Giant and tunable electric field enhancement in the ... - OSA Publishing

Giant and tunable electric field enhancement in the terahertz regime Xiaoyuan Lu,1 Rengang Wan,1 Guoxi Wang,1 Tongyi Zhang,1, and Wenfu Zhang1,2 1 State

∗

Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China 2 [email protected] ∗ [email protected]

Abstract: A novel array of slits design combining the nano-slit grating and dielectric-metal is proposed to obtain giant and tunable electric field enhancement in the terahertz regime. The maximum amplitude of electric field is more than 6000 times larger than that of the incident electric field. It is found that the enhancement depends primarily on the stripe and nano-slits width of grating, as well as the thickness of spacer layer. This property is particularly beneficial for the realization of ultra-sensitive nanoparticles detection and nonlinear optics in the terahertz range, such as the second harmonic generation (SHG). © 2014 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (310.0310) Thin films; (310.6628) Subwavelength structures, nanostructures.

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#221878 - $15.00 USD Received 27 Aug 2014; revised 9 Oct 2014; accepted 13 Oct 2014; published 23 Oct 2014 (C) 2014 OSA 3 November 2014 | Vol. 22, No. 22 | DOI:10.1364/OE.22.027001 | OPTICS EXPRESS 27001

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1.

Introduction

Terahertz (THz) technology has significant progresses in various fields such as material inspection, chemistry recognition, and security control [1–3]. However, the pulse energy supplied by current THz generator is still limited [4, 5]. Some THz applications, including terahertz nonlinearity, nanoparticle detection and small terahertz signal detection in astronomy, need extreme enhanced electric field. It is necessary to enhance the energy of the THz field for these applications. In general, there are two ways to overcome the limit of low power. One is using dielectric lens, such as gold-plated parabolic mirrors and silicon THz lenses, to focus the THz wave. However, the obtained field strength is restricted by the diffraction limit. The other is employing subwavelength structures such as holes, slits and their arrays to concentrate the THz light into extremely sub-wavelength volumes, which will lead to strong field enhancement [6–9]. Recently, THz nanoresonators have been investigated extensively. Park et al. proposed a nanoresonator with nanohole arrays punctuated in a thin metal film and realized an electric field enhancement of 170 at resonance in the THz regime [10]. The same group demonstrated the field enhancement using THz nanoresonators with two paired nanoholes separated by a nanobarrier and tuned the resonant frequency and the field enhancement through changing the width of nanobarrier [11]. Razzari et al. showed a nanoresonators with nanostripes and obtained the field enhancement factor of 280 at resonance [12]. Beside, nanoslits still can be used to enhance the electric field. Seo et al. introduced a single nanoslit in a gold film with thickness on nano scale and obtained near field enhancement about 1000 folds at non-resonant frequency of 0.1 THz [13]. It is found that the electric field enhancement is a 1/ f -type frequency dependence and narrower slitwidth leads to the larger electric field enhancement. However, it is rarely reported that using nanoslits combining with the subwavelength cavity to obtain the giant electric field enhancement in the nanoslits at the resonant frequency in the THz regime. In this paper, we propose a novel device that combines nano-slits with metal-dielectric-metal cavities (NMDMC) to obtain giant and tunable electric field enhancement in the THz regime due to the resonance effect. We numerically demonstrate that the peak value of the electric field #221878 - $15.00 USD Received 27 Aug 2014; revised 9 Oct 2014; accepted 13 Oct 2014; published 23 Oct 2014 (C) 2014 OSA 3 November 2014 | Vol. 22, No. 22 | DOI:10.1364/OE.22.027001 | OPTICS EXPRESS 27002

Fig. 1. (a) Schematics of the NMDMC. A Si layer with thickness L is sandwiched between a metallic grating and a planar metal substrate.

magnitude at the resonance frequency using NMDMC is more than 6000 folds larger than that of the incident electric field. In addition, the position of peak value of electric field enhancement can be tuned in the range of 0.1 − 0.25 THz by changing the resonance condition with the help of varying structure parameters. This NMDMC structure has important potential applications in designing ultra-sensitive THz sensors, single-molecule detection, second harmonic generation (SHG), and other aspects. 2.

Theoretical model

The schematic of the proposed NMDMC is shown in Fig. 1(a). The NMDMC consists of a airfilled metallic slit grating, a planar metallic substrate, and a dielectric spacer layer sandwiched between the grating and substrate. The grating period, thickness, stripe width, slit width and the thickness of the dielectric layer are denoted by p, h, a, d and L, respectively. The normally incident wave is transverse magnetic (TM) polarized THz wave with the electric field vector along x axis, as shown in Fig.1(a). The metal is chosen as Au, and the frequency dependent permittivity is described by the Drude model [14–17]:

εm ( ν ) = 1 −

1.52 × 1030 , ν (ν − i1.6 × 1013 )

(1)

where ν represents the frequency of incident electromagnetic wave. The dielectric layer is set as silicon (Si) which has a constant permittivity of 11.6 [16]. The electric field enhancement factor is defined as:

α=

|Eslit |dS , |Einc |dS

(2)

where |Eslit | and |Einc | represent the electric field amplitude in the nano-slits and the incident THz wave, respectively. dS is the surface element. The surface integral is over the cross section of nano-slits. 3.

Simulation results

In the THz range, the enhancement of electric field is not high enough for the metal-dielectric grating with nanoslits structure [10,11], as well as the enhancement is hardly tuned. To increase the enhancement factor even further, we propose the NMDMC structure which consists of a metal dielectric grating and an metallic ground plane, as Fig. 1 shows. All data are calculated using the finite element method (FEM), the adaptive refinement mesh of quadratic triangle [18] is used in the calculating procedure. To save the memory and computing time, periodic boundary condition [19] is used in the x direction. Perfectly matched layers [19] are used in the y #221878 - $15.00 USD Received 27 Aug 2014; revised 9 Oct 2014; accepted 13 Oct 2014; published 23 Oct 2014 (C) 2014 OSA 3 November 2014 | Vol. 22, No. 22 | DOI:10.1364/OE.22.027001 | OPTICS EXPRESS 27003

Fig. 2. (a) Numerically simulated reflective spectrum and the electric field enhancement factor as a function of frequency for the NMDMC. The black solid line and blue dot line represent the electric field enhancement and reflective spectrum, respectively. (b)-(e) Electric (b)(c) and magnetic (d)(e) field distributions of the NMDMC at the resonance frequency of 0.184 THz and the non-resonant frequency of 0.3 THz. Parameters: p = 100 μ m, d = 40 nm, L = 20 μ m. (a)

(b)

(c)

Fig. 3. (a) Electric field enhancement factor as a function of frequency for the NMDMC with different periods of grating. Parameters: d = 40 nm, h = 60 nm, L = 50 μ m. (b) Relationship between field enhancement factor and the period of grating when the incident frequency is 0.117 THz. (c) Dependence of the resonance frequency on the grating period.

direction to simulate the free space. The minimum size and maximum size of grids are set as 0.1 nm and 0.1 μ m, respectively. As shown in Fig. 2(a), the resonant dip in the reflection spectrum is sharp. The reflectivity is zero at the resonant frequency. It is valuable for enhancing the sensing performance that our proposed structure can obtain a large intensity variation of the reflected light when the refractive index of the medium surrounding the structured surface varies slightly [20–22]. The low reflection at the resonant frequency implies almost total energy of the incident light is localized by the NMDMC structure. The enhancement of the electric field is giant at the resonant frequency, while the enhancement decreases sharply at the off-resonant frequency. The variation tendency of reflectivity is contrary to that of the enhancement as varying the frequency. This can be explained by the surface plasmons concept. At the resonant frequency, the surface plasmons on the nanoslit edges are strongly coupled with the reflected electromagnetic wave by the metallic plane [23,24]. The strong optical coupling leads to the giant enhancement of electric field for the NMDMC structure [25]. It can be seen that the maximum value of the field enhancement factor at the resonant frequency reaches 2300 for the NMDMC, as shown in Fig. 2(a). Due to the giant electric field enhancement, the proposed NMDMC structure is feasible for the applications in the designs of ultra-sensitive THz detectors, single molecular detection and other enhanced THz field aspects. To verify the results in Fig. 2(a), we calculate the field distributions at- and off- resonance frequency, as shown in Figs. 2(b)-(e). We find that the electric and magnetic fields can be strongly localized in the structure at resonant frequency which leads to giant field enhancement.


(a)

(b)

(c)

Fig. 4. (a) Electric field enhancement factor as a function of frequency for the NMDMC. The curves represent the enhancement factor of the NMDMCs with different L, as indicated on the graph. Here, the other parameters are p = 100 μ m, d = 40 nm, h = 60 nm. (b) Electric field enhancement factor dependence on the thickness of spacer when the incident frequency is 0.152 THz. (c) Resonance frequency as a function of the thickness L. Here, parameters: p = 100 μ m, d = 40 nm and h = 60 nm.

In the following, we demonstrate the tunability of proposed structure and study the influence of the geometrical parameters on the electric field enhancement factor. Firstly, we investigate the dependence of the enhancement factor on the grating period, while other geometric parameters are unchanged. The relationship between the enhancement factor and the grating period for NMDMC are shown in Figs. 3(a). It is found that for the NMDMC, the peak value of the enhancement factor increases and the resonant frequency has a red-shift with the increasing of grating period. In addition, we show the relationship between the enhancement factor and the grating period for NMDMC in Fig. 3(b). In the calculations, the incident frequency is 0.117 THz. It is found that when the grating period is about 100 μ m, the enhancement factor of the NMDMC reaches a maximum value. Especially, by appropriately tuning the grating period, the enhancement factor of NMDMC can reach to 3600. The resonance frequency for the NMDMC are shown in Fig. 3(c). It is found that the resonance frequency decreases with the increasing of grating period. Secondly, the dependence of the electric field enhancement factor on the thickness of dielectric layer is investigated. The relationship between the enhancement factor and the thickness of the dielectric layer for NMDMC is displayed in Fig. 4(a). It indicates that for the NMDMC, the peak value of the enhancement factor increases and a red-shift of the resonant frequency can be observed when the thickness of the dielectric layer is increased. We demonstrate the relationship between the enhancement factor and the thickness of the dielectric layer for NMDMC in Fig. 4(b). In the calculations, the incident frequency is 0.152 THz. It is found that when the thickness of dielectric layer is about 30 μ m, the enhancement factor of the NMDMC reaches a peak value. Notably, by appropriately tuning the thickness of the dielectric layer, the peak value of the enhancement factor for the NMDMC can reach to 3600. The resonance frequency for the NMDMC are demonstrated in Fig. 4(c). We find that the resonance frequency decreases with the increasing of thickness of the dielectric layer. In the end, we investigate the electric field enhancement factor dependent on the slit width of the top metallic grating while the other geometric parameters are fixed. The relationship between the enhancement factor and the slit width of the grating for NMDMC is shown in Fig. 5(a). It can be seen that for the NMDMC, the peak value of the enhancement factor increases and the resonant frequency has a red-shift with narrower slits of the metallic grating. The enhancement factor of the electric field is significantly sensitive to the slit width of the grating. In addition, we show the relationship between the enhancement factor and the slit width of the grating for NMDMC in Fig. 5(b). In the calculations, the incident frequency is 0.113 THz. It is found that when the slit width of grating is narrower, the enhancement factor of the NMDMC


(a)

(b)

(c)

Fig. 5. (a) Electric field enhancement factor as a function of frequency for the NMDMC. Here, p = 100 μ m, L = 50μ m, h = 60 nm, d as the figure legend shows. (b) Electric field enhancement factor dependence on the slit width of grating when the incident frequency is 0.113 THz. (c) Resonance frequency dependence on d for the NMDMC with parameters p = 100 μ m, L = 50 μ m and h = 60 μ m.

rises sharply. Apparently, the enhancement factor of NMDMC can reach to 6200, through appropriately tuning the slit width of the grating. The enhancement factor is 6 times larger than that in [10]. The resonance frequency for the NMDMC are shown in Fig. 5(c). It is found that the resonance frequency increases with the slit width of the grating increased. Based on the above analysis, we can conclude that the field enhancement of the proposed structure can be flexibly tuned by properly changing the structure parameters. 4.

Conclusion

In conclusion, we have investigated numerically the enhancement of the electric field for the NMDMC in the THz regime. Because the cavity effects, the NMDMC structure exhibits the giant electric field enhancement in the slits of the top metal grating. The enhancement is giant at the resonant frequency of NMDMC. This can be attribute to strong coupling between plasmons at the edges of slits with the reflected wave while the thickness of the central dielectric layer has a deep subwavelength. The giant enhancement can be tuned through modulating the geometrical parameters such as period of the top grating, the thickness of the central dielectric layer and the nanoslit width of the grating. It can be seen that the nano slit width significantly effects the enhancement of the electric field. This structure is particularly beneficial for the design of sensitive THz sensors and nonlinear optics in the THz regime, such as SHGs. Acknowledgments Xiaoyuan Lu acknowledges stimulating discussions with Xianghua Yu. This work has been partly supported by the National Natural Science Foundation of China (Grant No. 61176084, 11174282, and 61475191). Guoxi Wang, and Wenfu Zhang gratefully acknowledges funding from the National Natural Science Foundation of China (Grant No. 61405243, 11404388, 61275062, 11304375, and 61475188).
