Thermally tunable electric mie resonance of dielectric cut-wire type metamaterial Fuli Zhang,1,* Lei Chen,1 Ying Wang,1 Qian Zhao,2 Xuan He,1 and Ke Chen1 1
Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Department of Applied Physics, School of Science, Northwestern Polytechnical University, Xi’an, 710072, China 2 State Key Lab of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China * [email protected]
Abstract: In this manuscript, we present on a thermally tunable electric Mie resonance of dielectric cut-wire type metamaterial. Dielectric cut-wire exhibits Lorentz-type frequency dependent negative effective permittivity followed by zero value around its fundamental Mie resonance, resulting from dipole-oscillation of displacement currents. Furthermore, the operation frequency of electric resonance frequency can be varied by wire length and temperature variation. As environmental temperature changes by 40 °C, electric Mie resonance can be reversibly tuned by 1000 MHz, due to the thermal dependent permittivity character of ceramic. ©2014 Optical Society of America OCIS codes: (160.3918) Metamaterials; (290.4020) Mie theory; (280.6780) Temperature.
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#223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24908
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1. Introduction During last decade, metamaterials have undergone rapid development since it exhibits unique properties which cannot be found in naturally occurring materials. From the oscillation of microstructure, the effective parameters of metamaterial can reach negative/zero, which is far beyond that of traditional materials. Since the response of matter to EM/optics wave mainly relies on effective parameters, as a consequence, the ability to tailor EM/optics wave via artificial metamaterial opens door to deepen understanding of interaction between wave and matter as well as the design of novel devices, such as metasurface [1–3], cloaking [4–7], perfect absorber [8–11], etc. In essence, the sources of unique property of most metamaterials come from LC resonance of metallic microstructures, which inevitably suffer from the ohmic loss. Such loss becomes more severe as the operation frequency moves to infrared and visible range. To alleviate such challenge, Mie resonance, the intrinsic characteristics of dielectrics to EM/optics wave, has been explored [12–28]. Recently, dielectric metamaterials with single negative or even double negative parameters have been demonstrated. Modifying the aspect ratio of shape parameter of dielectric resonators enables the different tuning range of magnetic and electric resonances, thus, allowing the feasibility of overlap of magnetic and electric resonances in single dielectric resonator [24–26]. Up to now, most works of dielectric metamaterials are concentrated on the magnetic resonance as the lowest Mie resonance mode of dielectric sphere /cube whereas few works are involved in the second mode of electric Mie resonance of dielectric resonator [25, 27]. Actually, engineering effective permittivity via electric resonance plays an important role on the development of metamaterial, since it allows the #223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24909
realization of new phenomena of epsilon near zero (ENZ), such as directive beam control [29–31], perfect coupler [32, 33], as the effective permittivity approaches zero. Besides, due to the dispersion of resonant character, the effective permittivity of metamaterial with negative/zero value is only preserved in limited bandwidth, which greatly limits the potential application. In this manuscript, we present experimentally a thermally tunable electric Mie resonance of cut-wire type dielectric metamaterial. Dielectric cut-wire exhibits a dipole-oscillation of displacement currents at the lowest Mie resonance. The effective permittivity experiences a Lorentz-type frequency dependent permittivity with negative and zero value around its resonance frequency. Finally, operation frequency of electric Mie resonance can be tuned reversibly by 1000 MHz when the environmental temperature changes by 40 °C. 2. Results and discussions Figure 1(a) depicts schematically dielectric cut-wire inside a rectangular waveguide. The dielectric cut-wire is prepared using Ba0.5Sr0.5TiO3 (BST) ceramic with high relative permittivity and moderate dielectric loss (εr = 1600, tanδ = 0.03) (Fig. 1(b)). It has a square cross section with dimension of 0.6 mm × 0.6 mm. The scattering parameters are measured inside an X-band standard waveguide whose cross section is 22.86 mm × 10.16 mm and recorded by using vector network analyzer (VNA) AV3629D. Unlike previous work dealing with dielectric rod with finite length excited by electric field perpendicular to rod axis , an incident beam is excited with electric field polarized along dielectric cut-wire axis. Due to the periodic boundary condition of waveguide surface, single dielectric cut-wire is equal to periodic array with infinite elements along transverse directions.
Fig. 1. (a) Schematic view of dielectric cut-wire placed inside an X-band rectangular waveguide. (b) Photograph of single dielectric cut-wire sample. The dielectric cut-wire has a square cross section of smallest surface with side length of w = 0.6 mm.
At the first stage, transmission and reflection spectra of dielectric cut-wire are recorded under the environmental temperature of t = 30 °C. As shown in Fig. 2, a well-pronounced transmission dip occurs at 10.5 GHz. Further simulation and dispersion analysis confirms this transmission dip corresponds to its lowest mode of dielectric cut-wire (not shown here). According to Mie theory of dielectric particles , depending on the particles shapes and excitation approach, either magnetic or electric resonances can be excited as the lowest mode. To clarify the underlying physics of such resonance dip, effective parameter is retrieved by converting the experimental scattering parameters with a well-established algorithm for waveguide system . As seen in Fig. 2(b), Lorentz-type frequency dependent permittivity
#223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24910
experiences abrupt transition from positive to negative around the transmission dip. The abrupt change of effective permittivity sign demonstrates the electric Mie resonance character. The magnitude of local electric and magnetic field of dielectric cut-wire are monitored and given in Fig. 2(c). Obviously, electric field shows an antinode and magnetic field with a node, revealing electric resonance character. Such local field is similar to that of its metallic counterpart but without conduction currents. Actually, electric or magnetic resonance character for the ground Mie resonance mode mainly depends on the aspect ratio between wire height, L, and side length, w , and the periodicities along E and H field directions, the latter of which plays an important role on the frequency and oscillation strength of magnetic/electric resonance of metamaterial [13, 26, 35]. Note that the effective permittivity undergoes increases trend of frequency above its resonance dip and becomes zero at ɷENZ = 12.36 GHz. As the effective index is a square root of the product of permittivity and permeability, an effective index of zero near ɷENZ can be expected.
Fig. 2. (a) Experimental transmission and reflection (a) and effective permittivity (b) of dielectric cut-wire with L = 9.8 mm. (c) Local electric field and magnetic field distribution of dielectric cut-wire at electric Mie resonance frequency of 10.5 GHz.
Moreover, ENZ property of dielectric cut-wire is further confirmed by using a refraction check of dielectric prism. As shown in Fig. 3, the dielectric prism is composed of dielectric cut-wire array with a five-stair configuration. Absorber layers are used along the sides of input waveguide and dielectric prism to avoid scattering effect. At the frequency with effective permittivity near zero, the incident beam is refracted parallel to the surface normal of prism, confirming the effective index approaches zero. Strong magnitude contrast between incident and refraction wave is attributed to the impedance mismatch caused by only effective permittivity approaches zero. The refraction magnitude can be further improved by tailoring effective permittivity and permeability to approach simultaneously zero, i.e., the equality between electric plasma frequency and magnetic plasma frequency [30, 31]. One way is to incorporate another magnetic element such as dielectric sphere/cube whose magnetic plasma frequency shares the same frequency as electric plasma frequency of dielectric cut-wire. Another approach is to overlap the electric and magnetic plasma frequencies inside single dielectric wire by reducing the aspect ratio between height and side length .
#223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24911
Fig. 3. Refraction behavior of dielectric wire prism at frequency point around which effective permittivity approaches zero.
To pursue the ability to tailor the operation frequency of electric Mie resonance of dielectric metamaterial, the transmission response versus wire length is investigated and given in Fig. 4. When the dielectric wire length decreases from 9.8 mm to 9.0 mm with a step of 0.2 mm, the electric transmission dip is shifted gradually from 10.5 GHz towards 12.1 GHz, accounting for 1.6 GHz for the length variation of 0.8 mm. The numerical calculation reproduces well the experimental results. Little frequency discrepancy is attributed to minor difference of cut-wire shape and dielectric constant between simulation and experiment.
Fig. 4. Transmission spectra of dielectric cut-wire with various heights.
Furthermore, we carry out the temperature tunable property investigation of electric Mie resonance of dielectric metamaterial. The waveguide including dielectric cut-wire is placed inside a temperature test chamber and connected to VNA with a pair of high temperature cables. As shown in Fig. 5(a), the transmission dip of dielectric cut-wire occurs at 10.0 GHz for the environmental temperature of 10 °C. When the environmental temperature increases gradually to 50 °C, transmission dips shifts from 10.0 GHz towards 11.0 GHz. More importantly, effective permittivity of dielectric cut-wire shows the same trend with respect to the temperature variation, as shown in Fig. 5(b). The frequency with zero permittivity, ɷENZ, increases from 11.0 GHz to 12.95 GHz, hence, results in almost 2000 MHz frequency shift. Compared to frequency variation of transmission dip, larger tuning range of ENZ is presumably due to the nonlinear dispersion of permittivity a function of frequency around the electric Mie resonance. Note that such tuning effect can be reversibly controlled, providing the potential application in broadband ENZ metamaterial and related devices. Moreover, this dynamic control of electric resonance enables the feasibility to switch permittivity sign for a given frequency point. Taking the frequency of 11.63 GHz for instance, effective permittivity experiences gradual decrease from 2.1, zero and final down to −2.8 during the temperature increase by 40 °C.
#223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24912
As described by Mie theory of dielectrics [12, 15], related resonance frequency of dielectric resonator mainly depends on the relatively permittivity. With respect to dielectric cut-wire used herein, the dependence of permittivity of ferroelectrics on temperature can be described by [13, 26]
ε (T ) = ε 00 [η (T )]−1 ,
η (T ) = (θ F / Tc) 1/ 16 + (T / θ F ) 2 − 1,
where ε00 and θF are the analogs to the Curie–Weiss constant and the Debye temperature, respectively, TC is the Curie temperature. One can see that BST has a reverse relationship between relative permittivity and temperature above its Curie temperature. Consequently, the relative permittivity of dielectric cut-wire decreases with the increasing environmental temperature, hence, resulting in the blue shift of electric Mie resonance.
Fig. 5. Experimental transmission (a), effective permittivity (b) of dielectric cut-wire as a function of temperature. The dielectric cut-wire under test has a height of L = 9.8 mm.
In conclusion, we reported a dynamic control of electric Mie resonance of dielectric cut-wire type metamaterial. Around its lowest mode, dielectric metamaterial shows an electric resonance character with Lorentz–type dispersion of effective permittivity. The operation frequency of electric Mie resonance can be modulated either by wire length or temperature variation. When the temperature changes by 40 °C, the operation frequency can be reversibly tuned by 1000 MHz. Considering the advantage of low loss of dielectric resonator becomes more visible at higher frequencies, this work will be useful to promote dielectric metamaterial and related application development at infrared and optical range. Acknowledgments
We gratefully acknowledge the financial support from National Natural Science Foundation of China (Grant Nos. 61101044, 11372248, 61275176), National High Technology Research and Development Program of China (863 Program) (Grant No. 2012AA030403), Program for New Century Excellent Talents in University, Aeronautical Science Foundation of China (Grant No. 20120153001), NPU Foundation for Fundamental Research (Grant No. JCY20130138), NPU Aoxiang Star Project, and Project of Key Laboratory for Advanced Displays and System Application, Ministry of Education (Shanghai University).
#223154 - $15.00 USD Received 15 Sep 2014; revised 27 Sep 2014; accepted 28 Sep 2014; published 6 Oct 2014 (C) 2014 OSA 20 October 2014 | Vol. 22, No. 21 | DOI:10.1364/OE.22.024908 | OPTICS EXPRESS 24913