the Au antenna array shows qualitatively the same tendency in the transmission.Although two transmission peaks are slightly shifted to longer wavelengths and have broader spectral widths, which are caused by the finite skin depth of Au, the absorptive ε 2 results in the same amount of the transmission reduction at the peak near the Rayleigh anomaly.
Next, we investigate the influence of the substrate on the transmission decrease.For Fig. 3 we repeat the calculations as done in Fig. 2 but with ε 3 = 2.25.In transmission spectra both for PEC (Fig. 3(a)) and Au (Fig. 3(b)) we can find additional transmission peaks caused by the Rayleigh anomaly at the output interface (z = h/2).According to the Rayleigh anomaly position determined by λ , the first and the second order Rayleigh anomalies at the dielectric interface are located at λ d 1,0 = 1275 nm and λ d 1,1 = 735 nm with much narrower spectral widths, as found in PEC and Au arrays.Although the dielectric substrate brings about overall smaller changes of the transmission between the non-absorptive and the absorptive ε 2 , the transmission reduction at the peak near λ d 1,0 is more substantial than those at other peak positions.
The results calculated by our REM models are compared with the rigorous FDTD simulations [29] presented in Fig. 4. For the PEC slot array (Fig. 3 and Fig. 4(a)), both methods show a good agreement in the transmission peak at λ a 1,0 and its reduction by the absorptive ε 2 .At the transmission peak near λ d 1,0 , although the peak value from the REM model differs from the one calculated by FDTD, the absorptive ε 2 results in a similar amount of the transmission decrease in both calculations.For the Au slot antenna array (Fig. 3 and Fig. 4(b)), the REM and FDTD simulation results show differences in transmission spectra.Two transmission peaks near λ a 1,0 and λ d 1,0 are shifted to longer wavelengths and have broader spectral widths by the FDTD simulation (Fig. 4(b)).These differences are originated from the insufficient consideration of the boundary condition in the REM where the SIBC are considered only at the interfaces inside the aperture.Anyway, the substantial transmission reduction by the absorptive ε 2 at λ d 1,0 is reproduced by the FDTD simulations as well.
Finally, we investigate the transmission variance of the Au slot antenna array when the absorptive ε 2 has a dispersive property like atoms and molecules.In order to stress the resonance absorption of the ε 2 , ε 2 is described by a Lorentz oscillator model where the resonance wavelength is matched to that of the maximum transmission peak found in the REM or FDTD simulations, but the maximum imaginary value of ε 2 is fixed to 0.1 in both cases with a constant value of the decay rate Γ = 10 13 rad/s.The numerical results computed by two independent methods are presented in Fig. 5(a) and (b).In both calculations over 50 % of the transmission decrease can be found.Especially, Fig. 5(b) shows a narrow spectral dip at the resonance peak, whereas Fig. 5(a) presents overall decrease of the transmission peak value.This qualitative difference in the transmission spectrum is caused by the spectral width difference between the absorption of ε 2 and the transmission peak.Figure 5(a) belongs to the case when the spectral width of the absorption is larger than that of the transmission peak.On the contrary, Fig. 5(b) can appear when the spectral width of the absorption is smaller than that of the transmission peak.

Conclusion
In summary, we theoretically studied the transmission of light propagating through absorptive materials which are embedded in periodic metal slot arrays.We derived an analytical form of the transmission with a Rayleigh expansion method and showed a simple criterion that a substantial decrease of the transmission could be measured, when the attenuation length at the resonance wavelength is a similar order of the spectral width of the resonant transmission peak.Our criterion was numerically confirmed with a periodic slot antenna array with a Fano resonance in NIR wavelength regime.By the low absorptive material embedded in the slot antenna cavity, the narrower transmission peaks near Rayleigh anomalies were substantially decreased than the broader peaks at the resonance wavelength of the antennas.We discussed also the transmission reduction for a real metal and an substrate and compared results with FDTD calculations.We foresee that our criterion suggested in this study can contribute to efficient design of periodic slot antenna arrays for label-free chemical and biological sensing.