Switchable metamaterial for enhancing and localizing electromagnetic field at terahertz band

Junxing Liu; Kailin Zhang; Xiankuan Liu; Zeyu Zhang; Zuanming Jin; Xiaoyong He; Guohong Ma

doi:10.1364/OE.25.013944

1. Introduction

Terahertz (THz) technology and its applications have made a dramatic growth in THz communication, material analysis, bio-medical technology, and security, etc [1–4]. However, THz technology still suffers from a deficiency in efficient detectors, high-power sources, and other functional devices, such as amplifiers, modulators, and switches due to the lack of materials that naturally respond well to THz radiation. Metamaterials are structured composites with patterned metallic sub-wavelength inclusions which can show many electromagnetic properties that ordinary materials do not have, such as negative refraction [5], “perfect lens [6], the cloak [7], etc. The resonant response of the electric or/and magnetic field of the electromagnetic wave to these specially designed mesoscopic systems can significantly enhance their interaction with THz radiation. Metamaterials can be designed utilizing this feature to yield a desired response at THz band thus offers a route towards helping to fill the so-called “THz gap” [8]. The development of metamaterials has greatly broadened people’s horizons in realizing the interaction between light and matter that cannot be obtained via natural materials. Specially, the functionality of some kind of metamaterials can convert optical radiations into intense, engineered, and localized field distributions, thus provides a good platform for studying the interaction between light and matter. Recently, ultrafast control of spins in antiferromagnetic material is the core issue in technological applications such as spintronics and spin-based information processing [9,10]. Especially, terahertz technology has emerged as alternative to optical techniques for studying magnetic excitation [11,12]. Magnetic field localization and enhancement in the vicinity of metamaterials fabricated on objects crystal can provide a good platform for studying magnetic excitations in condensed matter. Those metamaterials have strong nonlinear response via field localization to the incident impulse which can open a way to dynamically control [13] the THz field itself. In this regime, structural design with particular characteristic is the core goal.

At optical and microwave band, highly localized and strongly enhanced electromagnetic field is very useful for triggering nonlinear effects. On the one hand, many kinds of metamaterials, such as bowtie antennas [14], U-shaped cavities [15] and V-shaped optical resonant antennas [16], share the same functionality of the electric filed localization of the incident pulse in a narrow gap, which enables the optical resonant antennas many applications such as nonlinear optics [17,18], surface modification [19,20], scanning near-field optics applications [21,22], and surface-enhanced Raman spectroscopy [23] etc. On the other hand, some nanostructures were proposed for enhancing and localizing the magnetic field of the nanostructures, such as the diabolo nanostructure [24], cross-diabolo nanoantenna [25], etc.

Active controllable terahertz metamaterials have intrigued people’s interest and many novel schemes were proposed recently. In 2006, W. J. Padilla and A. J. Taylor characterized the electromagnetic response of a planar array of split ring resonators (SRRs) fabricated on a high resistivity GaAs substrate, and they demonstrated the potential of such structures as terahertz switches by photogeneration of free carriers in the GaAs substrate [26]. H. T. Chen et al have demonstrated many kinds of switchable metamaterials such as electrically switchable THz metamaterials and the Schottky diode structure [27,28]. In 2012, J. Q. Gu et al. proposed a scheme of actively controlling of electromagnetically induced transparency analogue in terahertz metamaterials through active tuning of the dark mode, allowing for an optically tunable group delay of the terahertz light [29]. In 2015, X. Q. Su et al designed a metasurface which can realize the efficient real-time control and amplitude manipulation of broadband anomalous diffraction in the terahertz regime [30].

Inspired by the novel schemes mentioned above, we demonstrate a switchable scheme to actively control the functionality of the diabolo-like metamaterial. The structure is composed of two metal triangles and a GaAs cube (called “gap” in the following), in which the GaAs cube is inserted in the center gap of the facing metal triangles. A specially combined pulse of a synchronized femtosecond pump pulse and THz pulse is adopted to normally illuminate the diabolo-like structure in our scheme. The field localization can be switched from electric-field to both the electric and magnetic fields for the incident THz pulse with the femtosecond laser pulse off and on. The pump pulse acts as an optical switch in our scheme, and the GaAs gap plays a crucial role in switching the field localization. The outstanding merit of our scheme-including three aspects: Firstly, the switchable feature, to the best of our knowledge, this is the first model ever proposed; Secondly, the enhancement on electric- and/or magnetic-field can be obtained individually or simultaneously by artificial structure design, which can overcome the limit of natural materials; Thirdly, the high efficiency for enhancing the electromagnetic field of the incident pulse, which is very difficult generated via other scheme, all these advantages can bring great freedom in many research fields at THz band. In this article, we will demonstrate by simulations that the field localization and switchable properties can be realized in the specially designed metamaterial at THz frequency, also, the influence of various factors on the performance of the metamaterial, such as the length of the structure, the size of the gap as well as the power of the incident femtosecond laser pulse are discussed.

2. Enhancement of the electric field of the incident terahertz pulse

A sketch of the proposed metamaterial is shown in Figs. 1(a) and 1(b), the metamaterial is considered to be fabricated onto a fused silica substrate with refraction index of 2.25 surrounded by air above. The design of the metamaterial can be described as a combined structure with a pair of planar metal triangles with 45^。flare angles joined together through their facing tips by GaAs semiconductor, gold is selected as the material of the planar metal triangles. In our scheme “l” represents the length of the structure, and “G” defines both the width and the length of the gap, the height of the structure (along the z axis) is given by “t” whereas “T_s” represents the thickness of the substrate. The structural parameters under study are “l=28.28μm”, G = 1μm, t = 0.3μm and T_s = 400μm the periodicity of the structure is set to be 100μm along both the x and y directions. The structure is illuminated by normal incident azimuthally polarized combined pulses that is composed of a ~50 fs laser pump pulse with a central wavelength of 800 nm and a THz pulse, the pump pulse is timed to arrive 5 ps before the peak of the THz waveform as shown in Fig. 1(c). The polarization of the linearly polarized THz radiation is also indicated in Fig. 1(c).

Fig. 1 Scheme of the simulation model under study: (a) top view in the (XY) plane and (b) side view along the (XZ) plane, and the schematic diagram (c). The red point in (b) corresponds to the position where the spectra are calculated, 101 nm away from centered of the gap; the dashed plane in (b) corresponds to the plane where the three dimensional near-field amplitude distributions of the electromagnetic field are calculated, 101 nm away from and parallel to the structure. The vectors $\overset{⇀}{k}$ and $\overset{⇀}{E}$ represent the direction of propagation and the polarization of the electric field, respectively. The vectors $\overset{⇀}{H}$ and $\overset{⇀}{E}$ are denoted for magnetic field electric field, respectively.

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Firstly, the optical pump pulse is off, and the structure is illuminated with a THz pulse only. As predicted, a hot spot of electromagnetic field is resonantly generated at the center of the semiconductor gap. Figures 2(a) and 2(b) show the three dimensional near-field amplitude distributions of the electric and magnetic fields generated by the structure respectively, more than 2 orders of magnitude of enhancement is observed at a resonance frequency of 4.05 THz for the electric component. It is worth noting that the electric field is highly confined at the scope of the gap as shown in Fig. 2(a). In contrast, the magnetic field is widely distributed onthe configuration and takes the shape of “X” with a relatively low intensity and fails to be confined at the scope of the gap, as shown in Fig. 2(b). Figure 2(c) presents the electric spectral response of the structure, which is calculated at the red point placed 101 nm above the center of the GaAs gap, in air (see Fig. 1(b)). The result in Fig. 2(c) clearly shows that the electric hot spot is generated resonantly, the resonance frequency is centered at 4.05 THz with a full width at half maximum (FWHM) about 0.31 THz.

Fig. 2 Three dimensional near-field amplitude distribution of the electric (a) and magnetic field (b) in a plane 101 nm away from the GaAs gap surface, respectively; and (c) the electric spectral response of the structure, the results are obtained under the condition that the MSM diabolo metamaterial irradiated by the THz pulse alone, the inset in (c) is the THz transmission spectrum of the structure.

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3. Confinement and enhancement of the electric along with magnetic component of the incident terahertz pulse

In the following, let’s focus on another situation: the unit cell of the structure is illuminated normally by combined azimuthally polarized pulse, the average power is set as 164 mW, which is delivered from a femtosecond laser with a pulse duration of 50 fs and repetition rate of 1 KHz. The output of the laser power is illuminated on the unit cell with an area of 100μm × 100μm, which produces average power intensity of 1.64 × 10³ W/cm². As a result, photocarriers with density of n = 6.56 × 10¹⁸ cm⁻³ are generated in the GaAs gap. The near-field amplitude distributions of the electric field and magnetic field are demonstrated in Figs. 3(a) and 3(c), respectively. Interestingly, a hot electromagnetic spot with an area of 1-by-1μm is generated at the center of the semiconductor gap, where the electric and magnetic fields of the incident THz pulse are locally co-enhanced with a 2-order of magnitude. Figures 3(b) and 3(d) plot the electric and magnetic spectral responses of the structure, respectively. Obviously, the electric and magnetic spectral responses share the same resonance frequency centered around 0.6THz with a narrow bandwidth of ~0.08THz (FWHM), far narrower than the electric spectral response shows in Fig. 2(c).

Fig. 3 Near-field amplitude distribution of the electric field (a) and magnetic field (c); electric (b) and magnetic (d) spectral response of the structure, the data in both (b) and (d) are collected from a plane 101 nm above the GaAs surface. The structure under studying is given in the text.

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Hinted by the results above, we can extract the potential application of this system, a switchable metamaterial which can localize and enhance the electric and magnetic fields of the incident THz pulse in the scope of the gap, the femtosecond pump laser pulse plays the role of optical switch. The field of the incident THz pulse being locally enhanced can be switched from electric field to both electric and magnetic fields by switching on the pump pulse. We would like to mention that with femtosecond laser illumination, the electric field is further enhanced, and the resonance mode is shifted from 4.05 THz (without optical pump) down to 0.6 THz (with optical pump), which can be seen clearly by comparing the Figs. 2(c) and 3(a). Moreover, the spectra response of both electric and magnetic field enhancement factor with optical illumination shows much narrower bandwidth than that without light illumination, this feature makes the structure has more potential applications in some special research fields.

4. Physical mechanisms

The basic principle for the electric field localization in the MSM diabolo metamaterial arises from the electrically isolated two facing metal triangles. Without light illumination, the two metal triangles are connected with an insulating GaAs, and the dielectric constant of GaAs is 12.96 in the investigated THz frequency. After THz pulse illumination, the charges are accumulated at the apexes of the two closely spaced metal triangles, and as a result, giant electric field localization occurs in the scope of the GaAs gap.

After illuminated with the optical pump pulse at 800 nm, the GaAs semiconductor turns into a metal-like character due to the photodoping. Consider a Drude model in photoexcited wafer, the dielectric can be expressed as:

\tilde{ε} (ω) = ε_{\infty} + \frac{ω_{P}^{2}}{ω^{2} + i γ ω},

where

ω_{P} = \sqrt{\frac{n e^{2}}{m^{*} ε_{0}}}

is the plasma oscillation frequency, and

γ = \frac{1}{τ} = \frac{e}{m^{*} μ}

is damping factor, with

m^{*} = 0.067 m_{e}

of the effective carrier mass, and

m_{e}

of the free electron mass.

During our simulation, we take the high frequency dielectric constant of GaAs as $ε_{\infty} = 12.9$ [31–33], the pump power of 164mW is illuminated onto an area of 100μm × 100μm, and as a consequence the photocarriers density of n = 6.65 × 10¹⁸ cm⁻³ is generated. And the conductivity of the GaAs after photoexcitaion is:

\tilde{σ} (ω) = \frac{i ε_{0} ω_{P}^{2}}{ω + i γ},

Here, $ω$ is the frequency of the incident THz pulse. As mentioned above, the femtosecond laser pump pulse is timed to arrive at 5 ps before the peak of the THz waveform, as the lifetime of the photoexcitation carriers in GaAs is significantly longer than the one of the THz pulse, this enable us to characterize the electromagnetic phenomenon of the GaAs as a quasisteady metal-like state.

The surface current with photoexcitation of the structure is shown in Fig. 4(a), it is seen clearly that the excitation of a plasmon mode of the structure is observed when the GaAs gap is photoexcited by the pump pulse. Illuminated with a y-polarized optical pump pulse, the photocarriers generated in the GaAs gap have enough life-time (longer than 1ns) to electrically connect the metal triangle pair, and the metal triangle pair acts as an electric funnel which reinforces the optical current density across the semiconductor gap, results in greatly enhancement of the magnetic field in the hot spot according to the Ampere theorem. Due to the huge carrier density difference between the gold tips and photodoped GaAs gap, the carriers could be accumulated at the interface of the gap, which forms a capacitance-like effect in the structure. Such a capacitance effect is the main reason for the locally enhancement of electric field in the hot spot (see Fig. 4(a)). We also examined the case that the gap is formed with gold (called “all-metal” MSM diabolo structure), however, the phenomenon of locally enhancement of the electric filed is vanished as shown in Fig. 4(b), obviously, and the main reason is the absence of capacitance effect between the gold triangles due to the balance of the carrier density.

Fig. 4 (a) Schematic diagram is used to illustrate the physical principle for locally co-enhancement of both the electric and magnetic field of the incident THz pulse; (b) Near-field amplitude distribution of the electric field of the “all-metal” MSM diabolo structure; (c) The electric field enhanced factor at 0.6THz as a function of the photoexcitation carriers’ density; (d) The magnetic field enhanced factor at 0.6THz as a function of the photoexcitation carriers’ density. The dark circles in (c) and (d) correspond to the enhancement amplitude of the electric and magnetic field described in Figs. 3 (b) and (d). The geometric parameters are set as l = 28.28μm and G = 1μm in Figs. 4.

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As mentioned above, the electric field is further enhanced and the resonance frequency of the electric spectral response is changed when the incident pulse switches from THz pulse to the combined pulse. On the one hand, the photoexcitation of GaAs gap is the cause of this phenomenon. Without photoexcitation, the GaAs shows insulator character, and metal triangle pair is separated by an insulator GaAs, this structure shows a lowest resonance mode at 4.05 THz. It is noted that the electric field enhancement factor at low frequency band (0.1~3.0 THz) is almost flat with a magnitude of ~10, and this enhancement factor is much lower than that at the resonance mode of 4.05 THz. When the GaAs gap is photoexcited by the pump pulse, photocarriers accumulation occurs at the interface of the gap, while the carrier accumulation leads to the further enhancement of the electric field. On the other hand, the resonance mode at 0.60THz is corresponding to the plasmon mode of the photoexcited structure, in which the electrical connection between the two facing metal triangles when the GaAs is photoexcited. Therefore, the plasmon mode at 0.60THz is fundamentally different from the structural mode at 0.405 THz without photoexcitation.

Moreover, from Eq. (1) and (2), the larger photoconductivity is generated with higher pumping power. The magnitude of the electric field enhancement is expected to be increased with the carrier accumulation in the scope of the gap (see Fig. 4(c)). According to Ampere theorem, the magnetic field should be also increased with the increase of the carrier density as shown in Fig. 4(d). We notice that the magnitude enhancement of the optical magnetic field is slightly smaller than the electric field enhancements in our scheme when the structure is illuminated by the combined pulse. The largest magnetic fields are tangential to the metal surface, and the tangential magnetic fields are continuously across the interface. The high magnetic fields existing in the metal could lead to stronger losses. While at the tips of the two metal triangles, the largest electric field is perpendicular to the metal surface and has a discontinuity across the interface, the electric field in the metal is smaller than the field just outside, thus the losses in the metal are small. Consequently, only a moderate resonance enhancement of magnetic field can be obtained for the structure as compared to the electric field.

5. Further discussion

In fact, the MSM diabolo metamaterial can be regarded as an equivalent to a RLC circuit. The geometric parameters of the structure including the length and gap size are certainly determining its performance. In the following, we focus on the influence of the length and gap size on the localization of the electric- and magnetic-field derived from the structure. Gold and GaAs are chosen as the constructed material for the metal triangle pair and the gap, the photo-carrier density remains as 6.56 × 10¹⁸ cm⁻³, and the thickness of the structure t is set as 0.3μm and the structure is fabricated on the top of a 400μm thick fused silica substrate.

Figures 5(a) and 5(b) show the amplitude of electric field and the resonance frequency as the function of the unit length as well as the size of the GaAs gap, respectively. In Figs. 5(a) and (c), the gap size is set as G = 1μm and the unit length is spanned from 28.28 to 84.85μm, in Figs. 5(b) and 5(d), we set l = 28.28μm and the gap size is ranged from 0.4 to 4.4μm. It is seen clearly that the resonance frequency shifts to lower frequency with increasing the length of the unit structure. The electric field enhancement derived from the structure deceases slightly with the unit length. Figure 5(b) presents the amplitude and resonance frequency as a function of the gap size, obviously, the resonance frequency is not sensitive to the change of gap size, but the amplitude shows an obviously decreasing tendency with the increase of the gap size. The similar tendency is observed for the case of magnetic field as shown in Figs. 5(c) and 5(d), respectively.

Fig. 5 3D plot of the electric field distribution and resonance frequency as a function of the unit length of the MSM diabolo metamaterial (a) and the size of the GaAs gap (b); The 3D plot of magnetic field distribution and resonance frequency as a function of the unit length of the MSM diabolo metamaterial (c) and the size of the GaAs gap (d).

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The physical origin for this phenomenon is connected to the fact that the electromagnetic hot spot is resonantly generated by the structure through the plasmon mode excitation, thus the resonance frequency is largely determined by the geometrical parameter of the structure. The semiconductor gap is much smaller than the metal triangle pair in size, hence the resonance frequency is largely relies on the effective length of the structure. Consequently, the resonance frequency of the plasmon is expected to decrease with the length “l”, as shown in Figs. 5(a) and 5(c). Meanwhile, the carrier accumulation occurring in the facing tips of the structure is intended to generate larger electric field with the shrink of the semiconductor gap, just as shown in Fig. 5(b). Additionally the metal triangle pair act as electric funnel which reinforces the optical current density into the gap, a larger current density is expected to be generated with a narrower gap, which in return results in generating a stronger magnetic field according to the Ampere theorem as shown in Fig. 5(d).

6. Simulation method

The numerical simulations are carried out using the finite-element time-domain solver of the CST Microwave Studio. All boundaries of the computation volume are terminated with perfectly matched layers (PMLs) in order to avoid parasitic unphysical reflections around the structure. The periodicity of the structure is set to be $100μm$ along both the x- and y-direction. The incident wave is x-polarized and normally incident onto the MSM diabolo structure from the metamaterial side. The electromagnetic fields spectra response are defined as $| R_{E} (ω) | = | E_{S} (ω) / E_{R} (ω) |$ and $| R_{H} (ω) | = | H_{S} (ω) / H_{R} (ω) |$ respectively, where $E_{S} (ω)$ and $H_{S} (ω)$ are the transmitted electric and magnetic fields of the sample, respectively; $E_{R} (ω)$ and $H_{R} (ω)$ are incident electric and magnetic fields, respectively. All the field signals are extracted by setting field probes at the corresponding positions (101nm above the center of the gap, in air) of the structure. Whereas the field distributions of electromagnetic field are mapped by defining electric field monitoring at 0.60 THz. The Near-field amplitude distributions are obtained on a plane parallel to the structure with a distance of 100nm.

7. Conclusions

In this article, we have investigated numerically the properties of the switchable MSM diabolo metamaterial illuminated by a specially designed combined pulse, which can highly localize and enhance the electromagnetic field of the incident THz pulse. The MSM diabolo metamaterial is composed of a metal triangle pair connected by a GaAs semiconductor gap at their facing tips. In the case of illuminated by a THz pulse only, the metal triangle pair will be electrically isolated, and the charge accumulation occurs at the apexes of the closely spaced metal pair, as a result, a giant electric field enhancement is generated due to the strong capacitive effect. Importantly, by combining a synchronized a femtosecond laser pulse and a terahertz pulse, the metal triangle pair can acts as the electric funnel which reinforces the optical current density into the semiconductor gap, as a result, both the electric and magnetic fields are confined simultaneous at the scope of the photodoped GaAs gap. As an equivalent to a RLC circuit, the influence of the core structural parameters, such as the length and the gap size, are investigated. The results demonstrated here should be useful for designing field enhancement structure which is applicable to many fields such as nonlinear magnetic response, near-field optics, and optical antenna, etc.

Funding

National Natural Science Foundation of China((NSFC) grant #11674213, 11604202. Young Eastern Scholar at Shanghai Institutions of Higher Learning grant # QD2015020. Universities Young Teachers Training Funding Program of Shanghai Municipal Education Commission grant #ZZSD15098.

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Switchable metamaterial for enhancing and localizing electromagnetic field at terahertz band

Abstract

1. Introduction

2. Enhancement of the electric field of the incident terahertz pulse

3. Confinement and enhancement of the electric along with magnetic component of the incident terahertz pulse

4. Physical mechanisms

5. Further discussion

6. Simulation method

7. Conclusions

Funding

References and links

Cited By

Figures (5)

Equations (2)

Optics Express