Abstract

We report a design of low-loss THz Bragg fibers with a core size on the order of wavelength that operates near the cutoff frequency of its TE01 mode. We also propose a broadband Y-type mode converter based on branched rectangular metallic waveguides to facilitate coupling between the TE01 mode of the Bragg fiber and the TEM mode in free space with 60% efficiency. Our fiber holds strong promise to facilitate beam-wave interaction in gyrotron for high-efficiency THz generation.

© 2015 Optical Society of America

1. Introduction

Terahertz (THz) technology has aroused strong interest over the past decade due to its many promising applications in communication [1], imaging and spectroscopy [2], biology and medicine [3], and astronomy [4]. To improve performance, coherent THz sources with high power are sought after. Gyrotrons, which are the waveguide implementation of electron cyclotron maser (ECM), is able to generate high-power coherent THz radiation from energetic gyrating electrons, and has been a subject of intense research over the past few decades [5–7]. To achieve high power, high gain through efficient beam-wave interaction is necessary and a low-loss TE01 mode is generally employed [5]. Under the beam-wave synchronism condition, relativistic gyrating electrons would exhibit either azimuthal bunching, originating from the modulation of electrons’ gyrating frequency by transverse electric field, or axial bunching, originating from the modulation of electrons’ drift velocity by transverse magnetic field [6]. The competition between these two bunching mechanisms results in low gain and thus should be avoided [5, 6]. A small-core cylindrical metallic waveguide with an operating frequency close to the TE01 cutoff frequency is generally employed to suppress axial bunching. The near-cutoff operation, however, results in large ohmic loss where the power attenuation can be as high as 1 cm−1 around one terahertz [8, 9]. A low-loss THz waveguide with small-core dimension is therefore highly desirable for THz gyrotron.

In order to reduce the propagation loss in metallic waveguides, a single layer of dielectric coating has been added on the inner surface of metallic walls to form so-called hybrid-cladded waveguides [10–14]. By carefully choosing the thickness of the dielectric film, destructive interference at the operating frequency reduces the field strength at lossy metallic boundary and hence lowers the propagation loss. This low loss, however, is obtained at the expense of available bandwidth, as a thin-film etalon is typically very narrowband [10].

On a parallel front, hollow-core THz photonic bandgap (PBG) fibers, including photonic-crystal holey fibers that utilize two-dimensional index modulation [15, 16] or Bragg fibers that utilize radial index modulation [17–19], have become an active research topic recently. Because of the strong photonic bandgap confinement and their all-dielectric nature, these fibers can exhibit much lower loss compared to their hollow-core metallic or hybrid-cladded counterparts [10, 20]. To this end, the majority of efforts focused on PBG fibers with large core dimension (core diameter to wavelength ratio > 15), where the operating THz band is far above the cutoff frequency to render very low-loss and low-dispersion propagation [17–20]. Such PBG fibers can be used to transport broadband THz radiation for communication and sensing [1–3, 10], but are not suitable as the interaction tubes for gyrotron due to extremely serious mode competition and potentially unstable beam-wave synchronism caused by the competition between azimuthal bunching and axial bunching [6].

Another challenge for operating Bragg fibers in TE01 mode is its low coupling efficiency by traditional sources such as photoconductive-switching antenna [8] and optical rectification [21]. When the linearly polarized THz wave from these sources impinges on Bragg fibers, HE11 mode will be excited instead of the azimuthally polarized TE01 mode [8, 18]. To the best of our knowledge, only a couple experiments have succeeded in exciting/extracting TE01 mode in the visible/infrared regions [22, 23]. Consequently, efficient excitation of the TE01 mode in THz waveguides is a critical issue for the application as high-power THz sources.

In this work, we present a design of low-loss small-core Bragg fiber operated around one terahertz, which is slightly above the cutoff frequency of the TE01 mode for efficient gyrotron operation. In addition, we propose a novel coupling scheme based on a Y-type mode converter to excite the TE01 mode in the designed fiber, and quantify its coupling efficiency using rigorous eigenmode expansion method. It is well known that a hollow-core Bragg fiber is intrinsically a leaky waveguide whose eigenmodes are either a continuum of radiation modes or a discrete set of leaky modes [24]. While modal expansion utilizing the continuum has been demonstrated in one-dimensional open waveguides [24], it is very complicated to apply to a two-dimensional Bragg fiber. To effectively model the modal coupling between the mode converter and the Bragg fiber, we modify our fiber design by adding a copper outer cladding to the Bragg fiber such that electric field becomes zero at the dielectric-metal interface. Eigenmodes then become normalizable and discretized, facilitating the eigenmode expansion. The effect of this copper outer cladding upon the modal coupling will be shown to be negligible. As the typical interaction length for THz gyrotron is only several millimeters [6, 7], our Bragg fibers can be considered short and rigid. We therefore do not consider bending loss here.

This article is organized as follows. Section 2 briefly describes the design guideline for the small-core metal-cladded Bragg fibers. Section 3 presents the characteristics of the TE01 mode in the designed Bragg fiber, including its dispersion, field distribution, and ultra-low attenuation (power loss coefficient < 0.1 cm−1). Section 4 shows the characteristics of the additional twenty eigenmodes with azimuthal symmetry that are necessary for the coupling analysis. The design and performance of the Y-type mode converter is presented in Sec. 5, and the coupling efficiency of desired TE01 mode is analyzed and quantified in Sec. 6.

2. Design of a small-core Bragg fiber with metallic cladding operating in TE01 mode

As explained above, in this work we consider a hollow-core metal-cladded Bragg fiber. The index profile is shown in Fig. 1, where nhigh (nlow) and dhigh (dlow) represent the refractive index and the thickness of high-index (low-index) layer, followed by a metallic outer cladding. For low-loss operation, the materials used in Bragg layers should possess large refractive index contrast and low dielectric losses [18–20, 25–27]. We therefore choose high-density polyethylene (HDPE) as the high-index material which has a refractive index of 1.530 and low power attenuation constant of 0.098 cm−1 around one terahertz [28]. On the other hand, we choose air as the low-index material in this work. While the true “air layer” is impossible to realize, a reasonably low-index layer with index close to air can be implemented either by cobweb-type configuration [29] or by using the highly-porous polymer [18], both of which contain sub-wavelength supporting structures so that their effects on the dispersion and the attenuation of the guided wave are negligible [10].

 

Fig. 1 Schematics of a hollow-core Bragg fiber with metallic outer cladding. The central empty region is the air core and the outmost gray area is the metallic cladding. Red hatched area represents the high-index dielectric layers with a thickness dhigh, and blue hatched area the low-index layers with a thickness dlow. The profile of the refractive indices is also shown.

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Similar to traditional metallic waveguides, the core radius governs the cutoff frequency of guided modes in a Bragg fiber. The cutoff frequency of TE01 mode in a metallic waveguide with a radius equal to 202 μm is 0.905 THz, which is slightly below the operating frequency of one terahertz. We therefore adopt it as the core radius of our small-core Bragg fiber. Due to the near-cutoff operation, the light rays strike the Bragg layers at nearly normal incidence. To ensure its maximum reflection, the thickness of each layer can be obtained following the well-known quarter-wave stack condition: dhigh=λ0/(4nhigh) and dlow=λ0/(4nlow), where λ0 is the matching wavelength in vacuum [18, 30]. As the current stopband is expected broad due to the large index contrast between HDPE and air, we choose a matching frequency λ0 = 0.920 THz (λ0 = 326 μm) to ensure good power confinement in the vicinity of one terahertz. Hence, the thickness dhigh of the high-index HDPE dielectric is 53 μm and dlow of low-index air layer is 81 μm. The period of the Bragg pair (Λ=dhigh+dlow) is therefore 134 μm. The ratio of the core diameter to the operating wavelength is 1.24, which is at least an order of magnitude smaller than conventional THz PBG fibers [20,27]. The total number of Bragg pairs in the present design is chosen to be 10, which should be sufficient to suppress the leaky loss of TE modes, given the large-index-contrast employed in current design [20, 27]. These Bragg layers are finally enclosed by a copper cladding whose conductivity is 5.96 × 107 S/m at 20°C, with a thickness much larger than the skin depth of copper, which is < 1 μm at one terahertz.

3. Characteristics of the TE01 mode in the metal-cladded Bragg fiber

The complex propagation constant β+i(α/2) of the TE01 mode in the proposed fiber (denoted as TE01Bragg), where β is the propagation constant and α represents the power loss coefficient, is solved by the transfer matrix method with metallic boundary condition [25, 26]. The dispersion relation of the TE01 mode is shown as the black solid curve in Fig. 2. The projected photonic band structure associated with corresponding planar Bragg mirror is also shown in Fig. 2, where the grey/blank regions represent the pass/stop bands and the solid purple curve represents the light line. For comparison, the dispersion relation of TE01 mode in a cylindrical metallic waveguide with the same core size (denoted as TE01) is also shown as the blue dots. Even though the current design does not have large enough refractive index contrast to warrant an Omni-directional bandgap [20, 27], Fig. 2 indicates the dispersion of the Bragg fiber closely follows that of the metallic waveguide. In particular, the cutoff frequency of the TE01Bragg mode is 0.908 THz, very close to that of the TE01 mode in the metallic waveguide (0.905 THz).

 

Fig. 2 Dispersion curves of the TE01 mode in the proposed metal-cladded Bragg fiber (black solid line) and in the metallic waveguide with the same core dimension (blue dots). The grey (blank) areas are the pass (stop) bands of the corresponding planar multilayer mirror. The solid purple line is the light line.

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The similar behaviors of TE01Bragg and TE01 dispersions have rooted in their field patterns. Figure 3(a) compares the radial distributions of their transverse electric-field magnitude (|Eϕ|) at 1 THz. As indicated, these two modes have nearly identical field distributions inside the core. While the electric field of TE01 mode (blue dots) reduces to zero at the core’s boundary, the field of TE01Bragg mode (black solid) extends into the dielectric layers with oscillating magnitude before it is terminated at the outer metallic wall. This is a characteristic of a Bloch wave with the decaying amplitude in a photonic bandgap [31]. The field magnitude drops to below −20 dB in the last Bragg pair, which effectively reduces the ohmic loss at the dielectric-metal interface. The low ohmic loss, together with the low material loss of the selected dielectrics, renders a low power loss coefficient (α) less than 0.1 cm−1 (i.e., power is attenuated to 0.43 dB or 90.48% of its original value after propagating 1 cm) over a broad bandwidth from 0.966 to 1.500 THz as shown by the black solid curve in Fig. 3(b). Since α at 1 THz (0.076 cm−1) is nearly one order of magnitude smaller than that in the stainless-steel cylindrical waveguide (0.825 cm−1) [8], our proposed metal-cladded HDPE/air Bragg fiber is very promising for beam-wave interaction or THz transmission, compared to traditional small-core metallic waveguides. For comparison, the red dashed curve in Fig. 3(b) shows α of TE01Bragg mode in a fiber without the copper outer cladding, in which the leaky field extended beyond the Bragg layers is free to radiate. As demonstrated, there is no significant difference for α in the presence and the absence of copper cladding, indicating the negligible effect of outmost metallic boundary on TE01Bragg power attenuation.

 

Fig. 3 (a) Top row: 2D mode patterns showing electric-field magnitude at 1 THz in the metallic waveguide (left) and in the metal-cladded HDPE/air fiber (right). Bottom: radial profiles of electric-field magnitude in the designed fiber (black solid) and in the metallic waveguide (blue dots). The core radiuses of two waveguide systems are both fixed at 202 μm. Color codes: cyan (core), grey (HDPE), blank (air), and hatched (metallic outer cladding). (b) Power loss coefficients of TE01 modes in the Bragg fibers with copper cladding (black solid) and without copper cladding (red dashed), and in stainless-steel waveguide with a conductivity of 1.45 × 106 S/m (blue dots).

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4. Characteristics of the eigenmodes in the metal-cladded Bragg fiber

In this section we analyze the first twenty eigenmodes in the metal-cladded HDPE/air Bragg fiber that exhibit the same azimuthal symmetry as the TE01 mode. These results will be used later in the modal coupling analysis (Sec. 6). We calculate their dispersion relation, power loss coefficient, and the electric field distribution (i.e., the amplitude of Re[Eϕ×exp(iωt)]) using transfer matrix method, as shown in Figs. 4, 5, and 6, respectively. The 11th mode is the TE01 mode as described in details in Sec. 3.

 

Fig. 4 Dispersion relations of the first twenty eigenmodes in the HDPE/air Bragg fiber with metallic cladding: (a) modes 1 to 11 (propagating modes) and (b) modes 12 to 20 (evanescent modes).

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Fig. 5 Power loss coefficients of the first twenty eigenmodes in the HDPE/air Bragg fiber with metallic cladding: (a) modes 1 to 11 (propagating modes) and (b) modes 12 to 20 (evanescent modes).

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Fig. 6 Normalized transverse electric-field distribution (i.e., the amplitude of Re[Eϕ×exp(iωt)]) at 1 THz of (a) eleven propagating modes and (b) nine evanescent modes in the metal-cladded HDPE/air Bragg fiber. Color codes: light blue (core), grey (HDPE), blank (air), and hatched (metallic outer cladding).

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Modes 1-10 are propagating modes in the metal-cladded Bragg fiber other than the TE01 mode (11th mode). They represent the cladding modes, as their dispersions lie in the passband of the Bragg mirror [grey regions in Fig. 4(a)]. Since modes 1-7 lie below the light line (solid purple curve), their fields are evanescent in the core, while modes 9 and 10 have propagating field components in the core. In addition, these cladding modes have energy concentrated in the dielectric cladding and thus exhibit higher loss than the TE01 mode as shown in Fig. 5(a). The increase of loss originates primarily from the HDPE absorption while only a small contribution (0.2-2%) is due to the ohmic loss of metallic walls. Cladding modes with higher order have larger electric field energy density (|Eϕ|2) in the lossy HDPE, leading to the higher modal loss. Modes 12-20 represent the first 9 evanescent modes in the Bragg fiber. These modes have their cutoff frequencies higher than the current operating band (0.950 THz to 1.050 THz), rendering very small propagation constants (exactly zero in the absence of HDPE loss) and very large power loss coefficients. As their dispersion lie above the light line and within the bandgap, these evanescent modes have oscillatory transverse electric field Eϕwith a decaying amplitude in the cladding.

As mentioned in the introduction, the copper outer cladding in our fiber design is introduced to facilitate modal coupling analysis between the mode converter and the Bragg fiber (Sec. 6). It is therefore important to investigate the effect of this metallic cladding on the eigenmode characteristics, especially their power losses. We found the loss increment is negligible (less than 0.01%) for the TE01Braggmode (i.e. 11th mode), due to the strong confinement of the Bragg layers. The loss increases marginally by 0.2% - 2% for the propagating cladding modes (mode 1-10) as their transverse fields extend beyond the dielectric layers and into the metallic wall. The propagating loss does increase considerably (more than 10%) for the evanescent modes (mode 12-20) because of their extremely small propagation constants such that the fields spend considerable time in the copper. These higher-order modes, however, have negligible contribution to modal coupling, as will be discussed in Sec. 6.

5. Design and characteristics of a Y-type TE01 mode converter

In this section, we propose a new scheme to efficiently couple the traditional THz sources with linearly polarized TEM mode to the TE01Bragg mode of the Bragg fiber by employing a Y-type mode converter [32]. The scheme is illustrated in Fig. 7(a) where a mode converter, made of hollow tunnels carved out of a solid copper, is butt coupled to a Bragg fiber. The same scheme can also be used to convert the TE01Bragg mode back into linearly polarized TEM mode in free space. The basic idea behind this coupling scheme is to explore the similarity in the TE01 field distribution between the metallic cylindrical waveguide and the fiber, as shown in Fig. 3(a). A typical Y-type mode converter comprises two-stage power-dividing junctions made of branched rectangular metallic waveguides, followed by a mode-converting section made of cylindrical metallic waveguide [32]. The electric field distribution along with its polarization inside the proposed Y-type TE01 mode converter is depicted in Fig. 7(b). The input end of the rectangular metallic waveguide is operated in the fundamental TE10 mode (denoted as TE10), which can be easily excited by the linearly polarized free-space THz signal [8]. As the injected THz wave (TE10) travels to the 1st-stage power-dividing junction, it splits into two signals with equal magnitude and phase. The two divided signals propagate on their own along the waveguide tunnels and are further divided into four sub-signals by 2nd-stage power dividers, which are attached symmetrically on the side wall of the mode-converting cylindrical waveguide. These four linearly-polarized TE10 fields of the rectangular waveguides with equal amplitude and phase circumnavigate the cylindrical waveguide to jointly excite its TEnm modes with four-fold symmetry (i.e., n = 0, 4, 8...etc.). This precludes the excitation of lower-order modes of the metallic cylindrical waveguide (i.e., TE11, TM01, TE21, and TM11), owing to the mismatched azimuthal symmetry in field distribution and polarization. As the operating band is chosen slightly above the TE01 cutoff, only TE01 mode can be excited and all other higher-order TEnm modes (wheren = 0, 4, 8...etc.) are evanescent and thus are also precluded. Consequently, only the very high-purity TE01 mode will emerge at the output end of the mode converter, as shown in Fig. 7(b).

 

Fig. 7 (a) The proposed scheme to excite the TE01Bragg mode in a Bragg fiber using a Y-type mode converter. (b) A cross-sectional profile of the electric-field magnitude (in rainbow scale) and polarization (black arrows) in the mode converter.

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A simple design of Y-type mode converter that works at around one terahertz is presented as follows. The width (w) and height (h) of the input rectangular waveguide are respectively 239 μm and 119 μm, yielding a cutoff frequency of 0.628 THz for TE10 mode. As the rectangular waveguide is branched, its width stays the same (239 μm) to ensure a fixed cutoff as well as a fixed propagation constant of the TE10 mode. The height of the branched rectangular waveguide, on the other hand, is reduced by half (to 60 μm) at every branching point to divide the power equally. Before the second branch point, it is tapered back to its original value (119 μm). The core radius of the cylindrical waveguide in the mode-converting section is chosen to match that of the Bragg fiber (202 μm). Figure 8 shows the spectral characteristics of the mode converter, calculated by High Frequency Structural Simulator (HFSS, Ansys) using realistic material property of copper with conductivity of 5.80 × 107 S/m. As indicated, the mode converter has very high transmittance of the TE01 mode [> −0.4 dB or 90%], very low transmittances of other lower-order modes [< −40 dB], and a very low reflectance [< −20 dB or 1%], over the operating band from 0.971 THz to 1.024THz. This indicates a TE01 mode purity as high as 99.99%. The coupling loss is dominated by the ohmic loss of the conducting wall. The fractional bandwidth Δf/f of our mode converter, calculated based on a −0.2dB (or 95% of the peak transmission) bandwidth, is nearly 10%, which is one order of magnitude larger than previously reported coaxial-cavity couplers [33] or serpentine schemes [34, 35]. The broader bandwidth of proposed Y-type mode converter can be attributed to the non-resonance structure adopted for coupling, whereas in the coaxial-cavity couplers [33] TE011 cavity mode needs to be excited for further coupling of TE01 mode, which significantly limits their bandwidths. On the other hand, the superior performance compared to the serpentine couplers [34, 35] results from the shorter mode-conversion length in present scheme (several wavelengths), while serpentine couplers usually requires much longer length for mode conversion (more than ten wavelengths), suffering from serious ohmic loss and narrow transmission bandwidth in THz region.

 

Fig. 8 (a) Transmittance of the first five metallic waveguide modes (TE11O, TM01O, TE21O, TM11O, and TE01O) at the output of the mode converter. (b) Reflectance of the TE10 mode at the input of the mode converter.

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6. Excitation of the TE01 mode in Bragg fibers using a Y-type mode converter

In this section, we investigate the excitation efficiency of the TE01Bragg mode in the metal-cladded Bragg fiber by a TE01 mode generated at the end of the mode converter as depicted in the last section. According to the modal effect [8, 18], eigenmodes with the same azimuthal symmetry as the incoming TE01 mode, on both sides of the coupling interface, will be excited in order to meet boundary conditions. At the mode converter side, these modes are essentially TE0n, whereas at the Bragg fiber side the first twenty of these modes are calculated in Sec. 4. Denote the electric and magnetic fields of m-th (n-th) eigenmodes in the Bragg fiber (metallic waveguide) by Eϕ,mBF (Eϕ,n) and Hρ,mBF (Hρ,n), respectively. The boundary conditions at the coupling interface require

m=1Eϕ,mBFtm={Eϕ,1+n=1Eϕ,nrnfor0ρρ10forρ>ρ1,
m=1Hρ,mBFtm=Hρ,1n=1Hρ,nrnfor0ρρ1,
where tm is the field transmission (excitation) coefficient of the m-th mode in the Bragg fiber and rn is the field reflection coefficient of the n-th mode in the cylindrical waveguide section of the mode converter. The core radius of the metallic waveguide, which equals to that of the Bragg fiber in the present study, is denoted as ρ1. At the cladding interface between the mode converter and the Bragg fiber (ρ>ρ1), the total transverse electric field in the Bragg fiber (EϕBF) must be zero due to the transverse metallic boundary of the converter, whereas its total transverse magnetic field (HρBF) is not necessarily so due to the possibility of surface current at the metallic interface. As shown in the Appendix, the field reflection coefficients rn (1nNMWG) can be solved by the following equation expressed in a matrix form:
rn=p=1NMWGMnp-1Vp,
where NMWG is the total number of eigenmodes considered in the mode converter, and matrix Mnp and column vector Vp are constructed by the field overlapping integrals defined in the Appendix. Once all rn are obtained, the field transmission coefficient tm of each fiber mode (1mNBF) can be subsequently calculated according to
tm=0ρ1Eϕ,1Eϕ,mBF*ρdρ0ρN+1|Eϕ,mBF|2ρdρ+n=1NMWG0ρ1Eϕ,nEϕ,mBF*ρdρ0ρN+1|Eϕ,mBF|2ρdρrn,
where NBF is the total number of eigenmodes considered in the fiber and ρN+1 represents the inner radius of the outer metallic cladding as shown in Fig. 1. In principle, the larger the numbers of mode is considered in modal analysis (NMWG and NBF), the more accurate the result is expected at the expense of computation time. In practice we found that NMWG=20 and NBF=20 are sufficient to give converged values of rn and tm, and is used for the following analysis. Based on the field reflection and field transmission coefficients (rn and tm), the reflectance Rn and transmittance (conversion efficiency of fiber mode) Tm can be calculated from Poynting vectors according to

Rn=Re[0ρ1Eϕ,nHρ,n*ρdρ]Re[0ρ1Eϕ,1Hρ,1*ρdρ]|rn|2,
Tm=Re[0ρN+1Eϕ,mBFHρ,mBF*ρdρ]Re[0ρ1Eϕ,1Hρ,1*ρdρ]|tm|2.

Figure 9(a) shows |rn| of the first fifteen TE0n modes (1n15) in the mode converter. Notably, |rn|for 16n20 are all smaller than |r15| and are not shown for clarity. It is clear that not only the fundamental TE01 mode but also the higher-order modes are excited to meet the transverse boundary condition. These higher-order modes, however, do not carry power as they are evanescent for being under the below-cutoff operation. As shown in Fig. 9(b), the total reflection power is less than 0.05 for the whole operating band, indicating that most of the injected power is coupled into the fiber under the current coupling scheme.

 

Fig. 9 (a) Magnitude of the field reflection coefficient of TE0n mode (|rn| with 1n15) in the metallic waveguide. (b) Reflectance of theTE01 mode (R1). (c) Magnitude of the field transmission coefficient of TE0mBragg mode (|tm| with 1m13) in the metal-cladded Bragg fiber. (b) Transmittances of the eleven propagating TE0mBragg modes (Tm with 1m11) in the fiber.

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Figure 9(c) and 9(d) respectively show the magnitude of field transmission coefficient tm and the transmittance Tm of the first thirteen azimuthally symmetric eigenmodes in the Bragg fiber (1m13). Note that |tm| for m>13 are smaller than |t13| and thus are not displayed for clarity, and Tm for m12 are zero as they are evanescent modes and carry no power. A few observations can be made: firstly, most of the injected power is converted into TE01Bragg mode (the 11th mode) with an average conversion efficiency T11 ~60% over this frequency range. Secondly, among all the other excited modes, the transmittance increases from mode 1 to mode 8, then decreases for modes 9 and 10. Thirdly, although higher-order evanescent modes in the fiber (modes 12-20) are also expected to be excited to meet the boundary condition, we found their field transmission coefficients tm (m12) are negligible (on the order of 10−6). These trends can be understood as follows. The first term on the right-hand side of Eq. (4) is related to the mode overlap integral between the incident wave (TE01) in the mode converter and the targeted eigenmode of the Bragg fiber. The second term, on the other hand, contains contribution from all eigenmodes of the mode converter, each of which is proportional to the overlap integral between the TE0n mode of the mode converter and the targeted fiber mode, multiplied by the field reflection coefficient rn. Even though rn of each metallic-waveguide mode has similar order of magnitude as demonstrated in Fig. 9(a), higher-order mode has much larger kT,n and hence smaller Eϕ,n [see Eq. (9) in the Appendix], leading to diminishing mode overlap integral. The field transmission coefficient tm can therefore be approximated to become

tm(1+r1)0ρ1Eϕ,1Eϕ,mBF*ρdρ0ρN+1|Eϕ,mBF|2ρdρ,
which indicates the mode coupling is approximately proportional to the mode overlap integral between the incident TE01 wave and the targeted fiber eigenmode. Equation (7) can be used to explain the above observations: firstly, as TE01Bragg mode (the 11th mode) has similar field distribution as the TE01 mode, T11 is the largest among all the excited modes. Secondly, as seen in Fig. 6(a), modes 1-8 have increasing presence in the core, resulting in increasing mode overlap with the TE01 mode and therefore larger tm. Modes 9-10, on the other hand, have decreasing weight in the core and thus smaller tm. Thirdly, all evanescent modes of the Bragg fiber have very large mode order (m12) with rapid field oscillation in the core. This leads to diminishing mode overlap integral with the TE01 mode, which means they have very little contributions in modal coupling. Lastly, as tm is dominantly related to the overlap integral between the incident TE01 wave and the targeted fiber eigenmode, the significant increase of the modal loss of evanescent modes in Bragg fibers (m12) upon adding the metallic wall has little effect on the excitation of propagating modes (m11), as allured in last paragraph of Sec. 4.

Once excited at the coupling interface, each eigenmode propagates forward with its own complex propagation constant βmBF. The total transverse field EϕBF(ρ,z)will evolve along the propagation length due to modal interference and can be calculated according to

EϕBF(ρ,z)=m=1NBFtmEϕ,mBF(ρ)exp(iβmBFz).
As the power loss coefficient of TE01Bragg mode is several times smaller than that of other propagating cladding modes (Fig. 5), TE01Bragg mode would eventually dominate—so called effective single-mode regime [20]. Figure 10 shows the superimposed transverse electric field magnitude |EϕBF| calculated by Eq. (8) for several representative distances along the fiber. For comparison, |EϕBF|of TE01Braggis also shown (black dashed). As expected, within the core |EϕBF| at the coupling interface (z = 0 mm, red solid) resembles strongly TE01O of the cylindrical metallic waveguide (Fig. 3a). Due to the finite numbers of eigenmodes involved in the eigenmode expansion, |EϕBF| outside the core, although small (< −20 dB), is not exactly zero as required by the metallic transverse boundary condition. At 0.01 mm (yellow solid), |EϕBF|in the cladding near the core rises and exhibits some level of amplitude modulation. At 0.1 mm (green solid), |EϕBF|in the cladding has developed periodic pattern with the same periodicity as the Bragg layer, except its value is too high at the core-cladding interface and too low in the cladding compared to the TE01Bragg mode. The overshoot at the core-cladding interface is corrected at z = 10 mm (blue solid), while in the cladding it is over-corrected. At 1000 mm (orange solid), all cladding modes are nearly died off [|Tmexp(iβmBFz)|/T11exp(iβ11BFz)|<0.5% for all m10] and |EϕBF|has nearly converged to the pure TE01Bragg mode.

 

Fig. 10 Profiles of transverse electric field magnitude at five representative distances along the Bragg fiber: z=0mm (red solid), z=0.010mm (yellow solid), z=0.100mm (green solid), z=10.000mm (blue solid), and z=1000.000mm (orange solid). The field profile of the TE01Bragg mode is also shown as black dashed line. Color codes: light blue (core), grey (HDPE), blank (air), and hatched (metallic outer cladding).

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7. Conclusion

In this work we present a design of a hollow-core dielectric Bragg fiber with a copper outer cladding, intended to operate at 1 THz near the cutoff of the TE01 mode. The core diameter is on the order of the operating wavelength, which is at least an order of magnitude smaller than conventional THz PBG fibers. By employing a quarter-wave design at the cutoff frequency, our Bragg fiber exhibits a power loss coefficient as low as 0.1 cm−1 – a significant improvement compared to existing small-core stainless-steel THz waveguides. Characteristics of the first twenty azimuthally symmetry eigenmodes, including dispersion relation, power loss coefficient, and field distribution, are studied using transfer matrix method. We also propose a broadband Y-type mode converter based on symmetrically branched rectangular metallic waveguides to facilitate coupling between the TE01 mode of the Bragg fiber and the TEM mode in free space. The mode converter features a TE01 mode purity as high as 99.99% and has a fractional bandwidth Δf/f one order of magnitude larger than previously reported schemes. Using rigorous eigenmode expansion method involving the first twenty eigenmodes in the Bragg fiber and the mode converter, the excitation efficiency of TE01Bragg is as high as 60%. Although cladding and evanescent modes in the Bragg fiber are also excited, their propagation loss is significantly higher than that of the TE01Bragg, rendering an effective single-mode fiber after a propagation length of 1 meter. Due to its low loss, our proposed Bragg fibers holds strong promise to facilitate beam-wave interaction in gyrotron for high-power THz generation. Our Y-type mode converter is also expected to benefit other research that requires operating at TE01 mode in fibers.

8 Appendix

The following modal analysis is applied to analyze the field reflection coefficients rn and the field transmission coefficients tm at the junction between the mode converter and the Bragg fiber. The transverse electric and magnetic fields for the TE0n mode (Eϕ,n and Hρ,n) in the metallic cylindrical waveguide can be written analytically as

Eϕ,n=iωμ0kT,nJ0(kT,nρ),
Hρ,n=iβnkT,nJ0(kT,nρ),
where J0 is the derivative of Bessel function J0, kT,n=χ0,n/ρ1 is the transverse wave number, χ0,n is the n-th root of J0, and βn=(ω/c)2(kT,n)2 is the propagation constant of the metallic waveguide mode. Characteristics of these eigenmodes, including propagation constant, loss, and mode field distribution, are well documented in literatures [36]. On the other hand, the transverse electric and magnetic fields in the Bragg fiber (Eϕ,mBF and Hρ,mBF) do not have analytic expression but can be solved by the transfer matrix method as demonstrated in Fig. 6. The orthogonality condition in the metal-cladded Bragg fiber requires
02π0ρN+1Eϕ,mBFEϕ,pBF*ρdρdϕ=2πδmp0ρN+1|Eϕ,pBF|2ρdρ.
Similarly, the orthogonality condition in the metallic cylindrical waveguide requires [37]
02π0ρ1Hρ,nHρ,q*ρdρdϕ=π|βqρ1kT,qJ2(χ0,q)|2δnq.
In the above two equations δmp and δnq are the Kronecker delta and ρN+1 is the outer radius of the dielectric cladding of the fiber (Fig. 1). Equation (4) of Sec. 6 can be obtained by multiplying Eq. (1) with Eϕ,pBF* and integrating over the fiber’s cross-section. Following Eq. (11), we have
tm=I1,mEϕ0ρN+1|Eϕ,mBF|2ρdρ+n=1In,mEϕ0ρN+1|Eϕ,mBF|2ρdρrn,
where In,mEϕ0ρ1Eϕ,nEϕ,mBF*ρdρ is the mode overlap integral of transverse electric fields. Similarly, by multiplying Eq. (2) with Hρ,q*, integrating over the cross-section of the metallic cylindrical waveguide, and following Eq. (12), we obtain
m=1In,mHρtm=12|β1ρ1kT,1J2(χ0,1)|212|βnρ1kT,nJ2(χ0,n)|2rn,
where In,mHρ0ρ1Hρ,n*Hρ,mBFρdρis the mode overlap integral of transverse magnetic fields.

For numerical calculation, we must truncate the summation in Eq. (13) to NMWG, i.e. the total number of eigenmodes considered in the metallic waveguide. Similarly, the summations in Eq. (14) is truncated to NBF (the total number of eigenmodes considered in the Bragg fiber). In principle the larger NBF and NMWG are, the more accurate the final result would be at the expense of computation time. Equation (3) of Sec. 6 can be obtained by substituting Eq. (13)in to Eq. (14), which reduces to a set of linear equations for solving the field reflection coefficient rn:

p=1NMWGMpnrn=Vp,
where
Mpn=12|βpρ1kT,pJ2(χ0,p)|2δpn+m=1NBFIp,mHρIn,mEϕ0ρN+1|Eϕ,mBF|2ρdρ,
and

Vp=12|β1ρ1kT,1J2(χ0,1)|2δp1m=1NBFIp,mHρI1,mEϕ0ρN+1|Eϕ,mBF|2ρdρ.

From Eqs. (15), (16), and (17), the field reflection coefficients rn of the metallic-waveguide modes could be calculated. Substituting these results into Eq. (13), we can obtain the field transmission coefficients tm of the fiber modes.

Acknowledgment

This work was sponsored by the National Science Council of Taiwan under Contract No. NSC 101-2112-M-007-005-MY3. The authors appreciate technical support from Ansys Inc.

References and links

1. J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010). [CrossRef]  

2. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005). [CrossRef]  

3. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004). [CrossRef]  

4. C. Kulesa, “Terahertz spectroscopy for astronomy: from comets to cosmology,” IEEE Trans. THz Sci. Tech. (Paris) 1, 232–240 (2011).

5. N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009). [CrossRef]  

6. K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys. 76(2), 489–540 (2004). [CrossRef]  

7. G. S. Nusinovich, “Review of the theory of mode interaction in gyrodevices,” IEEE Trans. Plasma Sci. 27(2), 313–326 (1999). [CrossRef]  

8. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000). [CrossRef]  

9. R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of terahertz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24(20), 1431–1433 (1999). [CrossRef]   [PubMed]  

10. S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013). [CrossRef]  

11. B. Bowden, J. A. Harrington, and O. Mitrofanov, “Silver/polystyrene-coated hollow glass waveguides for the transmission of terahertz radiation,” Opt. Lett. 32(20), 2945–2947 (2007). [CrossRef]   [PubMed]  

12. Y. Matsuura and E. Takeda, “Hollow optical fibers loaded with an inner dielectric film for terahertz broadband spectroscopy,” J. Opt. Soc. Am. B 25(12), 1949–1954 (2008). [CrossRef]  

13. X. L. Tang, Y. W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission characteristics of terahertz hollow fiber with an absorptive dielectric inner-coating film,” Opt. Lett. 34(14), 2231–2233 (2009). [CrossRef]   [PubMed]  

14. B. S. Sun, X. L. Tang, X. Zeng, and Y. W. Shi, “Characterization of cylindrical terahertz metallic hollow waveguide with multiple dielectric layers,” Appl. Opt. 51(30), 7276–7285 (2012). [PubMed]  

15. Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008). [CrossRef]  

16. J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “THz propagation in kagome hollow-core microstructured fibers,” Opt. Express 19(19), 18470–18478 (2011). [CrossRef]   [PubMed]  

17. M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90(11), 113514 (2007). [CrossRef]  

18. A. Dupuis, K. Stoeffler, B. Ung, C. Dubois, and M. Skorobogatiy, “Transmission measurements of hollow-core THz Bragg fibers,” J. Opt. Soc. Am. B 28(4), 896–907 (2011). [CrossRef]  

19. B. Ung, A. Dupuis, K. Stoeffler, C. Dubois, and M. Skorobogatiy, “High-refractive-index composite materials for terahertz waveguides: trade-off between index contrast and absorption loss,” J. Opt. Soc. Am. B 28(4), 917–921 (2011). [CrossRef]  

20. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001). [CrossRef]   [PubMed]  

21. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995). [CrossRef]  

22. F. K. Fatemi, M. Bashkansky, E. Oh, and D. Park, “Efficient excitation of the TE01 hollow metal waveguide mode for atom guiding,” Opt. Express 18(1), 323–332 (2010). [CrossRef]   [PubMed]  

23. Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Excitation of a single hollow waveguide mode using inhomogeneous anisotropic subwavelength structures,” Opt. Express 15(20), 13404–13414 (2007). [CrossRef]   [PubMed]  

24. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009). [CrossRef]  

25. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68(9), 1196–1201 (1978). [CrossRef]  

26. Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25(24), 1756–1758 (2000). [CrossRef]   [PubMed]  

27. M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003). [CrossRef]   [PubMed]  

28. Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

29. R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007). [CrossRef]  

30. G. R. Hadley, J. G. Fleming, and S. Y. Lin, “Bragg fiber design for linear polarization,” Opt. Lett. 29(8), 809–811 (2004). [CrossRef]   [PubMed]  

31. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]  

32. T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008). [CrossRef]  

33. A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999). [CrossRef]  

34. D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996). [CrossRef]  

35. W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000). [CrossRef]  

36. D. M. Poza, Microwave Engineering (John Wiley & Sons, 2006).

37. R. Sorrentino and G. Bianchi, Microwave and RF Engineering (John Wiley & Sons, 2010).

References

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  • |

  1. J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010).
    [Crossref]
  2. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
    [Crossref]
  3. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004).
    [Crossref]
  4. C. Kulesa, “Terahertz spectroscopy for astronomy: from comets to cosmology,” IEEE Trans. THz Sci. Tech. (Paris) 1, 232–240 (2011).
  5. N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
    [Crossref]
  6. K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys. 76(2), 489–540 (2004).
    [Crossref]
  7. G. S. Nusinovich, “Review of the theory of mode interaction in gyrodevices,” IEEE Trans. Plasma Sci. 27(2), 313–326 (1999).
    [Crossref]
  8. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000).
    [Crossref]
  9. R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of terahertz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24(20), 1431–1433 (1999).
    [Crossref] [PubMed]
  10. S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
    [Crossref]
  11. B. Bowden, J. A. Harrington, and O. Mitrofanov, “Silver/polystyrene-coated hollow glass waveguides for the transmission of terahertz radiation,” Opt. Lett. 32(20), 2945–2947 (2007).
    [Crossref] [PubMed]
  12. Y. Matsuura and E. Takeda, “Hollow optical fibers loaded with an inner dielectric film for terahertz broadband spectroscopy,” J. Opt. Soc. Am. B 25(12), 1949–1954 (2008).
    [Crossref]
  13. X. L. Tang, Y. W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission characteristics of terahertz hollow fiber with an absorptive dielectric inner-coating film,” Opt. Lett. 34(14), 2231–2233 (2009).
    [Crossref] [PubMed]
  14. B. S. Sun, X. L. Tang, X. Zeng, and Y. W. Shi, “Characterization of cylindrical terahertz metallic hollow waveguide with multiple dielectric layers,” Appl. Opt. 51(30), 7276–7285 (2012).
    [PubMed]
  15. Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
    [Crossref]
  16. J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “THz propagation in kagome hollow-core microstructured fibers,” Opt. Express 19(19), 18470–18478 (2011).
    [Crossref] [PubMed]
  17. M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90(11), 113514 (2007).
    [Crossref]
  18. A. Dupuis, K. Stoeffler, B. Ung, C. Dubois, and M. Skorobogatiy, “Transmission measurements of hollow-core THz Bragg fibers,” J. Opt. Soc. Am. B 28(4), 896–907 (2011).
    [Crossref]
  19. B. Ung, A. Dupuis, K. Stoeffler, C. Dubois, and M. Skorobogatiy, “High-refractive-index composite materials for terahertz waveguides: trade-off between index contrast and absorption loss,” J. Opt. Soc. Am. B 28(4), 917–921 (2011).
    [Crossref]
  20. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
    [Crossref] [PubMed]
  21. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
    [Crossref]
  22. F. K. Fatemi, M. Bashkansky, E. Oh, and D. Park, “Efficient excitation of the TE01 hollow metal waveguide mode for atom guiding,” Opt. Express 18(1), 323–332 (2010).
    [Crossref] [PubMed]
  23. Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Excitation of a single hollow waveguide mode using inhomogeneous anisotropic subwavelength structures,” Opt. Express 15(20), 13404–13414 (2007).
    [Crossref] [PubMed]
  24. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
    [Crossref]
  25. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68(9), 1196–1201 (1978).
    [Crossref]
  26. Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25(24), 1756–1758 (2000).
    [Crossref] [PubMed]
  27. M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
    [Crossref] [PubMed]
  28. Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).
  29. R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
    [Crossref]
  30. G. R. Hadley, J. G. Fleming, and S. Y. Lin, “Bragg fiber design for linear polarization,” Opt. Lett. 29(8), 809–811 (2004).
    [Crossref] [PubMed]
  31. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977).
    [Crossref]
  32. T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
    [Crossref]
  33. A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999).
    [Crossref]
  34. D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
    [Crossref]
  35. W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
    [Crossref]
  36. D. M. Poza, Microwave Engineering (John Wiley & Sons, 2006).
  37. R. Sorrentino and G. Bianchi, Microwave and RF Engineering (John Wiley & Sons, 2010).

2013 (1)

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

2012 (1)

2011 (4)

2010 (2)

F. K. Fatemi, M. Bashkansky, E. Oh, and D. Park, “Efficient excitation of the TE01 hollow metal waveguide mode for atom guiding,” Opt. Express 18(1), 323–332 (2010).
[Crossref] [PubMed]

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010).
[Crossref]

2009 (3)

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

X. L. Tang, Y. W. Shi, Y. Matsuura, K. Iwai, and M. Miyagi, “Transmission characteristics of terahertz hollow fiber with an absorptive dielectric inner-coating film,” Opt. Lett. 34(14), 2231–2233 (2009).
[Crossref] [PubMed]

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

2008 (3)

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

Y. Matsuura and E. Takeda, “Hollow optical fibers loaded with an inner dielectric film for terahertz broadband spectroscopy,” J. Opt. Soc. Am. B 25(12), 1949–1954 (2008).
[Crossref]

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

2007 (4)

M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90(11), 113514 (2007).
[Crossref]

B. Bowden, J. A. Harrington, and O. Mitrofanov, “Silver/polystyrene-coated hollow glass waveguides for the transmission of terahertz radiation,” Opt. Lett. 32(20), 2945–2947 (2007).
[Crossref] [PubMed]

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Y. Yirmiyahu, A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Excitation of a single hollow waveguide mode using inhomogeneous anisotropic subwavelength structures,” Opt. Express 15(20), 13404–13414 (2007).
[Crossref] [PubMed]

2006 (1)

Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

2005 (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

2004 (3)

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys. 76(2), 489–540 (2004).
[Crossref]

G. R. Hadley, J. G. Fleming, and S. Y. Lin, “Bragg fiber design for linear polarization,” Opt. Lett. 29(8), 809–811 (2004).
[Crossref] [PubMed]

2003 (1)

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

2001 (1)

2000 (3)

Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25(24), 1756–1758 (2000).
[Crossref] [PubMed]

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000).
[Crossref]

1999 (3)

R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of terahertz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24(20), 1431–1433 (1999).
[Crossref] [PubMed]

G. S. Nusinovich, “Review of the theory of mode interaction in gyrodevices,” IEEE Trans. Plasma Sci. 27(2), 313–326 (1999).
[Crossref]

A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999).
[Crossref]

1996 (1)

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

1995 (1)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

1978 (1)

1977 (1)

Abbott, D.

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

Afshar, V. S.

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

Anthony, J.

Argyros, A.

Arjona, M. R.

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

Atakaramians, S.

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

Bai, X. Z.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Bashkansky, M.

Biener, G.

Bowden, B.

Chang, T. H.

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

Chen, N. C.

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

Choi, J. J.

A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999).
[Crossref]

Chong, C. K.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

Chu, K. R.

K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys. 76(2), 489–540 (2004).
[Crossref]

Dubois, C.

Dupuis, A.

Engeness, T.

Engeness, T. D.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

Fatemi, F. K.

Federici, J.

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010).
[Crossref]

Federici, J. F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Fink, Y.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Fleming, J. G.

Gallot, G.

Gary, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Geng, Y. F.

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

Grischkowsky, D.

Hadley, G. R.

Harrington, J. A.

Hasman, E.

Hogan, B. P.

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

Hong, C.-S.

Hu, J.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Huang, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Ibanescu, M.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Ives, R. L.

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

Iwai, K.

Jacobs, S.

Jacobs, S. A.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

Jamison, S. P.

Jeon, S. G.

Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Jin, Y. S.

Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Joannopoulos, J.

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

Johnson, S.

Johnson, S. G.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

Kim, G. J.

Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

Kinney, C. F.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

Kleiner, V.

Kulesa, C.

C. Kulesa, “Terahertz spectroscopy for astronomy: from comets to cosmology,” IEEE Trans. THz Sci. Tech. (Paris) 1, 232–240 (2011).

Lawson, W.

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

Lee, R. K.

Leonhardt, R.

Leon-Saval, S. G.

Li, C. H.

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

Lin, S. Y.

Luhmann, N. C.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

Marom, E.

Matsuura, Y.

McCurdy, A. H.

A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999).
[Crossref]

McDermott, D. B.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

McGowan, R. W.

Menyuk, C. R.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Mitrofanov, O.

Miyagi, M.

Moeller, L.

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010).
[Crossref]

Monro, T. M.

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

Niv, A.

Nusinovich, G. S.

G. S. Nusinovich, “Review of the theory of mode interaction in gyrodevices,” IEEE Trans. Plasma Sci. 27(2), 313–326 (1999).
[Crossref]

Oh, E.

Oliveira, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Park, D.

Pretterebner, J.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

Razeghi, M. M.

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

Schulkin, B.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Shi, Y. W.

Siegel, P. H.

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

Skorobogatiy, M.

Soljacic, M.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Stoeffler, K.

Sun, B. S.

Takeda, E.

Tan, X. L.

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

Tang, X. L.

Tian, Z. G.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Ung, B.

Wang, P.

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

Weisberg, O.

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 (2001).
[Crossref] [PubMed]

Wu, C. N.

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

Wu, C. Q.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Wu, Q.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

Xu, Y.

Yao, J. Q.

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

Yariv, A.

Yeh, P.

Yirmiyahu, Y.

Yu, C. F.

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

Yu, R. J.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Yuan, C. P.

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

Zeng, X.

Zhang, B.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

Zhang, Y. Q.

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

Zimdars, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Adv. Opt. Photonics (2)

S. Atakaramians, V. S. Afshar, T. M. Monro, and D. Abbott, “Terahertz dielectric waveguides,” Adv. Opt. Photonics 5(2), 169–215 (2013).
[Crossref]

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

Y. F. Geng, X. L. Tan, P. Wang, and J. Q. Yao, “Transmission loss and dispersion in plastic terahertz photonic band-gap fibers,” Appl. Phys. B 91(2), 333–336 (2008).
[Crossref]

Appl. Phys. Lett. (4)

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

T. H. Chang, C. H. Li, C. N. Wu, and C. F. Yu, “Exciting circular TEmn modes at low terahertz region,” Appl. Phys. Lett. 93(11), 111503 (2008).
[Crossref]

M. Skorobogatiy and A. Dupuis, “Ferroelectric all-polymer hollow Bragg fibers for terahertz guidance,” Appl. Phys. Lett. 90(11), 113514 (2007).
[Crossref]

N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang, “A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range,” Appl. Phys. Lett. 94(10), 101501 (2009).
[Crossref]

IEEE Photonics Technol. Lett. (1)

R. J. Yu, B. Zhang, Y. Q. Zhang, C. Q. Wu, Z. G. Tian, and X. Z. Bai, “Proposal for ultralow loss hollow-core plastic Bragg fiber with cobweb-structured cladding for terahertz waveguiding,” IEEE Photonics Technol. Lett. 19(12), 910–912 (2007).
[Crossref]

IEEE Trans. Microw. Theory Tech. (4)

A. H. McCurdy and J. J. Choi, “Design and analysis of a coaxial coupler for a 35-GHz gyroklystron amplifier,” IEEE Trans. Microw. Theory Tech. 47(2), 164–175 (1999).
[Crossref]

D. B. McDermott, J. Pretterebner, C. K. Chong, C. F. Kinney, M. M. Razeghi, and N. C. Luhmann, “Broadband linearly polarized beat-wave TEml/TE1l mode converters,” IEEE Trans. Microw. Theory Tech. 44(2), 311–317 (1996).
[Crossref]

W. Lawson, M. R. Arjona, B. P. Hogan, and R. L. Ives, “The design of serpentine-mode converters for high-power microwave applications,” IEEE Trans. Microw. Theory Tech. 48(5), 809–814 (2000).
[Crossref]

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

IEEE Trans. Plasma Sci. (1)

G. S. Nusinovich, “Review of the theory of mode interaction in gyrodevices,” IEEE Trans. Plasma Sci. 27(2), 313–326 (1999).
[Crossref]

IEEE Trans. THz Sci. Tech. (Paris) (1)

C. Kulesa, “Terahertz spectroscopy for astronomy: from comets to cosmology,” IEEE Trans. THz Sci. Tech. (Paris) 1, 232–240 (2011).

J. Appl. Phys. (1)

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys. 107(11), 111101 (2010).
[Crossref]

J. Korean Phys. Soc. (1)

Y. S. Jin, G. J. Kim, and S. G. Jeon, “Terahertz dielectric properties of polymers,” J. Korean Phys. Soc. 49, 513–517 (2006).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (4)

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Ibanescu, S. G. Johnson, M. Soljacić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046608 (2003).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys. 76(2), 489–540 (2004).
[Crossref]

Semicond. Sci. Technol. (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Other (2)

D. M. Poza, Microwave Engineering (John Wiley & Sons, 2006).

R. Sorrentino and G. Bianchi, Microwave and RF Engineering (John Wiley & Sons, 2010).

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Figures (10)

Fig. 1
Fig. 1 Schematics of a hollow-core Bragg fiber with metallic outer cladding. The central empty region is the air core and the outmost gray area is the metallic cladding. Red hatched area represents the high-index dielectric layers with a thickness d high , and blue hatched area the low-index layers with a thickness d low . The profile of the refractive indices is also shown.
Fig. 2
Fig. 2 Dispersion curves of the TE01 mode in the proposed metal-cladded Bragg fiber (black solid line) and in the metallic waveguide with the same core dimension (blue dots). The grey (blank) areas are the pass (stop) bands of the corresponding planar multilayer mirror. The solid purple line is the light line.
Fig. 3
Fig. 3 (a) Top row: 2D mode patterns showing electric-field magnitude at 1 THz in the metallic waveguide (left) and in the metal-cladded HDPE/air fiber (right). Bottom: radial profiles of electric-field magnitude in the designed fiber (black solid) and in the metallic waveguide (blue dots). The core radiuses of two waveguide systems are both fixed at 202 μm. Color codes: cyan (core), grey (HDPE), blank (air), and hatched (metallic outer cladding). (b) Power loss coefficients of TE01 modes in the Bragg fibers with copper cladding (black solid) and without copper cladding (red dashed), and in stainless-steel waveguide with a conductivity of 1.45 × 106 S/m (blue dots).
Fig. 4
Fig. 4 Dispersion relations of the first twenty eigenmodes in the HDPE/air Bragg fiber with metallic cladding: (a) modes 1 to 11 (propagating modes) and (b) modes 12 to 20 (evanescent modes).
Fig. 5
Fig. 5 Power loss coefficients of the first twenty eigenmodes in the HDPE/air Bragg fiber with metallic cladding: (a) modes 1 to 11 (propagating modes) and (b) modes 12 to 20 (evanescent modes).
Fig. 6
Fig. 6 Normalized transverse electric-field distribution (i.e., the amplitude of Re[ E ϕ ×exp(iωt)] ) at 1 THz of (a) eleven propagating modes and (b) nine evanescent modes in the metal-cladded HDPE/air Bragg fiber. Color codes: light blue (core), grey (HDPE), blank (air), and hatched (metallic outer cladding).
Fig. 7
Fig. 7 (a) The proposed scheme to excite the TE 01 Bragg mode in a Bragg fiber using a Y-type mode converter. (b) A cross-sectional profile of the electric-field magnitude (in rainbow scale) and polarization (black arrows) in the mode converter.
Fig. 8
Fig. 8 (a) Transmittance of the first five metallic waveguide modes ( TE 11 O , TM 01 O , TE 21 O , TM 11 O , and TE 01 O ) at the output of the mode converter. (b) Reflectance of the TE 10 mode at the input of the mode converter.
Fig. 9
Fig. 9 (a) Magnitude of the field reflection coefficient of TE 0n mode ( | r n | with 1n15 ) in the metallic waveguide. (b) Reflectance of the TE 01 mode ( R 1 ). (c) Magnitude of the field transmission coefficient of TE 0m Bragg mode ( | t m | with 1m13 ) in the metal-cladded Bragg fiber. (b) Transmittances of the eleven propagating TE 0m Bragg modes ( T m with 1m11 ) in the fiber.
Fig. 10
Fig. 10 Profiles of transverse electric field magnitude at five representative distances along the Bragg fiber: z=0 mm (red solid), z=0.010 mm (yellow solid), z=0.100 mm (green solid), z=10.000 mm (blue solid), and z=1000.000 mm (orange solid). The field profile of the TE 01 Bragg mode is also shown as black dashed line. Color codes: light blue (core), grey (HDPE), blank (air), and hatched (metallic outer cladding).

Equations (17)

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m=1 E ϕ,m BF t m ={ E ϕ,1 + n=1 E ϕ,n r n for 0ρ ρ 1 0 for ρ> ρ 1 ,
m=1 H ρ,m BF t m = H ρ,1 n=1 H ρ,n r n for 0ρ ρ 1 ,
r n = p=1 N MWG M np -1 V p ,
t m = 0 ρ 1 E ϕ,1 E ϕ,m BF * ρdρ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ + n=1 N MWG 0 ρ 1 E ϕ,n E ϕ,m BF * ρdρ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ r n ,
R n = Re[ 0 ρ 1 E ϕ,n H ρ,n * ρdρ ] Re[ 0 ρ 1 E ϕ,1 H ρ,1 * ρdρ ] | r n | 2 ,
T m = Re[ 0 ρ N+1 E ϕ,m BF H ρ,m BF * ρdρ ] Re[ 0 ρ 1 E ϕ,1 H ρ,1 * ρdρ ] | t m | 2 .
t m ( 1+ r 1 ) 0 ρ 1 E ϕ,1 E ϕ,m BF * ρdρ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ ,
E ϕ BF ( ρ,z )= m=1 N BF t m E ϕ,m BF ( ρ )exp( i β m BF z ) .
E ϕ,n = iω μ 0 k T,n J 0 ( k T,n ρ),
H ρ,n = i β n k T,n J 0 ( k T,n ρ),
0 2π 0 ρ N+1 E ϕ,m BF E ϕ,p BF * ρdρ dϕ=2π δ mp 0 ρ N+1 | E ϕ,p BF | 2 ρdρ.
0 2π 0 ρ 1 H ρ,n H ρ,q * ρdρ dϕ=π | β q ρ 1 k T,q J 2 ( χ 0,q ) | 2 δ nq .
t m = I 1,m E ϕ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ + n=1 I n,m E ϕ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ r n ,
m=1 I n,m H ρ t m = 1 2 | β 1 ρ 1 k T,1 J 2 ( χ 0,1 ) | 2 1 2 | β n ρ 1 k T,n J 2 ( χ 0,n ) | 2 r n ,
p=1 N MWG M pn r n = V p ,
M pn = 1 2 | β p ρ 1 k T,p J 2 ( χ 0,p ) | 2 δ pn + m=1 N BF I p,m H ρ I n,m E ϕ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ ,
V p = 1 2 | β 1 ρ 1 k T,1 J 2 ( χ 0,1 ) | 2 δ p1 m=1 N BF I p,m H ρ I 1,m E ϕ 0 ρ N+1 | E ϕ,m BF | 2 ρdρ .

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