When light illuminates a narrow slit in a metal sheet, more light sometimes emerges on the other side than shone on the area of the slit. Since the original discovery of this extraordinary-transmission phenomenon,^{1} the field has witnessed some controversy, because several effects can contribute. For example, both surface excitations of the metal and electromagnetic modes localized at the slit can transfer light energy from the surrounding metal through the slit.

We performed a theoretical investigation of frequency doubling, commonly known as second harmonic generation (SHG), in addition to the linear transmission. SHG originates from the nonlinear, magnetic Lorentz force term from single and multiple apertures carved on metal substrates.^{2} Both the transmission and SHG processes depend mostly on the geometry of the slit. We investigated forward and backward SHG efficiencies and their link to linear response, for single and multiple apertures. Our results show that excitation of tightly confined modes, combined with enhanced transmission and nonlinear processes, may hold the promise of new applications, such as photolithography, scanning microscopy, and high-density optical data-storage devices.

Previously, light transmission and reflection from subwavelength holes on perfect-electric-conductor screens have been studied extensively. Including the finite metal permittivity in the calculations significantly changes the transmission peculiarities. A combination of cavity effects and longitudinal-surface-plasmon generation leads to extraordinary transmission and enhanced SHG in similar geometrical regimes. We solved Maxwell's equations by two independent means: a finite-difference, time-domain (FDTD) method and a time-domain fast-Fourier-transform beam propagation (FFT-BPM) method, which takes a completely different approach and confirms the FDTD results.

Light transmission from a subwavelength slit depends on two parameters: the thickness of the metallic substrate, and the slit width: see Figure1(a). We normalize the calculated linear transmittance of a silver layer to the energy that impinges on the geometrical area of the slit, assuming a Gaussian-shaped input beam with a wavelength λ=800nm. Figure 1(b) shows a two-dimensional map of transmittance as a function of the geometrical parameters.

**Figure 1.** (a) Schematic of the silver substrate. (b) Calculated transmission coefficient, presented as a two-dimensional map versus the substrate thickness, w, and slit size, a.

Our results suggest that the regime of extraordinary transmittance is closely correlated with the transmitted SHG and that cavity effects are simultaneously important in linear and nonlinear processes. We begin by examining transmitted and reflected second-harmonic signals of a single 32nm-wide slit on a silver substrate, shown in Figure 2. Clearly, the transmitted SHG signal reaches a maximum when the linear transmittance is maximum. The simultaneity of field localization^{2} and plasmonic effects gives rise to a strong increase in transmission, as high as ∼410%, and to the enhancement of SHG with respect to the bare metal.

**Figure 2.** Transmitted (red) and reflected (blue) second-harmonic generation (SHG) efficiencies calculated for a single, 32nm-wide slit in a silver substrate.

In the last few decades, several groups have shown that periodicity or periodic corrugations help to improve both linear and nonlinear responses.^{3} For this reason, we investigated multiple-aperture systems, starting with two apertures. This analysis revealed that the multiple-aperture system is also influenced by the substrate thickness and that the linear transmittance improves from T_{1_slits}∼407% to T_{2_slits}∼650% when a second slit is added. The nonlinear response also benefits from the enhancement of the pump inside the nanocavity, as shown in Figure 3. However, the response of the system as a function of the number of apertures saturates rapidly, reaching a maximum linear transmission just above 700%.

**Figure 3.** Reflected and transmitted SHG efficiency calculated for two 32nm-wide slits in a 200nm-thick silver substrate, the thickness with the largest single-slit response.

In summary, we have theoretically investigated enhanced transmission and SHG from single or multiple apertures in a metal substrate. A combination of cavity effects, field localization, and plasmon excitation leads to both the extraordinary transmittance and the enhancement of transmitted and reflected second harmonic signals. Our results show that enhanced linear transmission is obtained even for a single slit on a smooth metal surface, and that inside the aperture the fields may be enhanced by nearly two orders of magnitude. While we find that transmitted SHG is directly correlated to the enhancement of linear transmission, the reflected SHG signal has somewhat different sensitivities, since scattering for the aperture and the smooth surface change its resonance conditions. Further improvements of such systems will exploit both the linear and nonlinear enhanced response, together with the inclusion of nonlinear, polymeric materials for sensing devices or optical modulators.

Maria Antonietta Vincenti

Dipartimento di Elettrotecnica ed Elettronica

Politecnico di Bari

Bari, Italy

AMSRD-AMR-WS-ST, RDECOM

Redstone Arsenal

Huntsville, AL

Maria Antonietta Vincenti is completing her PhD in electronic engineering. Her main research activities concern optical sensors, imaging techniques based on metallo-dielectric structures, and plasmonics. She is currently a guest researcher at the Charles M. Bowden Research Center.

Antonella D'Orazio

Dipartimento di Elettrotecnica ed Elettronica

Politecnico di Bari

Bari, Italy

Antonella D'Orazio is a full professor in the field of electromagnetics. Since 2003 she has been coordinator of the teachers’ council for the PhD in electronic engineering. Her research interests are the design, fabrication, and characterization of linear and nonlinear optical devices together with the numerical modeling of photonic-bandgap devices.

Michael Scalora

Charles M. Bowden Research Center

AMSRD-AMR-WS-ST, RDECOM

Redstone Arsenal

Huntsville, AL

Michael Scalora is a senior scientist. He obtained MS and PhD degrees in physics from Rensselaer Polytechnic Institute, Troy, NY, in 1988 and 1990, respectively. His research activities include study of propagation phenomena in photonic-bandgap structures and metamaterials.

References:

2.

M. C. Larciprete, A. Belardini, M. G. Cappeddu, D. de Ceglia, M. Centini, E. Fazio, C. Sibilia, M. J. Bloemer, M. Scalora, Second harmonic generation from metallo-dielectric multilayer photonic band gap structures, *Phys. Rev. A* 77, pp. 013809, 2007.doi:10.1103/PhysRevA.77.013809