Slowing and stopping of wave in dispersive metamaterial loaded helical guide

Dushyant K. Sharma; Surya K. Pathak

doi:10.1364/OE.24.002687

1. Introduction

Devices that can slow or even stop the Electromagnetic (EM) wave are very much in demand, nowadays, since they can dynamically control the flow of wave. Electromagnetic wave structures possess these characteristics find applications in optical communication networks [1] and quantum information processing systems [2] to control the flow of optical data by realizing optical buffer and memory. Slow wave devices also cater solutions to many potential applications such as microwave photonics [3], terahertz filters [4], enhanced light matter interactions [1] etc. Different research groups have proposed different methods and EM wave guiding structures for achieving slow wave such as photonic crystal waveguide [1], quantum dot semiconductor optical amplifiers [5], electromagnetically induced transparency [6], direct coupled resonators [7], coherent population oscillations [8] and surface plasmon polaritons [9]. In addition to these methods, different hybrid waveguides such as metallic nanowire loaded silicon on insulated structures [10], dielectric nanowires covered or insulated with metal [11] have been also proposed and studied for deep-subwavelength light confinement and transport using metal and dielectric arrangement [12].

Tsakmakidis et al. [13] first proposed the slowing and stopping of EM wave through planar metamaterial waveguide in axially varying metamaterial core hetero structure. They explained this phenomenon through negative Goos-Hanchen effect at the interface of two media. These finding established a connection between two realms of science, metamaterial and slow light, and accelerated the research in that area. Thereafter different groups around the world proposed various slow waveguide structures by utilizing metamaterial properties [2, 14, 15, 16]. EM wave propagation characteristics of a metamaterial slab waveguide was explained by Suwailam et al. [17] in detail and they found that both TM- and TE- modes travel with less speed. A similar observation was also reported by Erfaninia et al. [18], where they found that group velocity is greatly reduced in multilayered metamaterial waveguide. Huang et al [19] have studied anisotropic metamaterial cylindrical guide and observed that EM wave can be slowed and even stopped inside the waveguide. Gan et al. [20] studied a waveguide structure made up of graded metallic grating and reported slow wave phenomenon over ultra wide bandwidth. Chen et al. [21] have demonstrated trapping of true rainbow through a dielectric grating with graded thickness on metallic film. Alekseyev et al. [22] studied strongly anisotropic dielectric waveguide and proposed their application in the area of slow wave and 3D imagining. Usually dispersion characteristics of most of these structures are explained in terms of FW, BW and mode-degeneracy phenomena where both FW and BW meet and group velocity is reduced significantly or becomes almost zero. In our previous work [23] we studied slow wave characteristics of metamaterial loaded helical guide with an aim to extract effective permittivity and permeability parameters numerically as well as analytically.

In this paper, we propose, a helical slow wave structure loaded with a dispersive metamaterial medium (having both ε and µ negative). The motivation behind this study is to combine the slow wave behaviour due to the metamaterial and that due to the helix geometry which already possess slow wave behaviour over a wide bandwidth [24, 25] and is being widely utilized in travelling wave tubes [26] and travelling wave antennas [27]. For the proposed structure, analytical dispersion relation is derived and computationally solved to visualize the modal characteristics in terms of FW, BW and mode-degeneracy phenomena. In order to realize dispersive metamaterial medium, an F-shaped Metamaterial cell is designed and arranged inside the helical guide. The designed structure has been electromagnetically simulated using CST Microwave Studio to verify the analytical findings. Finally, advantages of this slow waveguide device over other reported waveguide devices are discussed in conclusion.

2. Helical guide design and mode analysis using Drude model

Considered structure for analysis is a sheath helix of radius a and pitch angle ψ, as shown in Fig. 1(a), on which guided EM wave is travelling along the z-direction. The current flow along the sheath is constrained to a direction which makes a constant angle (90° − ψ) with the axis of the helix. The tangential component of the electric field, E_‖, (shown in Fig. 1(b)) is zero along the direction of current flow, and finite and continuous through the sheath along the direction perpendicular to the current flow. Region-I is a dispersive metamaterial media and its dispersive behaviour is described by the Drude model [28]. Region-II is a free space medium.

Fig. 1 (a) Sheath helix of radius a, pitch p and pitch angle (ψ = tan⁻¹ p/2πa). Region I (inner region) is metamaterial media and Region II (outer-region) is free-space. (b) Expanded view of sheath helix and its helical coordinates (figure taken from [24]).

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Here we consider lossless Drude model which models cold plasma medium and its governing equations are written as:

ε_{r 1} = 1 - \frac{ω_{p}^{2}}{ω^{2}}

μ_{r 1} = 1 - \frac{F ω^{2}}{ω^{2} - ω_{o}^{2}}

Here F is filling factor, ω_o and ω_p are resonant and plasma frequency respectively. The values of F=0.56, ω_o=8π and ω_p=20π are taken which are validated experimentally by Simth et al. [29]. Region II is free-space having permittivity and permeability values ε_r₂ and µ_r₂, respectively.

The dispersion relation of the proposed DMLHG structure, which describes the modal behaviour of an EM wave, is analytically derived from [25] by defining ε_r₁ and µ_r₁ as a dispersive metamaterial parameter inside the helical guide (region 1) and written as:

\begin{array}{l} k_{o} a^{2} c ε_{1} (ω) k_{1} \cot (ψ) \frac{I_{n}^{'} (k_{1} a)}{I_{n} (k_{1} a)} - \frac{Y^{2}}{k_{o} a^{2} c μ_{1} (ω) k_{1} \cot (ψ)} \frac{I_{n} (k_{1} a)}{I_{n}^{'} (k_{1} a)} - \\ k_{o} a^{2} c ε_{2} k_{2} \cot (ψ) \frac{K_{n}^{'} (k_{2} a)}{k_{n} (k_{2} a)} r^{2} + \frac{X^{2} r^{2}}{k_{o} a^{2} c μ_{2} k_{2} \cot (ψ)} \frac{K_{n} (k_{2} a)}{K_{n}^{'} (k_{2} a)} = 0 \end{array}

Here r = k₁a/k₂a, $X = k_{2}^{2} - n β \cot (ψ)$ , $Y = k_{1}^{2} - n β \cot (ψ)$ . $k_{1} = {(β^{2} - k_{o 1}^{2})}^{0.5}$ $k_{2} = {(β^{2} - k_{o 2}^{2})}^{0.5}$ , are transverse wave numbers. β is longitudinal phase coefficient. $k_{o 1} (= ω \sqrt{ε_{1} μ_{1}})$ and $k_{o 2} (= ω \sqrt{ε_{2} μ_{2}})$ are propagation vector of region I and II. (′) is derivative of Bessel function. For guided mode propagation field should decay exponentially in region-II and the opposite is expected in region-I. Thus, modified Bessel function of second (K_n(k₂a)) and first kind (I_n(k₁a)) is used in region-II and I respectively, where n describes the modal behaviour of the wave.

For EM wave propagation in helical guide, the components of poynting vectors are [16]:

S_{z} = \frac{1}{4 Π} (E_{r} H_{ϕ}^{*} - E_{ϕ} H_{r}^{*})

S_{r} = \frac{1}{4 Π} (E_{z} H_{ϕ}^{*} - E_{ϕ} H_{z}^{*})

S_{ϕ} = \frac{1}{4 Π} (E_{z} H_{r}^{*} - E_{r} H_{z}^{*})

Total power flow in different layers of waveguide is sum of power flow in each layer of guide [16]:

P_{z} = P_{z}^{i n} + P_{z}^{o u t}

P_{z}^{i n} = \int_{0}^{a} S_{z} r d r, P_{z}^{o u t} = \int_{a}^{\infty} S_{z} r d r

Obtained expression of $P_{z}^{i n}$ and $P_{z}^{o u t}$ for proposed structure is:

\begin{array}{l} P_{z}^{i n} = - \frac{A^{2} β ω ε_{1} x^{2} I_{n}^{2} (x) h_{n}^{'} (x)}{4} - \frac{B^{2} β ω μ_{1} x^{2} I_{n}^{2} (x) h_{n}^{'} (x)}{4} \\ + i A B (ω^{2} ε_{1} μ_{1} k_{1} - β^{2}) n \int_{0}^{x} I_{n} (x) I_{n}^{'} (x) d x \end{array}

\begin{array}{l} P_{z}^{o u t} = - \frac{C^{2} β ω ε_{2} y^{2} K_{n}^{2} (y) g_{n}^{'} (y)}{4} - \frac{D^{2} β ω μ_{2} y^{2} K_{n}^{2} (y) g_{n}^{'} (y)}{4} \\ + i A B (ω^{2} ε_{2} μ_{2} k_{2} - β^{2}) n \int_{y}^{\infty} K_{n} (y) K_{n}^{'} (y) d y \end{array}

Here x = k₁a, y = k₂a, $h_{n}^{'} (x) = - x h_{n}^{2} (x) - 2 / x h_{n} (x) + n^{2} / x^{3} + 1 / x$ , $g_{n}^{'} (x) = - x g_{n}^{2} (y) - 2 / y g_{n} (y) + n^{2} / y^{3} + 1 / y$ , $h_{n} (x) = I_{n}^{'} (x) / (x I_{n} (x))$ and $g_{n} (y) = K_{n}^{'} (y) / (y K_{n} (y))$ . A, B, C and D are field coefficients and inter related to each other. Normalized power flow is [16]:

〈 P_{z} 〉 = \frac{P_{z}^{i n} + P_{z}^{o u t}}{| P_{z}^{i n} | + | P_{z}^{o u t} |}

EM wave modal characteristics of DMLHG structure under study are described by solving dispersion Eq. (3) for its eigen-value solutions in terms of axial propagation constant, β. We have computed β as a function of k_o by using Findroot subroutine of MATHEMATICA 7.0 Package. For guided mode propagation, both k₁ and k₂ should be positive. Therefore only those roots are considered which are higher as compared to k_o₁ and k_o₂.

Figure 2 describes the EM-wave propagation characteristics of DMLHG structure for the dominant mode case (n = 0). Fig. 2(a), shows modal characteristics of DMLHG having pitch angle 30° and radius 100 mm, respectively. Fundamental mode labelled as mode-1, has lower cut-off frequency (LCF) at 4.72 GHz and exhibits a negative slope of d(k_o)/d(β). This mode represents BW characteristics having anti-parallel group- and phase- velocities. First higher order mode (labelled as 2, in Fig. 2(a)) has LCF at 5.21 GHz and is considered as FW mode as it propagates with opposite features in comparison to mode-1. Mode-1 exhibits enhanced slow wave characteristics since its observed minimum normalized phase velocity (v_p/c = k_o/β) is 0.044 which is almost 22 times less than velocity of light. Both modes propagate as Surface Plasmonic (SP) modes and meet at 5.36 GHz and this point is regarded as a mode-degeneracy point. Similar characteristics are also observed for other DMLHG parameters and are shown in Figs. 2(b), 2(c) and 2(d).

Fig. 2 Variations of effective index, n_eff = β/k_o as a function of frequency. Here Y-axis is plotted on log₁₀ scale and X-axis is on linear scale. Two modes labelled as mode 1 (backward wave) and mode 2 (forward wave) are propagating simultaneously and meeting at green circle represents the degeneracy point. Figs. (a) and (b) are plotted for pitch angle 30° and 10°, respectively, while helical guide radius, a, is 100 mm for both the cases. Figs. (c) and (d) are plotted for helical guide radius 8 mm and 5 mm, respectively, while helical guide pitch angle is 0.9° for both the cases.

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The helix parameters, namely, pitch angle (ψ) and its radius (a) provide a control of bandwidth spectrum of both BW- and FW- modes, effective index values as well as mode-degeneracy point. In Figs. 2(a) and 2(b) the effects of helix pitch angle variations (30° and 10°) are plotted by keeping helix radius (a = 100 mm) constant. From these two graphs it can be concluded that reduction in pitch angle increases the effective index and bandwidth spectrum of both modes. Also it can be seen that mode-degeneracy point is shifted at higher frequency. The effect of helix radius variations (8 mm and 5 mm) by keeping its pitch angle (0.9°) constant are plotted in Figs. 2(c) and 2(d). Contrary to earlier case, the reduction in guide radius reduces the effective index and bandwidth spectrum of both modes. At the same time mode-degeneracy point is also shifted to lower frequency. In Figs. 2(c) and 2(d), observed high value of effective index for the mode-1 resulted in minimum normalized phase velocity (v_p/c) 0.00120 and 0.00123, respectively. This substantial decrease in normalized phase velocity of mode-1 is attributed as ultra slow wave mode.

The characteristics of normalized group velocity (v_g/c) and normalized power flow (P_z) are plotted in Figs. 3(a) and 3(b) as a function of frequency. Both the graphs are derived from obtained values of axial propagation constant, β, from Eq. (3). For normalized group velocity (v_g/c = dk_o/dβ) calculation β value was used in the expression dk_o/dβ. In order to calculate normalized power flow obtained values of β were put in Eqs. (9) and (10). From this power flow in different layers of waveguide are obtained which are P_z₁ and P_z₂. Further the value of P_z₁ and P_z₂ were used in Eq. (11) to calculate P_z. From these graphs (shown in Figs. 3(a) and 3(b)), it can be seen that at mode degeneracy point group velocity reduces to zero and power flow vanishes. So, the point of mode-degeneracy corresponds to stopping of wave.

Fig. 3 Variations of group velocity (v_g/c), Fig. 3(a), and normalized power flow (P_z), Fig. 3(b), as a function of frequency for helix pitch angle 30° and radius 100 mm, respectively. Green circle represent the mode-degeneracy point, above that mode 2 and below that mode 1 are shown.

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When Eq. 3 is solved for higher mode (n = 1) case we obtained similar characteristics as we obtained for dominate (n = 0) mode case. A comparative study between two modes (n = 0, n = 1) are shown in Fig. 4. It can be seen from the graph that effective index n_eff is slightly increased for n = 1 mode in comparison to n = 0 mode. Thus due to increased value of effective index slow wave behaviour of higher mode case is more enhanced as compared to dominate mode case. The higher cut off frequency (HCF) of BW and FW mode is also increased marginally (for example HCF of n = 0 and 1 respectively is 5.36 GHz and 5.41 GHz). This resulted in slight increased in bandwidth spectrum of the guide.

Fig. 4 Variations of effective index, n_eff = β/k_o as a function of frequency for dominate (n = 0) and higher (n = 1) mode case at pitch angle 30° and radius 100 mm. Here Y-axis is plotted on log₁₀ scale and X-axis is on linear scale.

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3. Design and simulation of DMLHG using CST Microwave Studio

In above section for analytical characterization of DMLHG structure we used Drude model to include the dispersive nature of metamaterial. In order to realize such structure one needs to create metamaterial medium inside helical guide. Here we are presenting two possible designs.

3.1. First design

In our first design, we have chosen novel FF-shaped metamaterial cell (shown in Fig. 5(a)) as a unit cell for realizing metamaterial medium inside the helical guide. The used FF-shaped unit cell is a combination of FR-4 board of thickness 0.5 mm which is used as substrate on which highlighted double F-shaped area, having thickness of 35 µm, of copper is printed. The cell is single sided and opposite to the helical winding side to avoid direct contact between helical winding and metamaterial inclusions. The resonance characteristics of this unit cell are simulated using CST Microwave Studio. In Fig. 5(b), both transmission (S₂₁) and reflection (S₁₁) coefficients results are shown. From the results it is observed that pass band or resonance band exist between the spectrum 11.63 to 14.75 GHz.

Fig. 5 (a) The geometry of FF-shaped metamaterial cell (all dimensions are in mm). (b) The S-parameter transmission (S₂₁) and reflection (S₁₁) results of the FF-shaped metamaterial cell.

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In order to design a DMLHG structure following procedures have been adopted:

First we created a hollow cylindrical structure of a flexible FR-4 material. Its radius, width and thickness are 5.18 mm, 2.5 mm and 0.5 mm, respectively. On its inner wall FF-shaped metallic inclusions were arranged with a periodicity of 1 mm in azimuthal direction. This way an azimuthally arranged FF-shaped unit cell in cylindrical geometry as shown in Fig. 6(a) is created.
A helix having wire radius and pitch 0.05 mm and 0.08 mm respectively was wounded over this cylindrical structure. This whole arrangement formed a DMLHG unit cell as shown in Fig. 6(b).
An array of unit cells are now arranged axially to realize the DMLHG structure as shown in Fig. 7(a)

Fig. 6 (a) Azimuthally arranged FF-shaped unit cells. (b) The unit cell of DMLHG structure.

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Fig. 7 (a) The Designed DMLHG structure. (b) The S-parameter transmission (S₂₁) and reflection (S₁₁) results of DMLHG.

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To examine the pass band characteristics or resonance characteristics of designed DMLHG structure (shown in Fig. 7(a)) a full wave time domain simulation of the structure is performed. For this purpose, we excited EM wave in the structure through a coaxial-feed arrangement. It works as a source for our structure and its schematic is shown in Fig. 8(a). The detailed dimensions of coaxial-feed are dielectric core diameter b = 2.4 mm, dielectric permittivity ε_r = 2.1, inner conductor diameter a = 0.6 mm and it has cut off frequency of 43.9 GHz. The position of source during excitation of DMLHG structure is shown in Fig. 8(b). Obtained transmission- and reflection- coefficients results are shown in Fig. 7(b). Here, it can be seen that simulated DMLHG structure possess a pass band or resonance spectrum of bandwidth 12.5 to 14.5 GHz. This spectrum matches with the pass-band spectrum of FF-shaped metamaterial cell.

Fig. 8 (a) Schematic of coaxial feed. (b) Connection arrangement of coaxial feed with DMLHG structure.

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The pass band characteristics of DMLHG structure signify that within this spectrum DMLHG structure will exhibit the guided mode propagation characteristics, as well. In order to visualize and analyse the modal behaviour of this structure we have performed an Eigen-mode simulation of unit cell (shown in Fig. 6(b)) of the designed structure with periodic boundary conditions in +z and −z directions. The obtained Eigen-mode characteristics are plotted in Fig. 9(a). From the graph it can be seen that DMLHG structure supports both FW and BW mode. Both modes are propagating in the frequency-range of 13.7 to 14.5 GHz and they are degenerate at a critical frequency 14.4 GHz. The existence of BW mode in the DMLHG structure signifies the essence of metamaterial loading inside the structure. In order to bring out the significance of metamaterial loading an Eigen-mode simulation of unit cell of the helix has been performed when it is in free space. Obtained dispersion graph is shown in Fig. 9(b). It is observed that helix supports propagation of FW mode over a very wide bandwidth spectrum 15 to 60 GHz and there is no BW mode as well as degeneracy point.

Fig. 9 The dispersion graph of the cases: when helical guide is in (a) Loaded with FF-unit cells or DMLHG structure. (b) free-space

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The power flow and group velocity characteristics are plotted in Figs. 10(a) and 10(b), respectively. From these graphs it can be seen that at critical frequency or degeneracy point, power flow vanishes and group velocity also becomes zero. The high value of propagation coefficient and mechanism of degeneracy leads to slowing and eventually stopping of EM wave.

Fig. 10 The DMLHG structure plot of (a) Power flow Vs frequency. (b) Group velocity Vs frequency.

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At critical frequency, absolute longitudinal magnetic field (H_z) distributions are plotted in Fig. 11 at different time intervals. The presence of slow wave effect in the structure can be easily seen as wave packet gets more and more compressed as phase advances with time. At time of maximum wave packet compression (shown in time interval-3) wave packets become stand still or trapped for a while. Thereafter a new wave packet train gets started and this process repeats itself. However, it is not possible to hold or trap a wave packet forever in the lossy medium.

Fig. 11 At critical frequency the amplitude of longitudinal magnetic field (H_z) is plotted along the length of FF-Shaped Metamaterial Loaded DMLHG structure.

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3.2. Second design

An alternative to FF-shaped metamaterial cell the S-shaped metamaterial cell [30] is also considered in order to realize DMLHG structure. It has resonance spectrum between 8.72 to 9.28 GHz. The design procedure is same as we have described in earlier case. The S-Shaped loaded DMLHG structure is shown in Fig. 12(a).

Fig. 12 (a) The S-Shaped metamaterial cells loaded DMLHG structure (b) its transmission (S₂₁) and reflection (S₁₁) results.

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In order to figure out the pass band of this design we have performed a full wave time domain simulation of this structure (shown in Fig. 12(a)). For that purpose DMLHG structure is excited by coaxial feed at both ends. Obtained transmission-(S₂₁) and reflection-(S₁₁) coefficients results are shown in Fig. 12(b). It is observed that this arrangement also possess a pass-band or resonance band which almost overlaps the pass-band spectrum of S-shaped metamaterial cell.

The Eigen mode simulation of unit cell S-shaped DMLHG structure (shown in Fig. 13(a)), for its obtained pass band spectrum (shown in Fig. 12(b)), is performed as we did for the first case. The modal dispersion characteristics is shown in Fig. 13(b) where it can be seen that the this design also exhibits BW mode, FW mode and mode-degeneracy behaviour.

Fig. 13 (a) The unit cell of DMLHG structure loaded with SS-shaped metamaterial cells. (b) Its dispersion characteristics.

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The electromagnetic simulation of these two designs exhibit and reveal similar characteristics as reported in analytical characterization. But resonance characteristics or pass band characteristics are observed in a slightly shifted frequency spectrum. The reason behind this could be Drude model which is used as a dispersive parameter in analytical study. While in simulations study actual field configurations modify the effective constitutive parameters.

4. Engineering and manufacturing feasibility at different spectrum

In order to manufacture the DMLHG structure, one needs to design curved Metasurfaces inside helical guide, which is possible, by using flexible substrate materials [31] like polyimide, plastic, transparent conductive polyester, polyester, FR-4 etc. These substrates materials are widely used in manufacturing of Flexible electronics which can be folded and bended without any functional deformation.

The size of metamaterial inclusions on Metasurface is decided by the spectrum where DMLHG structure needs to operate. In order to realize DMLHG structure at very high frequency spectrum the size of metallic inclusions should be in the order of µm or nm. Using present day IC (integrated circuit) fabrication technologies such as electron beam lithography and photo lithography such miniaturized design is possible. For 1 THz [32], 6 THz [33], 70 THz [34] and 200 THz [35], Split Ring Resonator (SRR) have already been fabricated and its magnetic response is observed experimentally.

In present study, both analytical and simulation characteristics have been presented in GHz spectrum. As described, the frequency range where DMLHG structure exhibited the characteristics of slowing and trapping of EM wave belongs to the spectrum where loaded metamaterial cell have a pass-band. So, we can shift or tune this spectrum by scaling the size of metamaterial cells. In Table 1, we have presented the dimensions of FF-DMLHG structure for attaining similar characteristics in THz frequency range (in between 12 to 14 THz).

Table 1. Design of FF-DMLHG in THz Regime (dimensions in µm)

View Table

5. Conclusion

In this paper we have investigated the modal characteristics of a Dispersive Metamaterial Loaded Helical Guide (DMLHG). Analytical characterizations reveal that both FW and BW modes propagate simultaneously and are degenerate at the same frequency point. The mechanism of mode-degeneracy leads to stopping of wave. BW mode propagates as a fundamental mode which possess enhanced slow wave characteristic. Analytical findings have been verified by electromagnetic simulations of two practically feasible designs.

In this study, first time, we have coupled the characteristics of conventional helical slow wave structure with metamaterial properties for possible applications in contemporary field of slow waves and optoelectronics. There are various waveguide based metamaterial designs already been proposed for such applications. Most of these designs are in cylindrical [19, 36] or planer [2, 13, 17, 18, 22, 14, 15] in shape and support multi-modal characteristics. We believe that DMLHG structure have two distinguished advantages (i) it supports single mode operation, therefore excitation of the desired mode would be easier and (ii) at the same time its reconfigurability for different spectrum is much easier which in turn cuts down the re-engineering costs wherein helix pitch angle provides an additional knob to control the wave velocity.

Other slow wave methods which are based on surface plasmon polaritons having issues of sensitivity to surface roughness and are relatively difficult to excite [13]. At the same time photonics crystal based devices possess multimodal characteristics [13]. As compared to these methods our structure doesn’t have any issue of mode excitation and multimodal behaviour.

Acknowledgments

We would like to thank Dr. Alan Mickelson, Associate Professor, University of Colorado Boulder, USA and Mr. Vineet Kumar Dad, Scientist at Space Application Center, ISRO, India for fruitful discussions. We also want to thank Mr. JJU Buch, Scientist, Institute for Plasma Research, India in improving the manuscript.

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Slowing and stopping of wave in dispersive metamaterial loaded helical guide

Abstract

1. Introduction

2. Helical guide design and mode analysis using Drude model

3. Design and simulation of DMLHG using CST Microwave Studio

3.1. First design

3.2. Second design

4. Engineering and manufacturing feasibility at different spectrum

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (13)

Tables (1)

Equations (11)

Optics Express