Slant-gap plasmonic nanoantenna for optical chirality enhancement

We present a new design of plasmonic nanoantenna with a slant gap for optical chirality engineering. At resonance, the slant gap provides highly enhanced electric field parallel to external magnetic field with a phase delay of 90 degree, resulting in enhanced optical chirality. We show by numerical simulations that upon linearly polarized excitation our achiral nanoantenna can generate near field with enhanced optical chirality that can be tuned by the slant angle and resonance condition. Our design can be easily realized and may find applications in circular dichroism enhancement.

Interaction between circularly polarized light (CPL) and chiral matters is of interest because it reveals structural details of molecules that can be critical for their chemical functions. 1 However, such interaction is usually weak due to the mismatch between pitch length of CPL and electronic confinement of the chiral matter. 2,3 One example is the weak circular dichroism (CD) of chiral molecules. CD is the differential absorption of CPL by chiral matters, originating from the coupling between induced electric dipole and magnetic dipole moment. 4 Cohen and co-workers 5 have recently shown that the dissymmetry factor used for CD is proportional to the optical , where is the angular frequency of the time-harmonic electromagnetic field and K is a factor determined by the electric polarizability and isotropic mixed electric-magnetic dipole polarizability of the chiral matter. Accordingly, they showed enhanced contrast in fluorescencedetected circular dichroism (FDCD) of chiral molecules at energy minima of a standing wave. 7 However, the minimum energy density also means low excitation rate and thus low fluorescence intensity that might limit the detection sensitivity. According to equation (1), an alternative way to enhance CD is to directly enhance the optical chirality of the field. Since the optical chirality can be expressed as 5 , the key to an enhanced CD is to obtain strongly enhanced electric fields that are parallel to the magnetic field with a phase difference of 2 � . [8][9][10] Resonant plasmonic nanostructures can localize and enhance optical near field. Therefore, they may function as optical antennas and improve the mismatch between light and nanoscale objects. [11][12][13] The ability of plasmonic nanostructures to enhance and sculpt optical near fields have recently drawn research attention. On the one hand, various plasmonic nanostructures have been proposed to manipulate the polarization state of light field or to show chiroptical response themselves. [14][15][16][17][18][19][20][21][22][23][24][25][26] On the other hand, plasmonic nanostructures and dielectric particles have been reported to create light fields for enhancing chiral light-matter interaction. [8][9][10]27,28 Here we present a new design of slant-gap plasmonic nanoantennas and theoretically show that optical chirality of the field in the slant gap is greatly enhanced upon resonant excitation.
The working principle is based on the fact that the electric field lines at the vicinity of nanostructures are well perpendicular to the metal boundaries. Therefore, the optical near field in the slant gap automatically provides a component perpendicular to the longitudinal axis of antenna. At longitudinal resonance of the antenna, such electric field component is greatly enhanced in amplitude, delayed 2 � in phase and well parallel to the magnetic field of external excitation. As a result, an enhanced optical chirality is obtained inside the gap. We choose to excite the slant-gap nanoantenna with the near field of linearly polarized plane wave undergoing total internal reflection (TIR). Such TIR excitation scheme can efficiently suppress the noise from background and is particularly useful for CD analysis of ultra-dilute chiral matters at surface. [29][30][31][32] Since the slant-gap nanoantenna is achiral, the nanostructure itself does not give CD signal but creates optical near fields with enhanced OC that facilitates CD analysis of chiral matters. tilted in x-z plane by degree with respect to the surface normal, i.e. the z axis. The excitation source is s-polarized plane wave undergoing TIR at air/glass interface on x-y plane. For the excitation configuration in Figure 1(a), the significant near-field components at the TIR interface are ����⃑ = � 2 cos and ����⃑ = � 2 cos sin , where = tan −1 � �sin 2 − 2 � 1/2 cos �, is the TIR incident angle, = 2 / 1 < 1 and is the amplitude of s-polarized electric field component of the impinging plane waves. 29,31 For a nanoantenna on the interface and aligned in x direction, the ����⃑ component of the TIR near field excites the longitudinal surface plasmon resonance and results in highly enhanced optical near field with certain phase shift inside the gap. 13 The field in the gap, ����⃑ can be expressed as , where ����⃑ is the longitudinal electric field component of the TIR near field at the interface, is the phase delay relative to external excitation, is the field amplitude enhancement and � is the unit vector normal to the metal surface. At resonance, the phase shift approaches 90 degree and the field enhancement reaches a maximum value. Since the gap is slant, the enhanced field in the gap is no longer parallel to the antenna long axis, as shown in Figure 1(b). As a result, the resonant optical near field automatically provide an out-of-plane electric field component ����⃑ , which can be expressed as , with being the slant angle of the gap relative to the interface (x-y plane). Such an out-of-plane electric field component is parallel to the out-of-plane magnetic field components of the TIR near field ( ����⃑ ), leading to an enhanced optical chirality in the gap. Combining equation (2), (3), (6) and (7), the optical chirality can be expressed as For constant , and , optical chirality of the near field in the gap is a function of , , and .
In the following, we numerically study the optical chirality in the gap as a function of antenna resonance condition and the slant angle of the gap. corners also show OCE, the sign alternates and the contribution vanishes when OCE is integrated over space. 9 Therefore, the overall OCE is dominated by the field inside the gap. Since the magnitude of out-of-plane electric field is proportional to cos , it is intuitive to choose a small in order to obtain large OCE. However, varying slant angle can change the antenna geometry significantly and distort the resonance spectrum. Consequently, the field enhancement factor ( ) varies with the slant angle. Therefore, the slant angle must be optimized carefully such that × cos is maximized. Figure 3 Table 1. These geometries show either very small or zero overall OCE. For example, normally incident excitation (Figure 4(a)) gives large field enhancement in the gap but results in zero overall OCE because the enhanced electric fields are orthogonal to the magnetic field. As for the excitation geometry shown in Figure 4(b), it is similar to the geometry in Figure 1(a) but using p-polarized incident plane waves. Finite OCE is obtained due to the overlap of in-plane electric (E x ) and magnetic field component (H x ). However, the OCE is much smaller since it relies on the transverse resonance of the antenna that has relatively low field enhancement at 374 THz. In fact, the slant gap concept is general and the slant angle is not limited to out-of-plane direction (i.e. x-z plane in Figure 1). The gap may also be tilted in-plane (i.e. x-y plane in Figure 1), as long as the excitation geometry is adjusted accordingly.
In order to maximize the interaction area, the slant-gap concept can be extended into an array of grooves, as depicted in Figure 5(a). The lateral cross section in x-z plane is essentially an array of antenna arms. Similar to solitary gap nanoantennas, the resonance can be tuned by changing the material, the thickness, gap sized and the periodicity. Figure 5(b) and Figure 5(c) show the cross sectional distribution of OCE in x-z plane and x-y plane, respectively. The period of the gold slant groove array is 100 nm. The height and the gap size are 30 nm and 10 nm, respectively. Compared to solitary antennas, the resonance condition changes and the field enhancement decreases due to the inter-arm coupling and the extended dimension in y direction.
Nevertheless, the OCE inside the gap has a non-zero value with a sign that is slant angle dependent. The overall OCE obtained from integration over the cross sectional area of a unit cell also shows finite non-zero value that is dominated by the field in the gap. The OCE at outer corners exhibits alternating sign and do not contribute to overall OCE. In practice, depositing a layer of transparent dielectric material may further prevent the chiral matters from interaction with the corner fields. For FDCD detection, such a thin layer can also prevent fluorescence quenching. Slant groove array can be easily fabricated by modern nanofabrication techniques, for example by focused-ion beam (FIB) milling with a tilted angle. Figure 5(d) shows a representative example of an array of slant grooves on a single crystalline gold flake fabricated by FIB milling with a tilt angle of 52 degree relative to the sample surface normal. Other lithography methods such as e-beam lithography might also be applied to fabricate slant grooves by, for example, tilting the sample during the evaporation or dry etching. 36 For chiral matters that give CD response in the UV spectral regime, our concept is applicable but the material should be changed to aluminum. 13,37,38 In conclusion, we have presented the design of slant-gap nanoantennas excited by total internal reflection scheme. The slant gap offers strong field with enhanced optical chirality that can be controlled and optimized by the resonance condition and the gap slant angle. The slantgap nanoantenna is achiral and the excitation is linear. Therefore, the nanostructure itself does not give CD response (Supporting Information) but provides optical field with enhanced optical chirality for chiral matters. Together with total internal reflection excitation, the noise from the background can be greatly suppressed. Such enhanced optical chirality by linearly polarized light would be particularly useful for fluorescence-detected circular dichroism analysis of very dilute chiral matters at surface. 39 The enhanced optical chirality may also facilitate photo-induced enantiomeric excess control. 40,41 Our design is simple and easy to realize. We anticipate many applications in plasmon-enhanced chirality detection and control.

Configuration
Field enhancement (f e ) Overall OCE

CD of slant-gap nanoantenna
Figure S1 (a) shows the difference in the absorbance of the slant-gap nanoantenna (total antenna length = 160 nm) illuminated by left-handed and right-handed circularly polarized light. Corresponding dissymmetry factor is plotted in Figure S1 (b). The result shows that the slantgap nanoantenna is achiral and does not give CD signal.