Direct measurement of the THz near-magnetic field of metamaterial elements

Nishant Kumara, Andrew Strikwerdab, Kebin Fanc, Xin Zhangc, Richard Averittb,

Paul Plankena and Aurèle Adama

a Faculty of Applied Sciences, Delft University of Technology, Delft, The Netherlands

b Department of Physics, Boston University, Boston, Massachusetts, USA c Department of Mechanical Engineering, Boston University, Boston, Massachusetts, USA

Abstract—We have demonstrated direct measurement of the time-dependent terahertz (THz) magnetic near-field of split-ring resonators (SRRs) by using Terahertz Time-Domain Spectroscopy (THz-TDS). We also show that the local magnetic field in these structures is strongly enhanced relative to the THz magnetic field incident on these structures.

I. INTRODUCTION AND BACKGROUND

Electromagnetic metamaterials are artificial materials made of arrays of subwavelength-sized metallic building blocks such as split ring resonators (SRRs), which can have extraordinary optical properties, such as a negative index of refraction, and many potential applications, such as cloaking and superlensing. In our case, the building block is a split-ring resonator (SRR). A SRR is used to couple the incident electric field and create a local magnetic field. In this letter, we present the first direct measurements of the terahertz time-dependent magnetic near-field of single split-ring resonators (sSRRs) and double split-ring resonators (dSRRs). Although it has been possible to calculate the magnetic near-field from measurements of the electric near-field, no direct measurements of the magnetic near-field of these structures have been reported. [1] Deep subwavelength measurements of the magnetic near-field with a high spatial resolution will provide more information about the strength and distribution of the local magnetic field and the different interactions between the buildings blocks.

II. RESULTS

The metamaterial structure Fig. 1 (left) is made of a gold layer on the top of a terbium gallium garnet (TGG) magneto-optical crystal [2,3]. When a THz electric field is incident on the metamaterial, it induces temporally oscillating and spatially circulating currents in the ring, which generate a local magnetic field. In our experiment, a single-cycle, broadband THz pulse, with an electric field parallel to the arm containing the gap, is incident on a single resonator. At the same time, a synchronized, femtosecond probe laser pulse is focused in the crystal immediately below the structure. The Ge/SiO2 reflection coating on the crystal reflects the probe beam. Due to the presence of the local magnetic field induced by the resonator, the plane

of polarisation of the reflected probe beam is rotated. A differential detector, combined with a �/2 wave plate and a Wollaston prism measures this rotation. The THz magnetic near-field as a function of time is obtained by optically delaying the probe pulse with respect to the THz pulse while measuring the Faraday rotation. The result of this measurement is shown in Fig. 1 (right). This technique measures the field and thus both the amplitude and the phase of the magnetic near-field are obtained.

Fig. 1: Left: Design of a sSRR with dimensions shown in the figure. Right: Time trace of the THz magnetic near field inside the sSRR for two different in-plane orientations of the sample. To confirm that we measure the magnetic field, the structure is rotated by 180˚ in the plane of the structure. The incident electric field being unchanged, this should reverse the direction of the current and thus reverse the direction of the magnetic near-field vector. Figure 2 shows that the measured longitudinal component of this magnetic near field Hz(t) is opposite in sign compared to the previous measurement confirming that we indeed measure the magnetic near-field.

Fig. 2: Left: Frequency spectra calculated from the time-dependent magnetic field Hz(t) for the three different sSRRs with different dimensions. Right: Calculated surface current density at the resonance frequency.

������������������ �����������

Direct measurement of the THz near-magnetic field of metamaterial elements

Nishant Kumara, Andrew Strikwerdab, Kebin Fanc, Xin Zhangc, Richard Averittb,

Paul Plankena and Aurèle Adama

a Faculty of Applied Sciences, Delft University of Technology, Delft, The Netherlands

b Department of Physics, Boston University, Boston, Massachusetts, USA c Department of Mechanical Engineering, Boston University, Boston, Massachusetts, USA

Abstract—We have demonstrated direct measurement of the time-dependent terahertz (THz) magnetic near-field of split-ring resonators (SRRs) by using Terahertz Time-Domain Spectroscopy (THz-TDS). We also show that the local magnetic field in these structures is strongly enhanced relative to the THz magnetic field incident on these structures.

I. INTRODUCTION AND BACKGROUND

Electromagnetic metamaterials are artificial materials made of arrays of subwavelength-sized metallic building blocks such as split ring resonators (SRRs), which can have extraordinary optical properties, such as a negative index of refraction, and many potential applications, such as cloaking and superlensing. In our case, the building block is a split-ring resonator (SRR). A SRR is used to couple the incident electric field and create a local magnetic field. In this letter, we present the first direct measurements of the terahertz time-dependent magnetic near-field of single split-ring resonators (sSRRs) and double split-ring resonators (dSRRs). Although it has been possible to calculate the magnetic near-field from measurements of the electric near-field, no direct measurements of the magnetic near-field of these structures have been reported. [1] Deep subwavelength measurements of the magnetic near-field with a high spatial resolution will provide more information about the strength and distribution of the local magnetic field and the different interactions between the buildings blocks.

II. RESULTS

The metamaterial structure Fig. 1 (left) is made of a gold layer on the top of a terbium gallium garnet (TGG) magneto-optical crystal [2,3]. When a THz electric field is incident on the metamaterial, it induces temporally oscillating and spatially circulating currents in the ring, which generate a local magnetic field. In our experiment, a single-cycle, broadband THz pulse, with an electric field parallel to the arm containing the gap, is incident on a single resonator. At the same time, a synchronized, femtosecond probe laser pulse is focused in the crystal immediately below the structure. The Ge/SiO2 reflection coating on the crystal reflects the probe beam. Due to the presence of the local magnetic field induced by the resonator, the plane

of polarisation of the reflected probe beam is rotated. A differential detector, combined with a �/2 wave plate and a Wollaston prism measures this rotation. The THz magnetic near-field as a function of time is obtained by optically delaying the probe pulse with respect to the THz pulse while measuring the Faraday rotation. The result of this measurement is shown in Fig. 1 (right). This technique measures the field and thus both the amplitude and the phase of the magnetic near-field are obtained.

Fig. 1: Left: Design of a sSRR with dimensions shown in the figure. Right: Time trace of the THz magnetic near field inside the sSRR for two different in-plane orientations of the sample. To confirm that we measure the magnetic field, the structure is rotated by 180˚ in the plane of the structure. The incident electric field being unchanged, this should reverse the direction of the current and thus reverse the direction of the magnetic near-field vector. Figure 2 shows that the measured longitudinal component of this magnetic near field Hz(t) is opposite in sign compared to the previous measurement confirming that we indeed measure the magnetic near-field.

Fig. 2: Left: Frequency spectra calculated from the time-dependent magnetic field Hz(t) for the three different sSRRs with different dimensions. Right: Calculated surface current density at the resonance frequency.

In Fig. 2 (left), we show the frequency spectrum for three different sSRRs with different dimensions. Each sSRR shows a single large peak in its frequency spectrum, which corresponds to the strong oscillations shown in the time trace measurements. The peak frequency is a function of the dimension of the sSRR. In Fig. 2 (right) we show the calculated surface current density at the resonance frequency. The strongest current is inside the long arm of the structure, and it is particularly strong near the corner. The calculations also suggest that the local magnetic field around the corner is much stronger relative to the incident THz magnetic field. In addition to the single Split Ring Resonator (sSSR), we have performed measurements on a double Split Ring Resonator (dSRR), shown in Fig. 3 (left). These dSRRs are purposely designed to cancel the magnetic response creating a purely electrically resonant subwavelength element. When the THz electric field is polarised parallel to the gaps along the y-axis, it generates a current in the clockwise direction in the left ring and a counter-clock wise current in the right ring. Due to the opposite directions of the currents, we have a magnetic-field component pointing into the plane in the left ring, while in the right ring it is pointing out of the plane. Thus, the two time traces of the magnetic near-fields, are opposite in sign for the two locations, as shown in Fig. 3 (right).

Fig. 3: Left: Drawing of a metallic double split-ring resonator on a TGG crystal; the blue arrow represents the incident THz electric field polarisation, green gives the direction of the induced currents inside the metal and red shows the induced THz magnetic field lines. Right: Measurement of the time-dependent magnetic near-field Hz(t) of the dSRR structure inside the left and the right ring.

Fig. 4: Left: Frequency spectrum of dSRR Right: Calculated surface current density at the resonance frequency. The spectrum of the longitudinal magnetic near-field, calculated from the time-domain measurement, is plotted in Fig. 4 (left) and shows a strong peak at 0.17 THz. The current in the dSRR in the central arm is larger than the current in a sSRR and distributed uniformly across its width, because the current is fed by two identical resonators rather than just one, as shown in Fig 4 (right). Therefore, in a dSRR the magnetic field, which is mainly due to this high current in the middle arm, is much stronger than that for a comparable sSRR. Our technique is capable of measuring the time-dependent magnetic fields of opposite direction in a deep subwavelength sized region of space. It is interesting to note that fields of opposite sign emerging from such a small volume more or less cancel in the far-field and are thus difficult to measure in the far-field.

III. CONCLUSION In conclusion, we have observed strong enhancement in the local magnetic field compared to the incident THz magnetic field, due to the resonating behaviour of the structure. Moreover, we demonstrate a technique to directly measure the THz magnetic near-field of metamaterial elements with deep subwavelength resolution.

REFERENCES [1] A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, Opt. Express 17(5), 3826-3834, (2009) .[2] W.J. Padilla, M.T.Aronsson, C. Highstrete, Mark Lee, A.J. Taylor and R.D. Averitt, Phys. Rev. B 75, 041102(R) (2007). [3] H.-T. Chen, J. F. O'Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, Opt. Express, 15(3), 1084-1095 (2007). [4] J. A. Riordan, F. G. Sun, Z. G. Lu, and X. C. Zhang, App. Phys. Lett., 71(11), 1452–1454, (1997).