Antenna-enhancements of molecular vibrational responses in ultrafast infrared spectroscopy

We demonstrate surface-enhanced ultrafast vibrational spectroscopy employing periodic arrays of infrared-resonant gold nanoantennas. The antenna-enhancements of molecular vibrational responses are analytically formulated with a simple coupled-dipole model, and the linear/nonlinear local signal enhancements are evaluated to be ~104 and 107, respectively.


Introduction
Ultrafast infrared (IR) spectroscopy, including pump-probe and two-dimensional methods, is a powerful, label-free tool to resolve molecular conformational structures, structural dynamics, vibrational relaxations, etc. [1]. Despite their fascinating potential, however, their applications are somewhat limited because of insufficient detection sensitivity, which is due to small dipole moments of vibrational transitions. A promising approach for increasing the sensitivity is to amplify the interaction of molecular vibrations with IR ultrashort pulses by employing IR-resonant nanoantennas [2]. Recently, it has been demonstrated that nonlinear vibrational signals are amplified with colloidal gold nanoparticles [3] and randomly-arranged resonant nanoantennas [4]. However, further study is necessary to increase the sensitivity and to add new functionalities for wide use in materials science and life science.
In this contribution, we demonstrate surface-enhanced ultrafast vibrational spectroscopy by using periodically-arranged IR-resonant nanoantennas, which satisfy the condition near the collective resonance [5,6]. In addition, we analytically formulate the antennaenhancements of molecular vibrational responses with a simple coupled-dipole model ( Fig.  1(a)), and evaluate the linear/nonlinear local signal enhancement factors by analyzing the experimental data with the analytic formulae.

Experimental methods and results
We perform linear/nonlinear spectroscopies for a W(CO)6-dispersed 200-nm thick PMMA film, deposited on gold nanoantenna arrays. Each nanoantenna (100-nm wide, 30-nm high, and 1100-nm long) is arranged on a CaF2 substrate at a period of 2.7 µm (1.6 µm) in the direction of its shorter axis (longer axis). Figure 1 sample with nanoantennas (blue) and the absorption spectrum for the sample without nanoantennas (red). The broad resonance peak of the nanoantennas is modulated at the resonance frequencies of the two vibrational modes (T1u CO stretching mode of W(CO)6 at 1980 cm -1 and CO stretching mode of PMMA at 1737 cm -1 ), with spectral features characteristic to Fano resonance. The nonlinear pump-probe spectroscopy is performed in reflection geometry, as shown in Fig. 1(c). The transient reflectance change spectra for T1u mode of W(CO)6 is clearly observed with a pump energy of as low as 10 nJ, as shown in Fig.  1(d), which is due to the substantially-enhanced near-fields of the nanoantenna arrays. The increased reflectance is attributed to the depletion of the v = 0 state and the stimulated emission from the v = 1 state, and the decreased reflectance is attributed to the induced absorption of the v = 1-2 transition. Here we note that the relaxation dynamics, shown in the inset of Fig. 1(d), does not change due to coupling to the nanoantenna.

Analytical formulation and discussion
We consider a coupled-dipole model, where an antenna A and N-molecules (V1, V2, … ,VN) are coupled through their near-fields, as illustrated in Fig. 1(a). Here the antenna A and each molecule Vj is characterized by a linear polarizability " ( ) and & ( ), respectively. If the antenna polarizability " ( ) is much larger than the molecular polarizability & ( ) , coupled-dipole equations are given in a scalar form as where rj is the distance between the antenna and the j-th molecule, and G is a Green function, which defines the interaction between the antenna and each molecule. Equation which indicates that vibrational polarization is amplified by a factor of 8 " √ ̅ (A) 9 A ≡ M . By considering the third-order nonlinear responses of the molecules, the total dipole moment of the antenna is expressed in the same manner as where & (N) denotes the third-order nonlinear polarizability of each molecule. Here we see that the nonlinear polarization is amplified by a factor of 8 " √ O ̅ (P) 9 P ≡ RM . Equations (5, 6) describe that the signal enhancement factors of FL and FNL increase monotonically with each of the nanoantenna polarizability, the coupling strength, and the number of molecules coupled to the nanoantenna.
By analyzing the data shown in Fig. 1(b, d) using Eqs. (5, 6), we evaluate the signal enhancement factors to be M~1 0 P and RM~1 0 V . From these numbers, the field enhancement factor is estimated to be ~10 2 , which is in reasonable agreement with FDTD simulations.