^{1,a)}, Aliaksandra M. Ivinskaya

^{1}, Maksim Zalkovskij

^{1}, Radu Malureanu

^{1}, Peter Uhd Jepsen

^{1}and Andrei V. Lavrinenko

^{1}

### Abstract

We analyze ultra strong non-resonant field enhancement of THz field in periodic arrays of nanoslits cut in ultrathin metalfilms. The main feature of our approach is that the slit size and metalfilm thickness are several orders of magnitude smaller than the wavelength of the impinging radiation. Two regimes of operation are found. First, when the grating period , frequency-independent enhancement is observed, accompanied by a very high transmission approaching unity. With high accuracy, this enhancement equals the ratio of *P* to the slit width *w*. Second, when the grating period approaches the THz wavelength but before entering the Raleigh-Wood anomaly, the field enhancement in nanoslit stays close to that in a single isolated slit, i.e., the well-known inverse-frequency dependence. Both regimes are non-resonant and thus extremely broadband for . The results are obtained by the microscopic Drude-Lorentz model taking into account retardation processes in the metalfilm and validated by the finite difference frequency domain method. We expect sensor and modulation applications of the predicted giant broadband field enhancement.

Support of the Danish Research Council for Technology and Production Sciences via the project THz COW was acknowledged. Authors thank Dr. D. Shyroki for fruitful discussions.

I. INTRODUCTION

II. SIMPLE MODEL OF FREQUENCY-INDEPENDENT FIELD ENHANCEMENT

III. MICROSCOPIC MODEL

A. Field enhancement

B. Transmission through an array of slits

IV. NUMERICAL MODELING OF SLIT ARRAYS

A. 10-nm-wide slit in gratings of different periods

B. Changing slit width in gratings with

V. DISCUSSIONS AND CONCLUSIONS

### Key Topics

- Electric fields
- 21.0
- Metallic thin films
- 19.0
- Diffraction gratings
- 13.0
- Metal surfaces
- 7.0
- Gold
- 6.0

## Figures

Sketch of the periodic slit array illuminated by *p*-polarized light. Slits are infinitely long in the *y*-direction. Contour *C* is intended for the enhancement estimation Eq. (2) in the static regime.

Sketch of the periodic slit array illuminated by *p*-polarized light. Slits are infinitely long in the *y*-direction. Contour *C* is intended for the enhancement estimation Eq. (2) in the static regime.

FDFD simulations of components (a) and (b) of the electric field, absolute values of (c) the magnetic field and (d) the Poynting vector near the 10-nm-wide slit of thickness *h* = 50 nm in a gold grating with a period of at a frequency *f* = 0.01 THz resulting in *G* = 100. Bounds for color maps are chosen so to show better peculiarities of field distribution. (e) Profiles of the electric field component in different slits, all giving enhancement of 100. Parameters of gratings are given in the legend. (f) Mesh refinement (thin, grey lines) at the metal-slit boundaries (thick, black lines).

FDFD simulations of components (a) and (b) of the electric field, absolute values of (c) the magnetic field and (d) the Poynting vector near the 10-nm-wide slit of thickness *h* = 50 nm in a gold grating with a period of at a frequency *f* = 0.01 THz resulting in *G* = 100. Bounds for color maps are chosen so to show better peculiarities of field distribution. (e) Profiles of the electric field component in different slits, all giving enhancement of 100. Parameters of gratings are given in the legend. (f) Mesh refinement (thin, grey lines) at the metal-slit boundaries (thick, black lines).

(a) Enhancement factor *G* (see Eq. (12)) for different slit widths (compare with numerical simulation in Fig. 6(a)). (b) Enhancement factor for slit-average field *G* and field at the slit center , if 2*M* slits act on the slit under consideration. In the inset, the long periods *P* approaching to the wavelength are considered. Enhancement factor versus (c) slit width and (d) metal thickness.

(a) Enhancement factor *G* (see Eq. (12)) for different slit widths (compare with numerical simulation in Fig. 6(a)). (b) Enhancement factor for slit-average field *G* and field at the slit center , if 2*M* slits act on the slit under consideration. In the inset, the long periods *P* approaching to the wavelength are considered. Enhancement factor versus (c) slit width and (d) metal thickness.

Evolution of transmission spectra with period *P* for thin metal films (*w* = *h* = 20 nm). Spectra are calculated for the homogenized material with dielectric permittivity (28).

Evolution of transmission spectra with period *P* for thin metal films (*w* = *h* = 20 nm). Spectra are calculated for the homogenized material with dielectric permittivity (28).

(a) Field enhancement and (b) transmittance of 10-nm-wide slits cut in a 20-nm-thick film versus frequency for different grating periods *P* (FDFD simulation). The enhancements in the quasi-static limit are chosen to be , where *A* changes from 2 to 10 and *B* from 0 to 3 (increment is 1 both for *A* and *B*). The period of the grating is *P* = *wG*. (c) The dependence of the enhancement on the dimensionless parameter for a single slit (*h* = 20 nm). Each line is obtained by varying at some slit width *w*, so that a total of 23 curves are plotted for a set of 23 slit widths (taking values between 10 nm and ). For all the curves, the incident wavelength is changed from to corresponding to the frequency range between and

(a) Field enhancement and (b) transmittance of 10-nm-wide slits cut in a 20-nm-thick film versus frequency for different grating periods *P* (FDFD simulation). The enhancements in the quasi-static limit are chosen to be , where *A* changes from 2 to 10 and *B* from 0 to 3 (increment is 1 both for *A* and *B*). The period of the grating is *P* = *wG*. (c) The dependence of the enhancement on the dimensionless parameter for a single slit (*h* = 20 nm). Each line is obtained by varying at some slit width *w*, so that a total of 23 curves are plotted for a set of 23 slit widths (taking values between 10 nm and ). For all the curves, the incident wavelength is changed from to corresponding to the frequency range between and

(a) Enhancement *G* and (b) transmittance *T* in gratings with periodicity and varying slit width *w* = *P/G* given by the following approximate set of numbers in nm: 400.0, 200.0, 100.0, 66.7, 50.0, 40, 33.3, 28.6, 25.0, 22.2, and 20.0, which correspond to enhancements 50 and 100 to 1000 with the increment 100 within the plateau zone (FDFD simulation). (c) Detailization of several curves for the enhancement from (a) on a logarithmic scale. Lines with open circles correspond to the enhancement in isolated slits of the same widths as indicated in the legend.

(a) Enhancement *G* and (b) transmittance *T* in gratings with periodicity and varying slit width *w* = *P/G* given by the following approximate set of numbers in nm: 400.0, 200.0, 100.0, 66.7, 50.0, 40, 33.3, 28.6, 25.0, 22.2, and 20.0, which correspond to enhancements 50 and 100 to 1000 with the increment 100 within the plateau zone (FDFD simulation). (c) Detailization of several curves for the enhancement from (a) on a logarithmic scale. Lines with open circles correspond to the enhancement in isolated slits of the same widths as indicated in the legend.

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