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We propose a broadband slow wave system based on the thin metal-insulator-metal (MIM) graded grating structure composed of two corrugated metal strips with periodic array of grooves on a thin dielectric substrate. The guided spoof surface plasmon polaritons (SSPPs) at different frequencies can be localized at different positions along the ultrathin MIM grating. By introducing specially designed non-corrugated MIM branches with specific lengths at the locations where the EM waves are trapped, the trapped EM waves can be released and propagate along these branches. A 4-way wavelength demultiplexer based on such plasmonic broadband slow wave system is then demonstrated and fabricated. To improve the isolations between different branches at lower frequencies, band-reject filters are inserted at the front of some MIM branches. The measurements and the simulation results have shown very good agreements, which validate the feasibility of the 4-way wavelength demultiplexer.
© 2014 Optical Society of America
1. Introduction
Slow light with remarkably reduced group velocity has attracted considerable interests due to its potential applications in information storage [1], optical memory [2], lasers [3], optical buffers [4], variable optical delays [5], optical modulators [6], and photonic sensors [7], etc. Many schemes have been developed to slow down the light including electromagnetically induced transparency (EIT) [8], stimulated Raman scattering [9], photonic crystal [10], etc. Rainbow trapping (broadband slow light) effect was first proposed by Tsakmakidis et al. [11]. A tapered left-handed heterostructure (LHH), which is composed of a left-handed material layer and two normal dielectric layers, can slow down and even stop the light for broadband and room-temperature operation. The “trapped rainbow” effect may be used in applications such as optical signal processing and enhanced light-matter interactions [12]. To make the LHH structure easily realizable and compensate the loss in the materials, many other improved structures were reported later [13, 14]. An experimental realization of the tapered LHH has been carried out to show the “trapped rainbow” effect [15]. Surface plasmon polaritons (SPPs) propagating toward the tip of a tapered plasmonic waveguide can be slowed down and asymptotically stopped when they tend to the tip, never actually reaching it [16]. The SPPs or spoof SPPs can confine electromagnetic (EM) waves within subwavelength dimensions over a wide spectral range [17–19]. It was shown that the SPPs or spoof SPPs (SSPPs) could be slowed down and trapped at terahertz (THz), telecommunication and visible frequencies [20–22]. Gan et al. reported the experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings [23]. However, the previous researches mainly focus on how to realize slowing and trapping the EM waves on the metal surface [16–23], which may result in large scattering loss due to the poor confinement of the EM waves.
The metal-dielectric-metal (MIM) structure has strong confinement of light with an acceptable length for SPPs propagation [24], which is promising for the design of compact all-optical devices [25]. Based on the MIM waveguides, some simple wavelength-selective structures have been proposed and investigated, such as plasmonic tooth-shaped filters [26], plasmonic filters with rectangular resonators [27], etc. It is important to investigate how to trap light in MIM plasmonic waveguides, which have better confinement of light and acceptable propagation length [28–30]. Many broadband slow light MIM systems have been reported, including a MIM graded grating waveguide [31], a dispersionless slow light MIM system based on a plasmonic analogue of EIT [32], a dual-channel dispersionless slow light system based on plasmon-induced transparency [33], a spoof-insulator-spoof (SIS) waveguide analogue of non-corrugated MIM waveguides in plasmonics [34], two parallel metallic slabs with periodic corrugations on their inner boundaries at THz frequencies [35, 36], etc. A plasmonic trapped rainbow based on a grapheme monolayer on a dielectric layer with grating substrate was proposed [37], whose advantages include compact size, wide frequency tunability, and compatibility with current micro/nanofabrication. Conformal surface plasmons (CSPs) supported by nearly zero-thickness metal strips printed on flexible, thin dielectric films have been proposed [38], which can be confined in the subwavelength scale along two transverse orthogonal directions and can propagate to long distances in a wide broadband range. High-order mode transmission of such SSPPs in the microwave frequency range was then investigated [39]. A double gratings CSPs waveguide, consisting of two ultrathin corrugated metallic strips, was proposed in the microwave frequency and demonstrates the excellent filtering characteristics such as low loss, wide band, and high square ratio [40]. These efforts have opened the way to implement compact surface plasmonic devices in the microwave frequency.
There has been an increasing interest in exploiting light trapping. However, the release of trapped light remains challenging. If we can release the trapped rainbow one by one, a wavelength demultiplexer (WDM) can be implemented. Plasmonic WDMs, which can filter specific wavelengths in different channels, will play very important role in the future all-optical communication systems [41]. Gan et al. proposed that the trapped EM waves on the graded metal grating structures can be released with a thermal-optical effect [21]. Theoretically by temperature-tuning the refractive index of the materials such as InAs, PbS, and PbSe that fill the grating groove, the trapped EM waves can be released theoretically. However, thermal effects are intrinsically slow and may not be adequate for many applications. Chen et al. came up with a one-dimensional (1D) chirped dielectric grating, by real time tuning the refractive index of the grating to trap and release the rainbow [22]. Real time tuning the refractive index of the grating might not be easy to realize in the THz regime. The capability of completely releasing the trapped SPPs by dynamically tuning the chemical potential of graphene by gate voltage was also investigated [37]. There have been many WDMs based on plasmonic MIM structures, such as nano-capillary resonators (F-P cavities) [42], arrayed F-P cavities [43], channel drop filters [44], a slot resonant cavity [45], and MIM plasmonic nanodisk resonators [46], etc. Chen et al. introduced a mechanism for trapping and releasing light in MIM structures through elastic or mechanical implementation [47]. Although high-speed modulation can be realized, as in metamaterial waveguides, the issues of loss and fabrication are yet to be addressed. Double graded metal gratings were designed to trap and release light through mechanical implementation, fulfilling the requisites of high-speed modulation, uncomplicated fabrication technology, low loss, and device flexibility [48].
Here we propose a plasmonic broadband slow wave system based on the thin MIM graded grating structure composed of two corrugated metal strips with periodic array of grooves on a thin dielectric substrate. It should be noted that the thin MIM grating structure is similar to the double gratings structure [40]. We propose a simple and real time method to release the trapped EM waves and implement the function of wavelength demultiplexing. The whole structure can be easily fabricated with the printed circuits board (PCB) technologies and is suitable for the integration with planar circuits. The transversal size of the compact WDM is only one wavelength. It can find important potential applications in the highly integrated surface plasmonic circuits in the microwave or THz frequencies. Firstly, a plasmonic broadband slow wave system based on the thin MIM graded grating structure is demonstrated. Then by introducing four non-corrugated MIM branches with specific lengths where the EM waves are trapped, the EM waves can be released and propagate along these branches and a 4-way WDM based on such slow wave system could be implemented. The experimental results and simulation analysis show excellent agreements.
2. Designing principles
2.1 The broadband slow wave system based on the thin MIM graded grating structure
The thin MIM graded grating structure consists of two corrugated metal strips with periodic array of grooves on a thin dielectric substrate (FR-4) shown in Fig. 1(a). The thickness t of the metal is 35 μm. The thickness d and dielectric constant of the FR-4 dielectric are 0.5 mm and 4.6, respectively. The slot period and slot width of the metal grating are denoted as p and w. The insulator between the two metal grating strips is air. It should be noted that the thin non-corrugated MIM structures are also called slot lines in the microwave frequencies [49], and the difference is that the width is finite here. Hereafter, we also call those non-corrugated structures slot lines to set them apart from the thin corrugated MIM grating structures. The slot line etched on one side of the substrate is crossed at a right angle by a microstrip conductor on the opposite side. Coupling between the slot line and microstrip line occurs by means of the magnetic field [49]. Gao et al. studied their optimized coupling between the slot line and microstrip line [40]. The SSPPs on the thin MIM graded grating are then excited by the EM waves on the slot line. The dispersion relation for the TM-polarized EM waves propagating in the x direction on the thin MIM gratings is first studied by use of the eigen-mode solver of the commercial software, CST Microwave Studio. The dispersion curves of the thin MIM gratings with different groove depths are plotted in Fig. 1(b), where g = 2 mm, p = 5 mm, and w = 2 mm. One can see that the dispersion characteristics of such structure are similar to those MIM structures in the optical frequencies and the dispersion curves become lowered when h increases, indicating that stronger EM field confinement can be achieved. Figure 1(c) gives the dispersion curves of the gratings with different insulator widths and slot widths, where h = 4 mm. It can be seen that the dispersion curves become lowered when w increases, however the curves change little when w is larger than 3mm. When g decreases, the dispersion curves become lowered. These dispersion curves are essential to guide the design of broadband slow wave system.
Fig. 1 (a) The proposed broadband slow wave system excited by the microstrip line at the bottom of the dielectric, where t = 35 μm, d = 0.5 mm, p = 5 mm, w = 2 mm and g = 2 mm. The depth h of the groove gradually changes from 3 mm to 8 mm with the step size 0.2 mm. (b) The dispersion curves for different h, where w = 2 mm and g = 2 mm. (c) The dispersion curves varying with w and g, where h = 4 mm. (d) Group velocities changing with different groove depths at different frequencies.
Since the dispersion curves are sensitive to the groove depths, we design the broadband slow wave system by changing the groove depths, while the insulator width g, the slot period p and the slot width w is fixed to 2 mm, 5 mm, and 2 mm. The group velocities vg of the SSPPs can be calculated according to the equation vg = dω/dβ. The vg of the SSPPs at the frequencies 6.1 GHz, 7.1 GHz, 8.1 GHz and 9.1 GHz are illustrated in Fig. 1(d). It can be seen that the group velocity of the SSPPs are reduced dramatically when the depths of the grooves are increasing, even down to zero. So the EM waves at different frequencies will be trapped at different locations of the MIM graded grating structure. The principle of such broadband slow wave system is similar to that proposed by Gan et al. [20]. From Fig. 1(d), we can deduce that the depths of those grooves where the EM waves from 6.1 to 9.1 GHz could be trapped are 7.31 mm, 5.98 mm, 4.98 mm and 4.19 mm, respectively. In our broadband slow wave system, the depths of the grooves are gradually changing from 3 mm to 8 mm with the step size 0.2 mm. So the EM waves from 6.1 to 9.1 GHz should stop before the grooves whose depths are 7.4 mm, 6.0 mm, 5.0 mm and 4.2 mm. The calculated vg at those four frequencies are 0.09c0, 0.07c0, 0.05c0 and 0.03c0 at the grooves whose depths are 7.2 mm, 5.8 mm, 4.8 mm and 4.0 mm, where c0 is the light velocity in vacuum. If the step size of these graded grating depths is sufficiently small, the vg at these four frequencies could slow down to zero.
The whole structure is modeled with the time-domain solver of CST microwave studio which is based on the finite integral time domain (FIT) methods. The two-dimensional (2D) electric field (E-field) distributions are illustrated in Fig. 2. The observed frequencies are 6.1 GHz, 7.1 GHz, 8.1 GHz and 9.1 GHz. The theoretical depths for those grooves where the EM waves cannot arrive are indicated in Fig. 2 with black arrows. It can be observed that most of the EM waves stop before the grooves indicated by these arrows. The E-field intensities are strongest one period before these arrows. That is because only when the groove depth, whose cutoff frequency is corresponding to the incident SSPPs frequency, is reached can the SSPP modes be stopped. Otherwise, they will be reflected back when the next groove cannot support them [20].
Fig. 2 (a)-(d) The 2D E-field distributions obtained from FIT simulations. The observed frequencies are 6.1 GHz, 7.1 GHz, 8.1 GHz and 9.1 GHz.
2.2 A 4-way WDM based on the broadband slow wave system
Here we propose a novel method to release the trapped SSPPs on the thin MIM graded grating structure. The proposed structure is schematically shown in Fig. 3(a), where four slot lines with specific lengths are introduced where the E-field intensities are strongest from 6.1 to 9.1 GHz. These locations are indicated by the red arrows in Fig. 3(a) and their groove depths are also given. The lengths of the slot lines are denoted as l1, l2, l3 and l4, respectively. According to the transmission line theory [49], the open-end slot lines whose lengths are an odd multiple of λ/4 are equivalent to the shorted junction at the input end. So the EM modes in such slot lines are the same as those in grooves, and the trapped EM waves will propagate along these slot lines. The propagation wavelength λ of the SSPPS on the slot lines, which is defined as the length between the E-field peaks as shown in Fig. 3(b), is obtained with FIT simulations. The observed frequency is 6.1 GHz in Fig. 3(b). The wavelengths for the EM waves at 6.1-9.1 GHz are 42mm, 36mm, 30mm and 28mm, respectively.
Fig. 3 (a) The proposed structure to release the trapped EM waves based on the thin MIM graded grating structure. The groove depths where the four slot lines are introduced are h = 4 mm, h = 4.8 mm, h = 5.8 mm and h = 7.2 mm, respectively; (b) The waveguide wavelength on the slot line at 6.1 GHz; (c) 2D E-field distributions at the plane of z = 1 mm for the broadband slow wave system with 2λg/4 slot lines; (d) 2D E-field distributions for the broadband slow wave system with 3λg/4 slot lines.
For comparisons, we model two broadband slow wave systems with four output ports. The first system is shown in Fig. 3(c), whose slot lines lengths are set to 2λg/4. The lengths of the four slot lines are l1 = 14 mm, l2 = 15 mm, l3 = 18 mm, and l4 = 21mm. The second system is shown in Fig. 3(d), whose slot lines lengths are set to 3λg/4. The lengths of the four slot lines are l1 = 21 mm, l2 = 22.5 mm, l3 = 27 mm, and l4 = 31.5mm. The width W of the four slot lines is 10 mm. The tapered depths at the end of the gratings can decrease the reflected EM waves from the open end. The simulation results based on FIT methods are illustrated in Figs. 3(c)-(d). Comparing Fig. 3(c) with Fig. 3(d), we notice that the trapped EM waves can be released and propagate along the four slot lines for the second system, while it is not the case for the first system. From Fig. 3(c), it can be seen that the EM waves at 6.1 GHz are released and propagate along the first slot line whose length is 14 mm. That is probably because its length is close to λg/4 (10.5mm). From Fig. 3(d), we can conclude that a 4-way WDM based on such broadband slow wave system can be implemented by introducing four slot lines with specific lengths. However, it should also be noted that the isolations between these four branches at lower frequencies are not good. From Fig. 3(d)-(i), it can be seen that there are leaky waves at 6.1 GHz propagating along the first slot line. This is probably related to the high-order modes of the SSPPs, which is similar to those investigated by Feng et al. [39] and needs more discussions in another paper. From Fig. 3(d)-(iii), we can see that the EM waves at 8.1 GHz can pass both the first and second slot lines, since the waveguide wavelengths on the slot lines at 8.1 GHz and 9.1 GHz are close.
To improve the isolations between slot lines at lower frequencies, we design the band-reject filters at the front of the first two branches as shown in Fig. 4(a), where the proposed 4-way WDM is depicted. The detailed structures of the band-stop filters are shown in Fig. 4(b). Filter 1 at the first slot line (l1) consists of two shallow grooves and two deep grooves. The depth h11 of the shallow groove is 2.5 mm and the depth h12 of the deep groove is 8 mm. Filter 2 at the second slot line (l2) consists of one shallow groove and one deep groove. The depths of the shallow and deep groove are h21 and h22, where h21 = 4 mm and h22 = 12 mm. The widths w1 and w2 of the grooves are 1 mm and the distance d1 between grooves for Filter 1 is 2 mm. Filter 1 is designed to specially reject the EM wave at 8.1 GHz and Filter 2 is designed to specially reject the EM wave at 6.1 GHz. Figure 4(c) gives the transmission spectra of the two band-stop filters. It can be seen that the transmission value at 9.1 GHz is high while the value at 8.1 GHz is nearly zero for Filter 1 and the transmission value at 8.1 GHz is nearly one while the value at 6.1 GHz is only 0.35 for Filter 2.
Fig. 4 (a) The proposed 4-way WDM with the band-stop filters; (b) The detailed structure of the band-stop filters, where h11 = 2.5 mm, h12 = 8 mm, h21 = 4 mm, h22 = 12 mm, w1 = w2 = 1 mm, d1 = 2 mm; (c) The transmission spectra of the band-stop filters.
3. Simulations and experimental verifications
The 4-way WDM with the band-stop filters is analyzed by use of FIT methods. The 2D distributions of the x-component electric fields on the xy-plane which is 1 mm away from the top surface of the thin MIM grating structure are observed. The simulation results at the frequencies of 6.1 GHz, 7.1 GHz, 8.1 GHz and 9.1 GHz are illustrated in Figs. 5(a)-(d), respectively. The electric fields have been normalized. It can be clearly seen that the electric fields intensities at the frequencies of 6.1 GHz, 7.1 GHz, 8.1 GHz and 9.1 GHz are the strongest propagating along Branch 4, Branch 3, Branch 2, and Branch 1, respectively.
Fig. 5 Results obtained from the FIT simulations. (a)-(d) 2D distributions of the x-component electric fields on the xy-plane which is 1 mm away from the WDM.
To show the isolations between the four branches more clearly, the normalized x-component electric fields along the red dashed lines denoted as Line 1-4 in Figs. 5(a)-(d) are given in Fig. 6(a). It can be seen that the isolations between the four branches at lower frequencies are very good. The insertion loss and propagation loss of the multi-way WDM are then investigated, which are defined by 10 × log10(Wout/Win), where Wout and Win are the output and input electric energy, respectively. The energy is calculated by doing area surface integrals on Faces 1-4 and Faces 11-44 shown in Fig. 6(b). The area of these surfaces is 10mm × 3mm. The electric energies on Faces 1-3 at 7.1 GHz are 3.9 × 10−9 J/m, 2.6 × 10−9 J/m, and 2.0 × 10−9 J/m, respectively. The average propagation loss is nearly 0.6dB/cm at 7.1 GHz. The input electric energy on the Face 1 and output electric energy on the Face 11 at 9.1 GHz are 3.2 × 10−9 J/m and 0.24 × 10−9 J/m. The input electric energy on the Face 2 and output electric energy on the Face 22 at 8.1 GHz are 1.1 × 10−9 J/m and 0.33 × 10−9 J/m. For the frequencies 7.1 GHz and 6.1 GHz, these values are 2.0 × 10−9 J/m on the Face 3 and 1.1 × 10−9 J/m on the Face 33, 0.58 × 10−9 J/m on the Face 4 and 0.35 × 10−9 J/m on the Face 44, respectively. It can be calculated that the losses are −2.2 dB, −2.6 dB, −5.2 dB, and −11 dB from 6.1 to 9.1 GHz, respectively. It can be seen that the losses at 8.1 GHz and 9.1 GHz are higher because of the additional insertion loss caused by the band-stop filters. The experimental setup is shown in Fig. 6(c). The 4-way WDM sample is pasted on the foam which is fixed to the motorized translation table. The motorized translation table consists of a pair of computer controlled linear stages, whose scanning range is 12.5 cm by 5.3 cm with the resolution of 1 mm. The Vector Network Analyzer (VNA, Agilent N5227A) provides the microwave signal source and the detection of the return signal. The microstripe line at the bottom of the WDM is welded to a coaxial cable (SFT-50-3). Another coaxial cable (SFT-50-1) is used as a detecting probe to sample the x-component of the electric fields on the xy-plane 1 mm away from the surface of the 4-way WDM. In order to reduce the disturbance of the probe, the probe is fixed onto the upper stationary shelf and is extended vertically down to the sample. Its inner conductor is extended about 1.5 mm and bended 90 degrees in order to sample the x-component electric fields.
Fig. 6 (a) The normalized x-component electric fields along the red dashed lines denoted as Lines 1-4 in Figs. 5 (a)-(d). (b)The surfaces used to evaluate the losses the demultiplexer, where Faces 11-44 are placed along the Lines 4-1 in Figs. 5(a)-(d).The area of these surfaces is 10mm × 3mm. (c) The photograph of the experimental setup. The sample is pasted on the foam which is mounted to two computer-controlled linear translation stages, enabling a scanning area of 12.5 cm by 5.3 cm with a resolution of 1mm. The detecting probe is SFT-50-1 cable and its inner conductor is extended 1.5 mm and bended 90 degrees in order to sample the x-component of the electric fields. The coaxial detecting probe is fixed onto the stationary shelf.
The measurement results are illustrated in Figs. 7(a)-(d). Comparing the Figs. 5(a)-(d) with Figs. 7(a)-(d), we can see that the measured and simulated results have very good agreements. It validates the feasibility of the 4-way WDM based on the plasmonic broadband slow wave system.
Fig. 7 (a)-(d) 2D distributions of the measured x-component electric fields on the xy-plane which is 1 mm away from the demultiplexer.
The design can be scaled down to the THz regime. The 4-way WDM in the THz frequencies is also simulated with CST software. The parameters are g = w = 20µm, p = 50µm, and t = d = 5µm. The groove depths vary from 30µm to 80µm with the grade 2µm. The 2D distributions of the x-component electric fields on the xy-plane which is 2µm away from the top surface of the whole structure are illustrated in Fig. 8. The observed frequencies are 0.61-0.91 THz, respectively. The electric fields have been normalized. One can see that the EM waves at the frequencies of 0.61 THz, 0.71 THz, 0.81 THz and 0.91 THz are propagating along different branches and the demultiplexer works.
Fig. 8 (a)-(d) 2D distributions of the x-component electric fields on the xy-plane which is 2 µm away from the demultiplexer in the THz frequencies.
4. Conclusion
We have proposed and fabricated a 4-way WDM based on a plasmonic broadband slow wave system, which integrates conventional microwave devices with the surface plasmonic devices very well. The trapped EM waves at different frequencies on the thin MIM graded grating structures can be released and propagate along specially designed MIM branches. The band-reject structures can improve the isolations between the branches at lower frequencies. The experimental and simulation results have shown good agreements. The whole structure can be easily manufactured by the existing PCB technologies. It is also believed that the whole design can be scaled down to the THz frequencies regime. The WDM can find important potential applications in highly integrated surface plasmonic circuits in the microwave or THz frequencies.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant No. 61307129, in part by the Shanghai Committee of Science and Technology under Grant No. 13ZR1454500, and in part by the Open Project Program of the State Key Laboratory of Millimeter Waves under Grant No. K201416.
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